Electrical engineering, students notes

Chap 1. An Introduction to Electrical Engineering

Jean de Dieu IYAKAREMYE

October, 201505/03/23 1

Overview

-Brief history, disciplines, curriculum-Review of electrical principles

Lecturer: Jean de Dieu IYAKAREMYE, Msc

Book: Electricity for Agriculture(Available in the Library)

05/03/23 2

Assignments and CAT

20/10/2015 Homework 1, 22/10/2015 , Assignment

05/03/23 3

What is electrical engineering?

The study of ELECTRICITY along with its numerous applications

05/03/23 4

A brief historyIn 1600, William Gilbert calledthe property of attractingparticles after being rubbed“electricus”.

De Magnete was a treatise ofelectricity and magnetism,noting a long list of elementsthat could be electrified.

A versorium

Gilbert invented the versorium, a device that detected statically-charged bodies

William Gilbert, arguably the first electrical engineer

05/03/23 5

A brief history1800 – voltaic pile developed by Alessandro Volta, a precursor to the battery

1831 – Michael Faraday discovers electromagnetic induction

1873 – Electricity and Magnetism published by James Maxwell, describing a theory for electromagnetism

Voltaic pile

Circuits containing inductors

Maxwell’s equations05/03/23 6

A brief history

1888 – Heinrich Hertz transmits and receives radio signals

1941 – Konrad Zuse introduces the first ever programmable computer

1947 – invention of transistor

Spark-gap transmitter

Z3 computer

Transistor05/03/23 7

A brief history

1958 – integrated circuit developed by Jack Kilby

1968 – first microprocessor is developed

Integrated circuits

Microprocessor05/03/23 8

So where is the field now?

05/03/23 9

Fields of study

Power: Creation, storage, and distribution of electricity

Control: Design of dynamic systems and controllers for the systems

Electronics/Microelectronics: Design of integrated circuits, microprocessors, etc.

Signal Processing: Analysis of signals

05/03/23 10

Telecommunications: Design of transmission systems (voice, data)

Computer: Design and development of computer systems

Instrumentation:Design of sensors and data acquisition equipment

Fields of study

05/03/23 11

Basic concepts

✴ Electricity ✴ Charge ✴ Current ✴ Voltage ✴ Power and Energy

05/03/23 12

Electricity

Physical phenomenon arising from the existence and interactions of electric charge

05/03/23 13

Charge

Where can we observe/experience/use charge?

05/03/23 14

ChargeCharacteristic property of subatomic

particles responsible for electric phenomena

1.602×10−19 C−1.602×10−19 C

- +Electron Proton

The unit of quantity of electric charge is coloumb (C)

1 coulomb = 6.25 × 1018 e

e = elementary charge = charge of proton05/03/23 15

Charge“Charged” particles exhibit forces

Opposite charges attract one another

Like charges repel each other

- -

+-

Charge is the source of one of the fundamental forces in nature (others?)05/03/23 16

Coulomb’s Law

q1 q2r (meters)

(Newtons)

F1,2 is the electrostatic force exerted on charge 1 due to the presence of charge 2

ke is the Coulomb constant ke = 8.987 x 109 N*m2*C-205/03/23 17

Electric current

Describes charge in motion, the flow of charge

This phenomenon can result from moving electrons in a conductive material or moving ions in charged solutions

05/03/23 18

Electric current

An ampere (A) is the number of electrons having a total charge of 1 C moving through a given cross section in 1 s.

As defined, current flows in direction of positive charge flow

n=Q/e , where n=number of electrons, e= -1.6x10exp-19

05/03/23 19

Electrical Circuits

05/03/23 20

Electric circuitAn electric circuit is an interconnection of electrical elements linked together in a closed path so that electric current may

flow continuously

Circuit diagrams are the standard for electrical engineers

05/03/23 21

Rate of flow of charge form node a to node b

Rate of flow of charge form node b to node a

(i = current)

A direct current (dc) is a current of constant magnitude

An alternating current (ac) is a current of varying magnitude and direction

05/03/23 22

Voltage

Driving “force” of electrical current between two points

Vab

Vba

Voltage at terminal a with respect to terminal b

Voltage at terminal b with respect to terminal a

Vab = -Vba

Note: In a circuit, voltage is often defined relative to “ground”05/03/23 23

VoltageThe voltage across an element is the work (energy) required to move a

unit of positive charge from the “-” terminal to the “+” terminal

A volt is the potential difference (voltage) between two points when 1 joule of energy is used to move 1 coulomb of charge from one point to the other

05/03/23 24

PowerThe rate at which energy is converted or work is performed

A watt results when 1 joule of energy is converted or used in 1 second

05/03/23 25

Circuit schematic example

05/03/23 26

Circuit elements

05/03/23 27

Resistors

Resistivity (ρ) is the ability of a material to resist current flow. The units of resistivity are Ohm-meters (Ω-m)

Resistance (R) is the physical property of an element that impedes the flow of current . The units of resistance are Ohms (Ω)

1.68×10−8 Ω·m

Example:

Resistivity of copper

Resistivity of glass 1010 to 1014 Ω·m05/03/23 28

Resistors

05/03/23 29

Resistors

05/03/23 30

Ohm’s Law

(remember, R is in Ω and ρ is in Ω-m)

05/03/23 31

Resistance and temperature

05/03/23 32

Capacitors

05/03/23 33

CapacitorsA capacitor consists of a pair of conductors separated by a dielectric (insulator).

