EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 1

PRACTICAL WORK BOOK

For The Course

EE-111 Linear Circuit Analysis

For

BE Electrical Engineering

Group Members

Degree Syndicate

Complied By Checked By

Lab Engineer Bahzad Zaib Assistant Professor Zubair Ahmad

DEPARTMENT OF ELECTRICAL ENGINEERING

College of Electrical amp Mechanical Engineering (CEME) NUST-Pakistan

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 2

LIST OF EXPERIMENTS

SNO TITLE OF EXPERIMENT Page

No

01 Introduction Basic Concepts and Lab Equipment 04

02 Experimental Verification of OHMrsquos Law 20

03 Verification of Current amp Voltage Divider Rule 25

04 Experimental Verification of Nodal Analysis 30

05 Experimental Verification of Mesh Analysis 35

06 Experimental Verification of Theveninrsquos Theorem 40

07 Study of Maximum Power Transfer Theorem amp its

Experimental Verification for a Network

44

Note PSICE solution for the task of each lab to be submitted with lab reports

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 3

LABORATORY WORK ESSENTIALS

COMPONENTS

Resistances ndashfixed (Ω) 50 x 280 x 2 100 x 2 120 x 2390 x 2430 x 2 1k x

6 22k x 5 25k x 3 5k x 2 10k x 2 100k x 4 20k x 4

Resistances ndashvariable (Ω) 1k x 2 2k x 2 5k x 2 10k x 2

Capacitor-fixed 1uF x 2

ICrsquos LM741 x 2

EQUIPMENTS

Digital Multi Meter

Oscilloscope

DC Power Supplies

Bread Board

Function Generator

SOFTWARES

Nil

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 4

EXPERIMENT NO ndash 01 INTRODUCTION BASIC CONCEPTS amp LAB EQUIPMENT

OBJECTIVE

- To know and understand basic function of laboratory equipment

- To become familiar with the correct ways of operating lab instruments

THEORY

A few tools are required for basic electronics work Most of these tools are inexpensive and easy

to obtain

Digital multi-meter First and foremost in your tool collection is a multi-meter This is an electrical instrument

designed to measure voltage current resistance and often other variables as well Multi-meters

are manufactured in both digital and analog form A digital multi-meter is preferred for precision

work but analog meters are also useful for gaining an intuitive understanding of instrument

sensitivity and range

Solder-less bread-board

Also essential is a solder-less breadboard sometimes called a prototyping board or proto-board

This device allows you to quickly join electronic components to one another without having to

solder component terminals and wires together

The internal structure layout of solder less bread-board can be depicted as

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 5

we can think of a breadboard as a board that can be divided in 2 functional areas

ndash the power strip(s) (in the drawing above A and D)

ndash the component grid(s) (in the drawing above B and C)

Most breadboards have at least 2 ldquocomponent gridsrdquo (B and C) separated at exactly the distance

between the two pin sides of a DIP IC package between B and C The pins of the component

grids (B and C) are connected vertically per column The grids B and C are not connected with

each other

Bench Top Power Supply

Bench Top Power Supplies are used for general design repair instructional or testing purposes

and includes both Fixed and Variable output supplies It is provided with 3 terminals for

connection purposes positive negative and ground The digital display shows the values of

voltage which is adjusted by coarse adjustment and fine adjustment knobs

Oscilloscope

The main purpose of an oscilloscope is to graph an electrical signal as it varies over time Most

scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis

Controls surrounding the scopersquos screen allow you to adjust the scale of the graph both

vertically and horizontally ndash allowing you to zoom in and out on a signal There are also controls

to set the trigger on the scope which helps focus and stabilize the display

In addition to those fundamental features many scopes have measurement tools which help to

quickly quantify frequency amplitude and other waveform characteristics In general a scope

can measure both time-based and voltage-based characteristics

rsaquo Timing characteristics

Frequency and period ndash Frequency is defined as the number of times per second a waveform

repeats And the period is the reciprocal of that (number of seconds each repeating waveform

takes) The maximum frequency a scope can measure varies but itrsquos often in the 100rsquos of MHz

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 2

LIST OF EXPERIMENTS

SNO TITLE OF EXPERIMENT Page

No

01 Introduction Basic Concepts and Lab Equipment 04

02 Experimental Verification of OHMrsquos Law 20

03 Verification of Current amp Voltage Divider Rule 25

04 Experimental Verification of Nodal Analysis 30

05 Experimental Verification of Mesh Analysis 35

06 Experimental Verification of Theveninrsquos Theorem 40

07 Study of Maximum Power Transfer Theorem amp its

Experimental Verification for a Network

44

Note PSICE solution for the task of each lab to be submitted with lab reports

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 3

LABORATORY WORK ESSENTIALS

COMPONENTS

Resistances ndashfixed (Ω) 50 x 280 x 2 100 x 2 120 x 2390 x 2430 x 2 1k x

6 22k x 5 25k x 3 5k x 2 10k x 2 100k x 4 20k x 4

Resistances ndashvariable (Ω) 1k x 2 2k x 2 5k x 2 10k x 2

Capacitor-fixed 1uF x 2

ICrsquos LM741 x 2

EQUIPMENTS

Digital Multi Meter

Oscilloscope

DC Power Supplies

Bread Board

Function Generator

SOFTWARES

Nil

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 4

EXPERIMENT NO ndash 01 INTRODUCTION BASIC CONCEPTS amp LAB EQUIPMENT

OBJECTIVE

- To know and understand basic function of laboratory equipment

- To become familiar with the correct ways of operating lab instruments

THEORY

A few tools are required for basic electronics work Most of these tools are inexpensive and easy

to obtain

Digital multi-meter First and foremost in your tool collection is a multi-meter This is an electrical instrument

designed to measure voltage current resistance and often other variables as well Multi-meters

are manufactured in both digital and analog form A digital multi-meter is preferred for precision

work but analog meters are also useful for gaining an intuitive understanding of instrument

sensitivity and range

Solder-less bread-board

Also essential is a solder-less breadboard sometimes called a prototyping board or proto-board

This device allows you to quickly join electronic components to one another without having to

solder component terminals and wires together

The internal structure layout of solder less bread-board can be depicted as

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 5

we can think of a breadboard as a board that can be divided in 2 functional areas

ndash the power strip(s) (in the drawing above A and D)

ndash the component grid(s) (in the drawing above B and C)

Most breadboards have at least 2 ldquocomponent gridsrdquo (B and C) separated at exactly the distance

between the two pin sides of a DIP IC package between B and C The pins of the component

grids (B and C) are connected vertically per column The grids B and C are not connected with

each other

Bench Top Power Supply

Bench Top Power Supplies are used for general design repair instructional or testing purposes

and includes both Fixed and Variable output supplies It is provided with 3 terminals for

connection purposes positive negative and ground The digital display shows the values of

voltage which is adjusted by coarse adjustment and fine adjustment knobs

Oscilloscope

The main purpose of an oscilloscope is to graph an electrical signal as it varies over time Most

scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis

Controls surrounding the scopersquos screen allow you to adjust the scale of the graph both

vertically and horizontally ndash allowing you to zoom in and out on a signal There are also controls

to set the trigger on the scope which helps focus and stabilize the display

In addition to those fundamental features many scopes have measurement tools which help to

quickly quantify frequency amplitude and other waveform characteristics In general a scope

can measure both time-based and voltage-based characteristics

rsaquo Timing characteristics

Frequency and period ndash Frequency is defined as the number of times per second a waveform

repeats And the period is the reciprocal of that (number of seconds each repeating waveform

takes) The maximum frequency a scope can measure varies but itrsquos often in the 100rsquos of MHz

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 3

LABORATORY WORK ESSENTIALS

COMPONENTS

Resistances ndashfixed (Ω) 50 x 280 x 2 100 x 2 120 x 2390 x 2430 x 2 1k x

6 22k x 5 25k x 3 5k x 2 10k x 2 100k x 4 20k x 4

Resistances ndashvariable (Ω) 1k x 2 2k x 2 5k x 2 10k x 2

Capacitor-fixed 1uF x 2

ICrsquos LM741 x 2

EQUIPMENTS

Digital Multi Meter

Oscilloscope

DC Power Supplies

Bread Board

Function Generator

SOFTWARES

Nil

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 4

EXPERIMENT NO ndash 01 INTRODUCTION BASIC CONCEPTS amp LAB EQUIPMENT

OBJECTIVE

- To know and understand basic function of laboratory equipment

- To become familiar with the correct ways of operating lab instruments

THEORY

A few tools are required for basic electronics work Most of these tools are inexpensive and easy

to obtain

Digital multi-meter First and foremost in your tool collection is a multi-meter This is an electrical instrument

designed to measure voltage current resistance and often other variables as well Multi-meters

are manufactured in both digital and analog form A digital multi-meter is preferred for precision

work but analog meters are also useful for gaining an intuitive understanding of instrument

sensitivity and range

Solder-less bread-board

Also essential is a solder-less breadboard sometimes called a prototyping board or proto-board

This device allows you to quickly join electronic components to one another without having to

solder component terminals and wires together

The internal structure layout of solder less bread-board can be depicted as

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 5

we can think of a breadboard as a board that can be divided in 2 functional areas

ndash the power strip(s) (in the drawing above A and D)

ndash the component grid(s) (in the drawing above B and C)

Most breadboards have at least 2 ldquocomponent gridsrdquo (B and C) separated at exactly the distance

between the two pin sides of a DIP IC package between B and C The pins of the component

grids (B and C) are connected vertically per column The grids B and C are not connected with

each other

Bench Top Power Supply

Bench Top Power Supplies are used for general design repair instructional or testing purposes

and includes both Fixed and Variable output supplies It is provided with 3 terminals for

connection purposes positive negative and ground The digital display shows the values of

voltage which is adjusted by coarse adjustment and fine adjustment knobs

Oscilloscope

The main purpose of an oscilloscope is to graph an electrical signal as it varies over time Most

scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis

Controls surrounding the scopersquos screen allow you to adjust the scale of the graph both

vertically and horizontally ndash allowing you to zoom in and out on a signal There are also controls

to set the trigger on the scope which helps focus and stabilize the display

In addition to those fundamental features many scopes have measurement tools which help to

quickly quantify frequency amplitude and other waveform characteristics In general a scope

can measure both time-based and voltage-based characteristics

rsaquo Timing characteristics

Frequency and period ndash Frequency is defined as the number of times per second a waveform

repeats And the period is the reciprocal of that (number of seconds each repeating waveform

takes) The maximum frequency a scope can measure varies but itrsquos often in the 100rsquos of MHz

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 4

EXPERIMENT NO ndash 01 INTRODUCTION BASIC CONCEPTS amp LAB EQUIPMENT

OBJECTIVE

- To know and understand basic function of laboratory equipment

- To become familiar with the correct ways of operating lab instruments

THEORY

A few tools are required for basic electronics work Most of these tools are inexpensive and easy

to obtain

Digital multi-meter First and foremost in your tool collection is a multi-meter This is an electrical instrument

designed to measure voltage current resistance and often other variables as well Multi-meters

are manufactured in both digital and analog form A digital multi-meter is preferred for precision

work but analog meters are also useful for gaining an intuitive understanding of instrument

sensitivity and range

Solder-less bread-board

Also essential is a solder-less breadboard sometimes called a prototyping board or proto-board

This device allows you to quickly join electronic components to one another without having to

solder component terminals and wires together

The internal structure layout of solder less bread-board can be depicted as

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 5

we can think of a breadboard as a board that can be divided in 2 functional areas

ndash the power strip(s) (in the drawing above A and D)

ndash the component grid(s) (in the drawing above B and C)

Most breadboards have at least 2 ldquocomponent gridsrdquo (B and C) separated at exactly the distance

between the two pin sides of a DIP IC package between B and C The pins of the component

grids (B and C) are connected vertically per column The grids B and C are not connected with

each other

Bench Top Power Supply

Bench Top Power Supplies are used for general design repair instructional or testing purposes

and includes both Fixed and Variable output supplies It is provided with 3 terminals for

connection purposes positive negative and ground The digital display shows the values of

voltage which is adjusted by coarse adjustment and fine adjustment knobs

Oscilloscope

The main purpose of an oscilloscope is to graph an electrical signal as it varies over time Most

scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis

Controls surrounding the scopersquos screen allow you to adjust the scale of the graph both

vertically and horizontally ndash allowing you to zoom in and out on a signal There are also controls

to set the trigger on the scope which helps focus and stabilize the display

In addition to those fundamental features many scopes have measurement tools which help to

quickly quantify frequency amplitude and other waveform characteristics In general a scope

can measure both time-based and voltage-based characteristics

rsaquo Timing characteristics

Frequency and period ndash Frequency is defined as the number of times per second a waveform

repeats And the period is the reciprocal of that (number of seconds each repeating waveform

takes) The maximum frequency a scope can measure varies but itrsquos often in the 100rsquos of MHz

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 5

we can think of a breadboard as a board that can be divided in 2 functional areas

ndash the power strip(s) (in the drawing above A and D)

ndash the component grid(s) (in the drawing above B and C)

Most breadboards have at least 2 ldquocomponent gridsrdquo (B and C) separated at exactly the distance

between the two pin sides of a DIP IC package between B and C The pins of the component

grids (B and C) are connected vertically per column The grids B and C are not connected with

each other

Bench Top Power Supply

Bench Top Power Supplies are used for general design repair instructional or testing purposes

and includes both Fixed and Variable output supplies It is provided with 3 terminals for

connection purposes positive negative and ground The digital display shows the values of

voltage which is adjusted by coarse adjustment and fine adjustment knobs

Oscilloscope

The main purpose of an oscilloscope is to graph an electrical signal as it varies over time Most

scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis

Controls surrounding the scopersquos screen allow you to adjust the scale of the graph both

vertically and horizontally ndash allowing you to zoom in and out on a signal There are also controls

to set the trigger on the scope which helps focus and stabilize the display

In addition to those fundamental features many scopes have measurement tools which help to

quickly quantify frequency amplitude and other waveform characteristics In general a scope

can measure both time-based and voltage-based characteristics

rsaquo Timing characteristics

Frequency and period ndash Frequency is defined as the number of times per second a waveform

repeats And the period is the reciprocal of that (number of seconds each repeating waveform

takes) The maximum frequency a scope can measure varies but itrsquos often in the 100rsquos of MHz

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 6

(1E6 Hz) range

Duty cycle ndash The percentage of a period that a wave is either positive or negative (there are both

positive and negative duty cycles) The duty cycle is a ratio that tells you how long a signal is

ldquoonrdquo versus how long itrsquos ldquooffrdquo each period

Rise and fall time ndash Signals canrsquot instantaneously go from 0V to 5V they have to smoothly rise

The duration of a wave going from a low point to a high point is called the rise time and fall

time measures the opposite These characteristics are important when considering how fast a

circuit can respond to signals

rsaquo Voltage characteristics

Amplitude ndash Amplitude is a measure of the magnitude of a signal There are a variety of

amplitude measurements including peak-to-peak amplitude which measures the absolute

difference between a high and low voltage point of a signal Peak amplitude on the other hand

only measures how high or low a signal is past 0V

Maximum and minimum voltages ndash The scope can tell you exactly how high and low the voltage

of your signal gets

Mean and average voltages ndash Oscilloscopes can calculate the average or mean of your signal and

it can also tell you the average of your signalrsquos minimum and maximum voltage

Oscilloscope Usage

Here are some of the important oscilloscope buzzwords you should be familiar with before

turning it on

Key Oscilloscope Specifications

Some scopes are better than others These characteristics help define how well you might expect

a scope to perform

rsaquo Bandwidth ndash Oscilloscopes are most commonly used to measure waveforms which have a

defined frequency No scope is perfect though they all have limits as to how fast they can see a

signal change The bandwidth of a scope specifies the range of frequencies it can reliably

measure

rsaquo Digital vs Analog ndash As with most everything electronic o-scopes can either be analog or

digital Analog scopes use an electron beam to directly map the input voltage to a display Digital