(ε indicates how penetrable a subtance is to an electric field)

Electric charge is stored in the plates – a capacitor can become “charged”

When a voltage exists across the conductors, it provides the energy to move the charge from the positive plate to the other plate.05/03/23 34

CapacitorsCapacitance (C) is the ability of a material to store charge in the

form of separated charge or an electric field. It is the ratio of charge stored to voltage difference between two plates.

Capacitance is measured in Farads (F)

05/03/23 35

CapacitorsThe capacitor plate attached to the negative terminal accepts electrons from the battery.

The capacitor plate attached to the positive terminal accepts protons from the battery.

What happens when the light bulb is initially connected in the circuit?

What happens if you replace the battery with a piece of wire?

05/03/23 36

Energy storage

Work must be done by an external influence (e.g. a battery) to separate charge between the plates in a capacitor. The charge is stored in the capacitor until the external influence is removed and the separated charge is given a path to travel and dissipate.

Work exerted to charge a capacitor is given by the equation:

05/03/23 37

Inductors

An inductor is a two terminal elementconsisting of a winding of N turns capableof storing energy in the form of a magneticfield

Inductance (L) is a measure of the ability ofa device to store energy in the form of amagnetic field. It is measured in Henries (H)

05/03/23 38

Inductors

μ0 = permeability of free space = 4π × 10−7 H/mK = Nagaoka coefficientN = number of turnsA = area of cross-section of the coil in m2

l = length of coil in m

Inductance in a cylindrical coil

05/03/23 39

InductorsThe magnetic field from an inductor can generate an induced

voltage, which can be used to drive current

While building the magnetic field, the inductor resists current flow

05/03/23 40

Inductors

What happens to the light bulb when the switch is closed?

What happens to the light bulb when the switch is then opened?05/03/23 41

Energy storage

The work required to establish current through the coil, and therefore the magnetic field, is given by

Inductors can store energy in the form of a magnetic field when a current is passed through them.

05/03/23 42

Transformers and alternators

Inductors are located in both transformers and alternators, allowing voltage conversion and current generation, respectively

Transformer converts from one voltage to another Alternator produces AC current

05/03/23 43

Electrical sources

An electrical source is a voltage or current generator capable of supplying energy to a circuit

Examples:

-AA batteries-12-Volt car battery-Wall plug

05/03/23 44

Ideal voltage sourceAn ideal voltage source is a circuit element where the voltage across the source is independent of the current through it.

Recall Ohm’s Law: V=IR

The internal resistance of an ideal voltage source is zero.

If the current through an ideal voltage source iscompletely determined by the external circuit, it is considered an independent voltage source

05/03/23 45

Ideal current sourceAn ideal current source is a circuit element where the current through the source is independent of the voltage across it.

Recall Ohm’s Law: I = V/R

The internal resistance of an ideal current source is infinite.

If the voltage across an ideal current source iscompletely determined by the external circuit, it is considered an independent current source

05/03/23 46

Dependent Sources

A dependent or controlled source depends upon a different voltage or current in the circuit

05/03/23 47

• 2.1 Series and Parallel Circuits• 2.2 Analysis of Circuits• 2.3 Electric Power, AC, and DC Electricity

Chapter 2. Electric Circuits and Power

Chapter 2. Objectives1. Recognize and sketch examples of series and parallel circuits.

2. Describe a short circuit and why a short circuit may be a dangerous hazard.

3. Calculate the current in a series or parallel circuit containing up to three resistances.

4. Calculate the total resistance of a circuit by combining series or parallel resistances.

5. Describe the differences between AC and DC electricity.

6. Calculate the power used in an AC or DC circuit from the current and voltage.

Chapter 2. Vocabulary Terms series circuit parallel circuit short circuit network circuit circuit analysis power Kirchhoff’s voltage

law voltage drop direct current (DC)

alternating current (AC)

kilowatt Kirchhoff’s current

law horsepower power factor circuit breaker watt kilowatt-hour

2.1 Series and Parallel CircuitsKey Question:How do series and parallel circuits work?

2.1 Series and Parallel Circuits

• In series circuits, current can only take one path.• The amount of current is the same at all points

in a series circuit.

2.1 Adding resistances in series

• Each resistance in a series circuit adds to the total resistance of the circuit.

Rtotal = R1 + R2 + R3...Total

resistance(ohms)

Individual resistances ()

2.1 Total resistance in a series circuit

• Light bulbs, resistors, motors, and heaters usually have much greater resistance than wires and batteries.