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 7

scopes incorporate microcontrollers which sample the input signal with an analog-to-digital

converter and map that reading to the display Generally analog scopes are older have a lower

bandwidth and less features but they may have a faster response (and look much cooler)

rsaquo Channel Amount ndash Many scopes can read more than one signal at a time displaying them all

on the screen simultaneously Each signal read by a scope is fed into a separate channel Two to

four channel scopes are very common

rsaquo Sampling Rate ndash This characteristic is unique to digital scopes it defines how many times per

second a signal is read For scopes that have more than one channel this value may decrease if

multiple channels are in use

rsaquo Rise Time ndash The specified rise time of a scope defines the fastest rising pulse it can measure

The rise time of a scope is very closely related to the bandwidth It can be calculated as Rise

Time = 035 Bandwidth

rsaquo Maximum Input Voltage ndash Every piece of electronics has its limits when it comes to high

voltage Scopes should all be rated with a maximum input voltage If your signal exceeds that

voltage therersquos a good chance the scope will be damaged

rsaquo Resolution ndash The resolution of a scope represents how precisely it can measure the input

voltage This value can change as the vertical scale is adjusted

rsaquo Vertical Sensitivity ndash This value represents the minimum and maximum values of your vertical

voltage scale This value is listed in volts per div

rsaquo Time Base ndash Time base usually indicates the range of sensitivities on the horizontal time axis

This value is listed in seconds per div

rsaquo Input Impedance ndash When signal frequencies get very high even a small impedance (resistance

capacitance or inductance) added to a circuit can affect the signal Every oscilloscope will add a

certain impedance to a circuit itrsquos reading called the input impedance Input impedances are

generally represented as a large resistive impedance (gt1 MΩ) in parallel (||) with small

capacitance (in the pF range) The impact of input impedance is more apparent when measuring

very high frequency signals and the probe you use may have to help compensate for it

Anatomy of An Oscilloscope

While no scopes are created exactly equal they should all share a few similarities that make

them function similarly On this page wersquoll discuss a few of the more common

systems of an oscilloscope the display horizontal vertical trigger and inputs

The Display

An oscilloscope isnrsquot any good unless it can display the information yoursquore trying to test which

makes the display one of the more important sections on the scope

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 8

Every oscilloscope display should be criss-crossed with horizontal and vertical lines

called divisions The scale of those divisions are modified with the horizontal and vertical

systems The vertical system is measured in ldquovolts per divisionrdquo and the horizontal is ldquoseconds

per divisionrdquo Generally scopes will feature around 8-10 vertical (voltage) divisions and 10-14

horizontal (seconds) divisions

Older scopes (especially those of the analog variety) usually feature a simple monochrome

display though the intensity of the wave may vary More modern scopes feature multicolor LCD

screens which are a great help in showing more than one waveform at a time

Many scope displays are situated next to a set of about five buttons ndash either to the side or below

the display These buttons can be used to navigate menus and control settings of the scope

Vertical System

The vertical section of the scope controls the voltage scale on the display There are traditionally

two knobs in this section which allow you to individually control the vertical position and

voltsdiv

The more critical volts per division knob allow you to set the vertical scale on the screen

Rotating the knob clockwise will decrease the scale and counter-clockwise will increase A

smaller scale ndash fewer volts per division on the screen ndash means yoursquore more ldquozoomed inrdquo to the

waveform

The display on the GA1102 for example has 8 vertical divisions and the voltsdiv knob can

select a scale between 2mVdiv and 5Vdiv So zoomed all the way in to 2mVdiv the display

can show waveform that is 16mV from top to bottom Fully ldquozoomed outrdquo the scope can show a

waveform ranging over 40V (The probe as wersquoll discuss below can further increase this range)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 9

The position knob controls the vertical offset of the waveform on the screen Rotate the knob

clockwise and the wave will move down counter-clockwise will move it up the display You

can use the position knob to offset part of a waveform off the screen

Using both the position and voltsdiv knobs in conjunction you can zoom in on just a tiny part of

the waveform that you care about the most If you had a 5V square wave but only cared about

how much it was ringing on the edges you could zoom in on the rising edge using both knobs

Horizontal System

The horizontal section of the scope controls the time scale on the screen Like the vertical

system the horizontal control gives you two knobs position and secondsdiv

The seconds per division (sdiv) knob rotates to increase or decrease the horizontal scale If you

rotate the sdiv knob clockwise the number of seconds each division represents will decrease ndash

yoursquoll be ldquozooming inrdquo on the time scale Rotate counter-clockwise to increase the time scale

and show a longer amount of time on the screen

Using the GA1102 as an example again the display has 14 horizontal divisions and can

show anywhere between 2nS and 50s per division So zoomed all the way in on the horizontal

scale the scope can show 28nS of a waveform and zoomed way out it can show a signal as it

changes over 70 seconds

The position knob can move your waveform to the right or left of the display adjusting the

horizontal offset

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 10

Using the horizontal system you can adjust how many periods of a waveform you want to see

You can zoom out and show multiple peaks and troughs of a signal

Or you can zoom way in and use the position knob to show just a tiny part of a wave

Trigger System

The trigger section is devoted to stabilizing and focusing the oscilloscope The trigger tells the

scope what parts of the signal to ldquotriggerrdquo on and start measuring If your waveform is periodic

the trigger can be manipulated to keep the display static and unflinching A poorly triggered

wave will produce seizure-inducing sweeping waves like this

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 11

The trigger section of a scope is usually comprised of a level knob and a set of buttons to select

the source and type of the trigger The level knob can be twisted to set a trigger to a specific

voltage point

A series of buttons and screen menus make up the rest of the trigger system Their main purpose

is to select the trigger source and mode There are a variety of trigger types which manipulate

how the trigger is activated

rsaquo An edge trigger is the most basic form of the trigger It will key the oscilloscope to start

measuring when the signal voltage passes a certain level An edge trigger can be set to catch on a

rising or falling edge (or both)

rsaquo A pulse trigger tells the scope to key in on a specified ldquopulserdquo of voltage You can specify the

duration and direction of the pulse For example it can be a tiny blip of 0V -gt 5V -gt 0V or it

can be a seconds-long dip from 5V to 0V back to 5V

rsaquo A slope trigger can be set to trigger the scope on a positive or negative slope over a specified

amount of time

rsaquo More complicated triggers exist to focus on standardized waveforms that carry video data

like NTSC or PAL These waves use a unique synchronizing pattern at the beginning of every

frame

You can also usually select a triggering mode which in effect tells the scope how strongly you

feel about your trigger In automatic trigger mode the scope can attempt to draw your waveform

even if it doesnrsquot trigger Normal mode will only draw your wave if it sees the specified trigger

And single mode looks for your specified trigger when it sees it it will draw your wave then

stop

The Probes

An oscilloscope is only good if you can actually connect it to a signal and for that you need

probes Probes are single-input devices that route a signal from your circuit to the scope They

have a sharp tip which probes into a point on your circuit The tip can also be equipped with

hooks tweezers or clips to make latching onto a circuit easier Every probe also includes

a ground clip which should be secured safely to a common ground point on the circuit under

test

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 12

While probes may seem like simple devices that just latch onto your circuit and carry a signal to

the scope therersquos actually a lot that goes into probe design and selection

Optimally what a probe needs to be is invisible ndash it shouldnrsquot have any effect on

your signal under test Unfortunately long wires all have intrinsic inductance capacitance and

resistance so no matter what theyrsquoll affect scope readings (especially at high frequencies)

There are a variety of probe types out there the most common of which is

the passive probe included with most scopes Most of the ldquostockrdquo passive probes are attenuated

Attenuating probes have a large resistance intentionally built-in and shunted by a small capacitor

which helps to minimize the effect that a long cable might have on loading your circuit In series

with the input impedance of a scope this attenuated probe will create a voltage divider between

your signal and the scope input

Most probes have a 9MΩ resistor for attenuating which when combined with a standard 1MΩ

input impedance on a scope creates a 110 voltage divider These probes are commonly

called 10X attenuated probes Many probes include a switch to select between 10X and 1X (no

attenuation)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 13

Attenuated probes are great for improving accuracy at high frequencies but they will also reduce

the amplitude of your signal If yoursquore trying to measure a very low-voltage signal you may

have to go with a 1X probe You may also need to select a setting on your scope to tell it yoursquore

using an attenuated probe although many scopes can automatically detect this

Beyond the passive attenuated probe there are a variety of other probes out here Active

probes are powered probes (they require a separate power source) which can amplify your signal

or even pre-process it before it get to your scope While most probes are designed to measure

voltage there are probes designed to measure AC or DC current Current probes are unique

because they often clamp around a wire never actually making contact with the circuit

Using an Oscilloscope

The infinite variety of signals out there means yoursquoll never operate an oscilloscope the same way

twice But there are some steps you can count on performing just about every time you test a

circuit Wersquoll show an example signal and the steps required to measure it

Probe Selection and Setup

First off yoursquoll need to select a probe For most signals the simple passive probe included with

your scope will work perfectly fine

Next before connecting it to your scope set the attenuation on your probe 10X ndash the most

common attenuation factor ndash is usually the most well-rounded choice If you are trying to

measure a very low-voltage signal though you may need to use 1X

Connect the Probe and Turn the Scope On

Connect your probe to the first channel on your scope and turn it on Have some patience here

some scopes take as long to boot up as an old PC

When the scope boots up you should see the divisions scale and a noisy flat line of a

waveform

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 14

The screen should also show previously set values for time and volts per div Ignoring those

scales for now make these adjustments to put your scope into a standard setup

rsaquo Turn channel 1 on and channel 2 off

rsaquo Set channel 1 to DC coupling

rsaquo Set the trigger source to channel 1 ndash no external source or alternate channel triggering

rsaquo Set the trigger type to rising edge and the trigger mode to auto (as opposed to single)

rsaquo Make sure the scope probe attenuation on your scope matches the setting on your probe (eg

1X 10X)

For help making these adjustments you can consult scopersquos userrsquos manual

Testing the Probe

Letrsquos connect that channel up to a meaningful signal Most scopes will have a built-in frequency

generator that emits a reliable set-frequency wave ndash on the GA1102CAL there is a 1kHz square

wave output at the bottom-right of the front panel The frequency generator output has two

separate conductors ndash one for the signal and one for ground Connect your probersquos ground clip to

the ground and the probe tip to the signal output

As soon as you connect both parts of the probe you should see a signal begin to dance around

your screen Try fiddling with the horizontal and vertical system knobs to maneuver the

waveform around the screen Rotating the scale knobs clockwise will ldquozoom intordquo your

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 15

waveform and counter-clockwise zooms out You can also use the position knob to further

locate your waveform

If your wave is still unstable try rotating the trigger position knob Make sure the trigger isnrsquot

higher than the tallest peak of your waveform By default the trigger type should be set to edge

which is usually a good choice for square waves like this

Try fiddling with those knobs enough to display a single period of your wave on the screen

Or try zooming way out on the time scale to show dozens of squares

Compensating an Attenuated Probe

If your probe is set to 10X and you donrsquot have a perfectly square waveform as shown above you

may need to compensate your probe Most probes have a recessed screw head which you can

rotate to adjust the shunt capacitance of the probe

Try using a small screwdriver to rotate this trimmer and look at what happens to the waveform

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 16

Adjust the trimming cap on the probe handle until you have a straight-edged square wave

Compensation is only necessary if your probe is attenuated (eg 10X) in which case itrsquos critical

Probing Triggering and Scaling Tips

Once yoursquove compensated your probe itrsquos time to measure a real signal Go find a signal source

eg frequency generator and start

The first key to probing a signal is finding a solid reliable grounding point Clasp your ground

clip to a known ground sometimes you may have to use a small wire to intermediate between the

ground clip and your circuitrsquos ground point Then connect your probe tip to the signal under test

Probe tips exist in a variety of form factors ndash the spring-loaded clip fine point hooks etc ndash try

to find one that doesnrsquot require you to hold it in place all the time

Once your signal is on the screen you may want to begin by adjusting the horizontal and vertical

scales into at least the ldquoballparkrdquo of your signal If yoursquore probing a 5V 1kHz square wave

yoursquoll probably want the voltsdiv somewhere around 05-1V and set the secondsdiv to around

100micros (14 divisions would show about one and a half periods)

If part of your wave is rising or falling of the screen you can adjust the vertical

position to move it up or down If your signal is purely DC you may want to adjust the 0V level

near the bottom of your display

Once you have the scales ball parked your waveform may need some

triggering Edge triggering ndash where the scope tries to begin its scan when it sees voltage rise (or

fall) past a set point ndash is the easiest type to use Using an edge trigger try to set the trigger level

to a point on your waveform that only sees a rising edge once per period

Now just scale position trigger and repeat until yoursquore looking at exactly what you need

Measure Twice Cut Once

With a signal scoped triggered and scaled it comes time to measure transients periods and

other waveform properties Some scopes have more measurement tools than others but theyrsquoll

all at least have divisions from which you should be able to at least estimate the amplitude and

frequency

Many scopes support a variety of automatic measurement tools they may even constantly

display the most relevant information like frequency To get the most out of your scope yoursquoll

want to explore all of the measure functions it supports Most scopes will calculate frequency

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 17

amplitude duty cycle mean voltage and a variety of other wave characteristics for you

automatically

Using the scopersquos measure tools to find VPP VMax frequency period and duty cycle

A third measuring tool many scopes provide is cursors Cursors are on-screen

movable markers which can be placed on either the time or voltage axis Cursors usually come in

pairs so you can measure the difference between one and the other

Measuring the ringing of a square wave with cursors

Once yoursquove measured the quantity you were looking for you can begin to make adjustments to

your circuit and measure some more Some scopes also

support saving printing or storing a waveform so you can recall it and remember those good

old times when you scoped that signal

To find out more about what your scope can do consult its userrsquos manual

Voltmeter Usage

A multi-meter is an electrical instrument capable of measuring voltage current and resistance

Digital multi-meters have numerical displays like digital clocks for indicating the quantity of

voltage current or resistance Analog multi-meters indicate these quantities by means of a

moving pointer over a printed scale

Some digital multi-meters are auto-ranging An auto-ranging meter has only a few

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 18

selector switch (dial) positions Manual-ranging meters have several different selector positions

for each basic quantity several for voltage several for current and several for resistance

In order to measure voltage of a battery set your multi-meterrsquos selector switch to the

highest-value lsquoDC voltrsquo position available Auto-ranging multi-meters may only have a single

position for DC voltage in which case you need to set the switch to that one position Touch the

red test probe to the positive (+) side of a battery and the black test probe to the negative (-) side

of the same battery The meter should now provide you with some sort of indication Reverse the

test probe connections to the battery if the meterrsquos indication is negative (on an analog meter a

negative value is indicated by the pointer deflecting left instead of right)

If your meter is a manual-range type and the selector switch has been set to a high-

range position the indication will be small Move the selector switch to the next lower DC

voltage range setting and reconnect to the battery The indication should be stronger now as

indicated by a greater deflection of the analog meter pointer (needle) or more active digits on the

digital meter display For the best results move the selector switch to the lowest-range setting

that does not lsquoover-rangersquo the meter An over-ranged analog meter is said to be lsquopeggedrsquo as the

needle will be forced all the way to the right-hand side of the scale past the full-range scale

value An over-ranged digital meter sometimes displays the letters lsquoOLrsquo or a series of dashed

lines This indication is manufacturer-specific

Ohmmeter Usage

Be sure to never measure the resistance of any electrically lsquoliversquo object or circuit In other words

do not attempt to measure the resistance of a battery or any other source of substantial voltage

using a multi-meter set to the resistance (ohms) function failing to heed this warning will likely

result in meter damage and even personal injury

Connect the meterrsquos test probes across the resistor as such and note its indication on the

resistance scale

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 19

If the needle points very close to zero you need to select a lower resistance range on the Meter

If you are using a digital multi-meter you should see a numerical figure close to 10 shown on the

display with a small rdquokrdquo symbol on the right-hand side denoting the metric prefix for rdquokilordquo

(thousand) Some digital meters are manually-ranged and require appropriate range selection

just as the analog meter If yours is like this experiment with different range switch positions

and see which one gives you the best indication

Ammeter Usage

Current is the measure of the rate of electron lsquoflowrsquo in a circuit It is measured in the unit of the

Ampere simply called lsquoAmprsquo (A)

The most common way to measure current in a circuit is to break the circuit open and insert an

lsquoammeterrsquo in series (in-line) with the circuit so that all electrons flowing through the circuit also

have to go through the meter Because measuring current in this manner requires the meter be

made part of the circuit it is a more difficult type of measurement to make than either voltage or

resistance

Some digital meters like the unit shown in the illustration have a separate jack to insert the red

test lead plug when measuring current Other meters like most inexpensive analog meters use

the same jacks for measuring voltage resistance and current

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 20

EXPERIMENT NO ndash 02 OHMrsquoS LAW

(EXPERIMENTAL VERIFICATION OF OHMrsquoS LAW)

OBJECTIVE

- To verify ohmrsquos law experimentally

APPARATUS

1 DC power supply

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM) Voltmeter Ammeter

THEORY

Ohmrsquos Law

When current I flows through a resistor then the potential difference V (often simply called

voltage) between its terminals is proportional to I as in equation (1) where R is the resistance

Basic Equation V = R I (1)

Combinations of Resistors

When two or more resistors ( R1 R2 R3hellip) are connected in series (Fig 1) then this

combination is equivalent to a single resisto of resistance Req given by (2)

Basic Formula Req = R1 + R2 + R3+ (2)

When two or more resistors are connected in parallel (Fig 2) then the equivalent resistance Req

is given by (3)

Basic Formula Req = 1 + 1 + 1 + 1

R1 R2 R3

(2)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 21

PROCEDURE amp OBSERVATIONS

Part I Ohmrsquos Law

rsaquo Make sure that the DC power supply is off and unplugged Make sure that the regulating

knobs are in minimum positions Your instructor will explain to you the operation of DC power

supply the ammeter and the voltmeter

rsaquo Construct the circuit as in Fig 3a using the resistor marked R1 in your sample Use the dc

ammeter scale and make sure that + and ndash markings are exactly as in Fig 3a

rsaquo Set the voltmeter scale to dc volts scale Attach connectors to your voltmeter (or DMM as

voltmeter suggestion use a red connector for the + terminal and a black one for -) Connect the

+ terminal to point B (where the current enters the resistor) and the other one to point A

rsaquo Make sure all connections are tight If you have a faulty connector immediately hand it to your

instructor Note Call your instructor to check your circuit Do not proceed without his or her permission rsaquo After your instructorrsquos approval prepare on your data sheet your first table as shown Plug in

the power supply With the regulating knob(s) in Min position turn the power ldquoONrdquo

Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to

increase (if not turn off the power at once and call your instructor)Keep doing this until the

ammeter reaches 50mA or the voltmeter reaches 5 volts whichever comes first Record the

current I and the voltage V to three significant digits by estimating fractions of smallest

divisions on the scales

Resistor R1 Resistor R2 Resistor R3

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 22

rsaquo Decreasing the current record I and V four more times (a total of 5 readings) in roughly equal

intervals The lowest current should be 5 to 10 mA

rsaquo Repeat the last two steps for your resistors R2 and R3 with maximum current close to 50 mA

but using the finest voltmeter scale possible for each given resistor

rsaquo Turn the power ldquoOFFrdquo and record

- The uncertainties in your readings on all scales of ammeter and voltmeter which you have

used

- The zero readings of your ammeter these are their readings when they are completely

disconnected from any circuits They should be close to zero but not necessarily exactly so

Procedure Part II Combinations of Resistors

rsaquo Connect all three resistors R1 R2 R3 in series and use the DC volt scale on the voltmeter

Record 5 runs as before (Note your maximum current may be less than 50 ma because the

voltage must not exceed 10mvolts)

rsaquo Connect all these resistors in parallel Again use the DC voltmeter scale with the maximum

current close to 50 mA Record 5 runs as before

rsaquo Estimate (from your data in Part I) the values of R1 R2 R3 Take the two higher

resistances (record which ones you are using) and connect them in parallel Connect this

combination in series with the remaining resistor Record 5 runs as usual

R1 R2 R3

in Series

R1 R2 R3

in Parallel

R1 R2 R3

2 Parallel in Series

with 3rd

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

Graphical Results

rsaquo Using graph paper plot V vs I for each of your resistors R1 R2 R3 Draw the line of best fit

in each case and (from the slope) determine the resistance in ohms 3 significant digits Display

all calculations on the graph sheet

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 19

If the needle points very close to zero you need to select a lower resistance range on the Meter

If you are using a digital multi-meter you should see a numerical figure close to 10 shown on the

display with a small rdquokrdquo symbol on the right-hand side denoting the metric prefix for rdquokilordquo

(thousand) Some digital meters are manually-ranged and require appropriate range selection

just as the analog meter If yours is like this experiment with different range switch positions

and see which one gives you the best indication

Ammeter Usage

Current is the measure of the rate of electron lsquoflowrsquo in a circuit It is measured in the unit of the

Ampere simply called lsquoAmprsquo (A)

The most common way to measure current in a circuit is to break the circuit open and insert an

lsquoammeterrsquo in series (in-line) with the circuit so that all electrons flowing through the circuit also

have to go through the meter Because measuring current in this manner requires the meter be

made part of the circuit it is a more difficult type of measurement to make than either voltage or

resistance

Some digital meters like the unit shown in the illustration have a separate jack to insert the red

test lead plug when measuring current Other meters like most inexpensive analog meters use

the same jacks for measuring voltage resistance and current

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 20

EXPERIMENT NO ndash 02 OHMrsquoS LAW

(EXPERIMENTAL VERIFICATION OF OHMrsquoS LAW)

OBJECTIVE

- To verify ohmrsquos law experimentally

APPARATUS

1 DC power supply

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM) Voltmeter Ammeter

THEORY

Ohmrsquos Law

When current I flows through a resistor then the potential difference V (often simply called

voltage) between its terminals is proportional to I as in equation (1) where R is the resistance

Basic Equation V = R I (1)

Combinations of Resistors

When two or more resistors ( R1 R2 R3hellip) are connected in series (Fig 1) then this

combination is equivalent to a single resisto of resistance Req given by (2)

Basic Formula Req = R1 + R2 + R3+ (2)

When two or more resistors are connected in parallel (Fig 2) then the equivalent resistance Req

is given by (3)

Basic Formula Req = 1 + 1 + 1 + 1

R1 R2 R3

(2)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 21

PROCEDURE amp OBSERVATIONS

Part I Ohmrsquos Law

rsaquo Make sure that the DC power supply is off and unplugged Make sure that the regulating

knobs are in minimum positions Your instructor will explain to you the operation of DC power

supply the ammeter and the voltmeter

rsaquo Construct the circuit as in Fig 3a using the resistor marked R1 in your sample Use the dc

ammeter scale and make sure that + and ndash markings are exactly as in Fig 3a

rsaquo Set the voltmeter scale to dc volts scale Attach connectors to your voltmeter (or DMM as

voltmeter suggestion use a red connector for the + terminal and a black one for -) Connect the

+ terminal to point B (where the current enters the resistor) and the other one to point A

rsaquo Make sure all connections are tight If you have a faulty connector immediately hand it to your

instructor Note Call your instructor to check your circuit Do not proceed without his or her permission rsaquo After your instructorrsquos approval prepare on your data sheet your first table as shown Plug in

the power supply With the regulating knob(s) in Min position turn the power ldquoONrdquo

Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to

increase (if not turn off the power at once and call your instructor)Keep doing this until the

ammeter reaches 50mA or the voltmeter reaches 5 volts whichever comes first Record the

current I and the voltage V to three significant digits by estimating fractions of smallest

divisions on the scales

Resistor R1 Resistor R2 Resistor R3

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 22

rsaquo Decreasing the current record I and V four more times (a total of 5 readings) in roughly equal

intervals The lowest current should be 5 to 10 mA

rsaquo Repeat the last two steps for your resistors R2 and R3 with maximum current close to 50 mA

but using the finest voltmeter scale possible for each given resistor

rsaquo Turn the power ldquoOFFrdquo and record

- The uncertainties in your readings on all scales of ammeter and voltmeter which you have

used

- The zero readings of your ammeter these are their readings when they are completely

disconnected from any circuits They should be close to zero but not necessarily exactly so

Procedure Part II Combinations of Resistors

rsaquo Connect all three resistors R1 R2 R3 in series and use the DC volt scale on the voltmeter

Record 5 runs as before (Note your maximum current may be less than 50 ma because the

voltage must not exceed 10mvolts)

rsaquo Connect all these resistors in parallel Again use the DC voltmeter scale with the maximum

current close to 50 mA Record 5 runs as before

rsaquo Estimate (from your data in Part I) the values of R1 R2 R3 Take the two higher

resistances (record which ones you are using) and connect them in parallel Connect this

combination in series with the remaining resistor Record 5 runs as usual

R1 R2 R3

in Series

R1 R2 R3

in Parallel

R1 R2 R3

2 Parallel in Series

with 3rd

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

Graphical Results

rsaquo Using graph paper plot V vs I for each of your resistors R1 R2 R3 Draw the line of best fit

in each case and (from the slope) determine the resistance in ohms 3 significant digits Display

all calculations on the graph sheet

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 20

EXPERIMENT NO ndash 02 OHMrsquoS LAW

(EXPERIMENTAL VERIFICATION OF OHMrsquoS LAW)

OBJECTIVE

- To verify ohmrsquos law experimentally

APPARATUS

1 DC power supply

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM) Voltmeter Ammeter

THEORY

Ohmrsquos Law

When current I flows through a resistor then the potential difference V (often simply called

voltage) between its terminals is proportional to I as in equation (1) where R is the resistance

Basic Equation V = R I (1)

Combinations of Resistors

When two or more resistors ( R1 R2 R3hellip) are connected in series (Fig 1) then this

combination is equivalent to a single resisto of resistance Req given by (2)

Basic Formula Req = R1 + R2 + R3+ (2)

When two or more resistors are connected in parallel (Fig 2) then the equivalent resistance Req

is given by (3)

Basic Formula Req = 1 + 1 + 1 + 1

R1 R2 R3

(2)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 21

PROCEDURE amp OBSERVATIONS

Part I Ohmrsquos Law

rsaquo Make sure that the DC power supply is off and unplugged Make sure that the regulating

knobs are in minimum positions Your instructor will explain to you the operation of DC power

supply the ammeter and the voltmeter

rsaquo Construct the circuit as in Fig 3a using the resistor marked R1 in your sample Use the dc

ammeter scale and make sure that + and ndash markings are exactly as in Fig 3a

rsaquo Set the voltmeter scale to dc volts scale Attach connectors to your voltmeter (or DMM as

voltmeter suggestion use a red connector for the + terminal and a black one for -) Connect the

+ terminal to point B (where the current enters the resistor) and the other one to point A

rsaquo Make sure all connections are tight If you have a faulty connector immediately hand it to your

instructor Note Call your instructor to check your circuit Do not proceed without his or her permission rsaquo After your instructorrsquos approval prepare on your data sheet your first table as shown Plug in

the power supply With the regulating knob(s) in Min position turn the power ldquoONrdquo

Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to

increase (if not turn off the power at once and call your instructor)Keep doing this until the

ammeter reaches 50mA or the voltmeter reaches 5 volts whichever comes first Record the

current I and the voltage V to three significant digits by estimating fractions of smallest

divisions on the scales

Resistor R1 Resistor R2 Resistor R3

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 22

rsaquo Decreasing the current record I and V four more times (a total of 5 readings) in roughly equal

intervals The lowest current should be 5 to 10 mA

rsaquo Repeat the last two steps for your resistors R2 and R3 with maximum current close to 50 mA

but using the finest voltmeter scale possible for each given resistor

rsaquo Turn the power ldquoOFFrdquo and record

- The uncertainties in your readings on all scales of ammeter and voltmeter which you have

used

- The zero readings of your ammeter these are their readings when they are completely

disconnected from any circuits They should be close to zero but not necessarily exactly so

Procedure Part II Combinations of Resistors

rsaquo Connect all three resistors R1 R2 R3 in series and use the DC volt scale on the voltmeter

Record 5 runs as before (Note your maximum current may be less than 50 ma because the

voltage must not exceed 10mvolts)

rsaquo Connect all these resistors in parallel Again use the DC voltmeter scale with the maximum

current close to 50 mA Record 5 runs as before

rsaquo Estimate (from your data in Part I) the values of R1 R2 R3 Take the two higher

resistances (record which ones you are using) and connect them in parallel Connect this

combination in series with the remaining resistor Record 5 runs as usual

R1 R2 R3

in Series

R1 R2 R3

in Parallel

R1 R2 R3

2 Parallel in Series

with 3rd

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

Graphical Results

rsaquo Using graph paper plot V vs I for each of your resistors R1 R2 R3 Draw the line of best fit

in each case and (from the slope) determine the resistance in ohms 3 significant digits Display

all calculations on the graph sheet

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 21

PROCEDURE amp OBSERVATIONS

Part I Ohmrsquos Law

rsaquo Make sure that the DC power supply is off and unplugged Make sure that the regulating

knobs are in minimum positions Your instructor will explain to you the operation of DC power

supply the ammeter and the voltmeter

rsaquo Construct the circuit as in Fig 3a using the resistor marked R1 in your sample Use the dc

ammeter scale and make sure that + and ndash markings are exactly as in Fig 3a

rsaquo Set the voltmeter scale to dc volts scale Attach connectors to your voltmeter (or DMM as

voltmeter suggestion use a red connector for the + terminal and a black one for -) Connect the

+ terminal to point B (where the current enters the resistor) and the other one to point A

rsaquo Make sure all connections are tight If you have a faulty connector immediately hand it to your

instructor Note Call your instructor to check your circuit Do not proceed without his or her permission rsaquo After your instructorrsquos approval prepare on your data sheet your first table as shown Plug in

the power supply With the regulating knob(s) in Min position turn the power ldquoONrdquo

Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to

increase (if not turn off the power at once and call your instructor)Keep doing this until the

ammeter reaches 50mA or the voltmeter reaches 5 volts whichever comes first Record the

current I and the voltage V to three significant digits by estimating fractions of smallest

divisions on the scales

Resistor R1 Resistor R2 Resistor R3

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 22

rsaquo Decreasing the current record I and V four more times (a total of 5 readings) in roughly equal

intervals The lowest current should be 5 to 10 mA

rsaquo Repeat the last two steps for your resistors R2 and R3 with maximum current close to 50 mA

but using the finest voltmeter scale possible for each given resistor

rsaquo Turn the power ldquoOFFrdquo and record

- The uncertainties in your readings on all scales of ammeter and voltmeter which you have

used

- The zero readings of your ammeter these are their readings when they are completely

disconnected from any circuits They should be close to zero but not necessarily exactly so

Procedure Part II Combinations of Resistors

rsaquo Connect all three resistors R1 R2 R3 in series and use the DC volt scale on the voltmeter

Record 5 runs as before (Note your maximum current may be less than 50 ma because the

voltage must not exceed 10mvolts)

rsaquo Connect all these resistors in parallel Again use the DC voltmeter scale with the maximum

current close to 50 mA Record 5 runs as before

rsaquo Estimate (from your data in Part I) the values of R1 R2 R3 Take the two higher

resistances (record which ones you are using) and connect them in parallel Connect this

combination in series with the remaining resistor Record 5 runs as usual

R1 R2 R3

in Series

R1 R2 R3

in Parallel

R1 R2 R3

2 Parallel in Series

with 3rd

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

Graphical Results

rsaquo Using graph paper plot V vs I for each of your resistors R1 R2 R3 Draw the line of best fit

in each case and (from the slope) determine the resistance in ohms 3 significant digits Display

all calculations on the graph sheet

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 22

rsaquo Decreasing the current record I and V four more times (a total of 5 readings) in roughly equal

intervals The lowest current should be 5 to 10 mA

rsaquo Repeat the last two steps for your resistors R2 and R3 with maximum current close to 50 mA

but using the finest voltmeter scale possible for each given resistor

rsaquo Turn the power ldquoOFFrdquo and record

- The uncertainties in your readings on all scales of ammeter and voltmeter which you have

used

- The zero readings of your ammeter these are their readings when they are completely

disconnected from any circuits They should be close to zero but not necessarily exactly so

Procedure Part II Combinations of Resistors

rsaquo Connect all three resistors R1 R2 R3 in series and use the DC volt scale on the voltmeter

Record 5 runs as before (Note your maximum current may be less than 50 ma because the

voltage must not exceed 10mvolts)

rsaquo Connect all these resistors in parallel Again use the DC voltmeter scale with the maximum

current close to 50 mA Record 5 runs as before

rsaquo Estimate (from your data in Part I) the values of R1 R2 R3 Take the two higher

resistances (record which ones you are using) and connect them in parallel Connect this

combination in series with the remaining resistor Record 5 runs as usual

R1 R2 R3

in Series

R1 R2 R3

in Parallel

R1 R2 R3

2 Parallel in Series

with 3rd

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

Graphical Results

rsaquo Using graph paper plot V vs I for each of your resistors R1 R2 R3 Draw the line of best fit

in each case and (from the slope) determine the resistance in ohms 3 significant digits Display

all calculations on the graph sheet

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 23

R1= R2= R3=

rsaquo Using graph paper plot V vs I for each of the three combinations Determine Req for each

case as in (1) above

rsaquo From your results in (1) calculate the predicted (= theoretical) values of Req for each of the

three combinations Display the calculations clearly

rsaquo Summarize your results in the table shown For discrepancies use the predicted values as

more reliable (that is refer to them as if they were exact)

COMBINATION PREDICTED R MEASURED R

DISCR

ALL IN SERIES

ALL IN PARALLEL

SERIES amp

PARALLEL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 24

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 25

EXPERIMENT NO ndash 03 DIVIDER RULES

(VERIFICATION OF CURRENT DIVIDER RULE amp VOLTAGE DIVIDER RULE)

OBJECTIVE

- Verify the divider rules for voltage (VDR) and current (CDR)

THEORY The Voltage Divider Rule (VDR) states that the voltage across an element or across a series

combination of elements in a series circuit is equal to the resistance of the element or series

combination of elements divided by the total resistance of the series circuit and multiplied by the

total impressed voltage

The Current Divider Rule (CDR) states that the current through one of two parallel branches is

equal to the resistance of the other branch divided by the sum of the resistances of the two

parallel branches and multiplied by the total current entering the two parallel branches That is

APPARATUS

1 Power Supply 2 Resistances 3 Digital Multi-Meter (DMM)

4 Connecting Wires 5 Bread Board

PROCEDURE

Part 1 Voltage Divider Rule (VDR)

Construct the circuit

rsaquo Without making any calculations what value would you expect for the voltage across each

resistor Explain your reasoning

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 26

rsaquo Calculate V1 using the VDR with the measured resistor values Measure V1 and determine the

percent difference between the theoretical and experimental results How do they compare

rsaquo If R2 = R3 then the VDR states the V2 = V3 and V1 = V2 + V3 Measure voltages V2 and V3

and comment on the validity of these statements

rsaquo Using VDR calculate the voltage Vab Measure Vab and determine the percent difference

between the theoretical and experimental results How do they compare

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 27

rsaquo Remove resistor R2 to construct the following open circuit

rsaquo Using the measured resistor values calculate the voltages V1 V2 and Vopen using VDR

Measure voltages V1 V2 and Vopen with the DMM and calculate the percent differences

Explain the reasoning

Part 2 Current Divider Rule (CDR)

Construct the circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 28

rsaquo Without making any calculations what value would you expect for the current through each of

the resistors Explain your reasoning

rsaquo Calculate the currents I1 I2 and I3 using the CDR from the measured value of Is Measure the

currents I1 I2 and I3

rsaquo Based on these measurements are your conclusions of earlier part verified Use a percent

difference to compare the theoretical and experimental results

rsaquo Set the maximum current coming from the power supply at 200 mA via a short Place a short

circuit across the 10kΩ-resistor to construct the following circuit

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 29

Part 3 Challenge Circuit

Construct the circuit below

rsaquo Calculate the voltages V1 V2 V3 and V4 using the VDR with measured resistor values

Measure the voltages V1 V2 V3 and V4 and use a percent difference to compare the calculated

and measured results How do they compare

rsaquo Using the results of earlier part calculate the voltage Vab using KVL

rsaquo Measure the voltage Vab and use a percent difference to compare the calculated and measured

results How do they compare Is the voltage Vab equal to V1 ndash V3 Equal to V2 ndash V4 Explain

your reasoning

rsaquo Suppose now that a short is placed across the terminal points ab Calculate the current Iab

through the short Measure the current Iab and use a percent difference to compare the theoretical

and experimental results How do they compare

Note Use separate sheet for the findings of above part

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 30

EXPERIMENT NO ndash 04 NODAL ANALYSIS

(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)

OBJECTIVE

- To analyze a circuit and to determine the unknown parameters of the circuit

THEORY

Under this method the following procedure is adopted

Assume the voltage of different independent nodes

rsaquo Write the equations for each node as per Kirchhoffrsquos Current Law

rsaquo Solve the above equations to get the node voltages

rsaquo Calculate the branch current from the values of node voltages

Let us consider the circuit shown in the figure below L and M are two

independent nodes M can be taken as a reference node Let the voltage of node L (with respect

to M) be VL

Using Kirchofflsquos Law we get

I1+I2=I3

Ohmrsquos law gives

I1= V1 R1= (E1-VL) R1

I2=V2R2 = (E2-VL) R2

I3 =VL R3

(E1-VL)R1 + (E2-VL)R2= VLR3

Rearranging the terms we get

VL (1R1+1R2+1R3)-E1R1-E2R2=0

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 31

It may be noted that the above nodal equation contains the following terms

rsaquo The node voltage multiplied by the sum of all the conductances connected to that node This

term is positive

rsaquo The node voltage at the other end of each branch (connected to this node) multiplied by the

conductance of the branch These terms are negative

rsaquo In this method of solving a network the no of equations required for the solution is one less

than the no of independent nodes in the network

In general the nodal analysis yields similar solutions

APPARATUS

1 Two DC power supplies

2 Five resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

Figure

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=10V and E2=5V

rsaquo Measure the currents through resistances R1 R2 R3 R4 amp R5 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=7V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 32

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 33

Resistors R1 R2 R3 R4 R5

Rated

Values

Measured

Values

For E1=10V and E2=5V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

E1=5V and E2=7V

Voltages VR1 VR2 VR3 VR4 VR5

Calculated

Values

Measured

Values

Percentage

Difference

Currents IR1 IR2 IR3 IR4 IR5

Calculated

Values

Measured

Values

Percentage

Difference

Challenge Swap the resistors R1 with R4 R5 with R2 and repeat all above steps to determine

unknown voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 34

ANSWER THE FOLLOWING QUESTIONS

(a) What is a node

(b) Calculate the equivalent resistance

(c) Solve the following circuit for power dissipation (P=VI) across R1 R2 and R3

(d) What do you meant by a super node

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 35

EXPERIMENT NO ndash 05 MESH ANALYSIS

(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE

- To analyze a two Mesh circuit and to determine the current in each branch of the circuit

THEORY

The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and

describes the branch voltages in terms of the mesh currents This will give us a set of equations

that we solve together to find the mesh currents Once we find the mesh currents we can use

them to calculate any other currents or voltages of interest

We know from KVL the algebraic sum of voltages around a close loop is zero so considering the

circuit shown below and applying KVL in each loop (mesh)

While writing equations for

Applying KVL to mesh 1

- E1 + I1R1 + (I1 - I2) R2 = 0

I1 (R1 + R2) - I2R2 = E1 (1)

Applying KVL to mesh 2

- E2 + (I2 - I1) R2 + I2R3 = 0

I2 (R2 + R3) - I1R2 = E2 (2)

Solving above two equations values of unknowns can easily be calculated

=

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 36

APPARATUS

1 Two DC power supplies

2 Three resistances of different values

3 Connecting wires

4 Digital multi meter (DMM)

PROCEDURE

rsaquo Construct the circuit shown in Figure below

rsaquo Pick the resistances Also verify their resistance by meter and record it in table

rsaquo Solve given circuit for the unknowns before moving to the circuit for measured values

rsaquo Set the DC supply E1=12V and E2=5V

rsaquo Measure the currents through resistances R1 R2 amp R3 and record it in table

rsaquo Also measure voltages across each resistor

rsaquo Now set the DC supply E1=5V and E2=12V

rsaquo Repeat all steps and record the values

Note Use measured values of resistances for all calculations Make these calculations on the space provided

OBSERVATIONS amp CALCULATIONS

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 37

Resistors R1 R2 R3

Rated Values

Measured Values

For E1=12V and E2=5V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 38

Percentage

Difference

E1=5V and E2=12V

Voltages VR1 VR2 VR3

Calculated Values

Measured Values

Percentage

Difference

Currents IR1 IR2 IR3

Calculated Values

Measured Values

Percentage

Difference

Challenge Swap the resistors R1 with R3 and repeat all above steps to determine unknown

voltages and currents both theoretically and practically

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 39

ANSWER THE FOLLOWING QUESTIONS

(a) What is the difference between a loop and a mesh

(b) What is an ideal voltage source How is it different from real voltage source

(c) What is an ideal current source How is it different from real current source

(d) Solve the following circuit for power dissipation across R1 R2 and R3

(e) What do you meant by a super mesh

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 40

EXPERIMENT NO ndash 06 THEVENINS THEOREM

(EXPERIMENTAL VERIFICATION OF THEVENINS THEOREM)

OBJECTIVE

- To Verify Thevenin Theorem by finding its Theveninrsquos Equivalent Circuit

THEORY

Any linear circuit is equivalent to a single voltage source (Thevenins Voltage) in series with

single equivalent resistance (Theveninrsquos Equivalent Resistances)

Applying Theveninrsquos Theorem

rsaquo Step 1 Remove the load and find voltage across the open-circuit terminals Vth All the circuit

analysis techniques presented can be used to compute this voltage

rsaquo Step 2 Determine the Thevenin equivalent resistance of the network at the open terminals with

the load removed Three different types of circuits may be encountered in determining the

resistance Rth

- If the circuit contains only independent sources they are made zero by replacing the voltage

sources with short circuits and the current sources with open circuits Rth is then found by

computing the resistance of purely resistive network at the open terminals

- If the circuit contains only dependent sources an independent voltage or current source is

applied at the open terminals and the corresponding current or voltage at these terminals is

measured The VoltageCurrent ratio at the terminals is the Thevenin equivalent resistance Since

there is no energy source the open circuit voltage is zero in this case

- If the circuit contains both the independent and dependent sources the open circuit terminals

are shorted and the short-circuit current between these terminals is determined The ratio of the

open circuit voltage to short circuit current is the resistance Rth

rsaquo Step 3 If the load is now connected to the Thevenin equivalent circuit consisting of Vth in

series with Rth the desired solution can be obtained

APPARATUS

1 DMM

2 Power Supply

3 Resistances (120Ω 1k Ω 390Ω)

PROCEDURE

rsaquo Calculate measured values of resistances

rsaquo Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A amp

B

rsaquo Calculate the Thevenin equivalent voltage across terminals ldquoArdquo and ldquoBrdquo for 5V 10V 15V

rsaquo Pertaining to circuit in figure III calculate values of IL for different values of RL

rsaquo Now construct circuit in figure I measure the value of Vth by removing RL

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 41

rsaquo Construct circuit in figure II to have measured value of Rth

rsaquo Construct circuit in figure III to determine measured values of IL for different values of RL

Figure-I

Figure-II

Figure-III

OBSERVATIONS amp CALCULATIONS

R1 R2 R3

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Calculated Values

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 42

Vs Vth Rth RL IL

5V 1kΩ

22kΩ

10V 1kΩ

22kΩ

15V 1kΩ

22kΩ

Table Measured Values

Challenge Replacing 1kΩ resistances by 22kΩ and keeping all other things same redo the

above analysis

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 43

ANSWER THE FOLLOWING QUESTIONS

(a) Use Theveninrsquos Theorem to find the current through the 5Ω resistance in the circuit diagram

shown below

(b)What is the importance of Theveninrsquos Theorem in circuit analysis

(c) Discuss the limitations of Theveninrsquos Theorem

(d) A light bulb draws 05A current at the input voltage of 230V Determine the resistance of the

filament and also the power dissipated

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 44

EXPERIMENT NO ndash 07 MAXIMUM POWER TRANSFER THEOREM

(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM FOR A NETWORK)

OBJECTIVE

- To prove maximum power transfer theorem practically

THEORY

The power transferred from a source supply source to load is at its maximum when the resistance

of the load is equal to the internal resistance of the source In other words ldquoA resistive will be

consuming maximum power from the supply when the load resistance is equal to the equivalent

(Thevenin) resistancerdquo

A graph of RL against P is shown in figure below the maximum value of power occurs at RL=

Rth

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 45

APPARATUS

1 DMM

2 Power Supply

3 Resistances fixed (22kΩ 1kΩ) variable (5kΩ)

PROCEDURE

rsaquo Connect the circuit shown in the figure below

rsaquo From the circuit it can be noted that Rth is fixed resistance of value 22kΩ but RL is variable

of value 5kΩ

rsaquo Set the value of Vth = 10 V

rsaquo Change the value of RL in steps as shown in table

rsaquo Measure the voltage VL and current IL and record it in table

rsaquo Plot the graph of power vs load resistance (RL)

rsaquo Using graph estimate P max (practical)

rsaquo Use P max = Vthsup2 4Rth to have the value of P max (theoratical)

rsaquo Repeat above steps by using Rth = 1kΩ

OBSERVATIONS amp CALCULATIONS

PART (I)

For Vth = 10 V Rth = 22kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 46

33kΩ

36kΩ

40kΩ

P max (theoratical)

P max (practical)

Difference

PART (II)

For Vth = 10V Rth = 1kΩ

RL IL VL Power = IL x VL

03kΩ

06kΩ

09kΩ

15kΩ

22kΩ

25kΩ

30kΩ

33kΩ

36kΩ

40kΩ

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 47

P max (theoratical)

P max (practical)

Difference

Challenge For Rth = 1kΩ +22kΩ estimate maximum power transferred to the circuit

practically Also compare it with theoretical value

Note Use separate sheets for analysis of above problem

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions

EE Department Linear Circuit Analysis

CEME (NUST) Rawalpindi 48

ANSWER THE FOLLOWING QUESTIONS

(a) What is meant by load matching

(b) Find the value of RL for maximum power transfer in the network shown below Also

calculate the maximum power that can be transferred to this load

Note Use separate sheets for answering above questions