2.1 Calculate current

• How much current flows in a circuit with a 1.5-volt battery and three 1 ohm resistances (bulbs) in series?

2.1 Voltage in a series circuit

• Each separate resistance creates a voltage drop as the current passes through.

• As current flows along a series circuit, each type of resistor transforms some of the electrical energy into another form of energy

• Ohm’s law is used to calculate the voltage drop across each resistor.


• In parallel circuits the current can take more than one path.• Because there are multiple branches, the current is not the

same at all points in a parallel circuit.


• Sometimes these paths are called branches.

• The current through a branch is also called the branch current.

• When analyzing a parallel circuit, remember that the current always has to go somewhere.

• The total current in the circuit is the sum of the currents in all the branches.

• At every branch point the current flowing out must equal the current flowing in.

• This rule is known as Kirchhoff’s current law.

2.1 Voltage and current in a parallel circuit• In a parallel circuit the voltage is the same

across each branch because each branch has a low resistance path back to the battery.

• The amount of current in each branch in a parallel circuit is not necessarily the same.

• The resistance in each branch determines the current in that branch.

2.1 Advantages of parallel circuits

Parallel circuits have two big advantages over series circuits:1. Each device in the circuit sees the full battery voltage.2. Each device in the circuit may be turned off independently without stopping the current flowing to other devices in the circuit.

2.1 Short circuit

• A short circuit is a parallel path in a circuit with zero or very low resistance.

• Short circuits can be made accidentally by connecting a wire between two other wires at different voltages.

• Short circuits are dangerous because they can draw huge amounts of current.

2.1 Calculate current

• Two bulbs with different resistances are connected in parallel to batteries with a total voltage of 3 volts.

• Calculate the total current supplied by the battery.

2.1 Resistance in parallel circuits

• Adding resistance in parallel provides another path for current, and more current flows.

• When more current flows for the same voltage, the total resistance of the circuit decreases.

• This happens because every new path in a parallel circuit allows more current to flow for the same voltage.

2.1 Adding resistance in parallel circuits

• A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel.

• Calculate the total resistance of the circuit.

2.2 Analysis of Circuits

Key Question:How do we analyze

network circuits?

*Students read Section 20.2 AFTER Investigation 20.2

2.2 Analysis of Circuits

• All circuits work by manipulating currents and voltages.

• The process of circuit analysis means figuring out what the currents and voltages in a circuit are, and also how they are affected by each other.

• Three basic laws are the foundation of circuit analysis.

2.2 Three circuit laws

2.2 Voltage divider circuit

2.2 Voltage divider

• A circuit divides any supplied voltage by a ratio of the resistors.

Output voltage (volts)

resistor ratio ()

V0 = R2 Vi R1 + R2

Input voltage (volts)

2.2 Solving circuit problems

1. Identify what the problem is asking you to find. Assign variables to the unknown quantities.

2. Make a large clear diagram of the circuit. Label all of the known resistances, currents, and voltages. Use the variables you defined to label the unknowns.

3. You may need to combine resistances to find the total circuit resistance. Use multiple steps to combine series and parallel resistors.


4. If you know the total resistance and current, use Ohm’s law as V = IR to calculate voltages or voltage drops. If you know the resistance and voltage, use Ohm’s law as I = V ÷ R to calculate the current.

5. An unknown resistance can be found using Ohm’s law as R = V ÷ I, if you know the current and the voltage drop through the resistor.

6. Use Kirchhoff’s current and voltage laws as necessary.


• A bulb with a resistance of 1Ω is to be used in a circuit with a 6-volt battery.

• The bulb requires 1 amp of current. • If the bulb were connected directly to the

battery, it would draw 6 amps and burn out instantly.

• To limit the current, a resistor is added in series with the bulb.

• What size resistor is needed to make the current 1 amp?

2.2 Network circuits

• In many circuits, resistors are connected both in series and in parallel.

• Such a circuit is called a network circuit.• There is no single formula for adding resistors

in a network circuit.• For very complex circuits, electrical engineers

use computer programs that can rapidly solve equations for the circuit using Kirchhoff’s laws.

2.2 Calculate using network circuits

• Three bulbs, each with a resistance of 3Ω, are combined in the circuit in the diagram

• Three volts are applied to the circuit.

• Calculate the current in each of the bulbs.

• From your calculations, do you think all three bulbs will be equally bright?

2.3 Electric Power, AC, and DC Electricity

Key Question:How much does

electricity cost and what do you pay for?

2.3 Electric Power, AC, and DC Electricity

• The watt (W) is a unit of power.

• Power is the rate at which energy moves or is used.

• Since energy is measured in joules, power is measured in joules per second.

• One joule per second is equal to one watt.

20.3 Reviewing terms

2.3 Power in electric circuits

• One watt is a pretty small amount of power. • In everyday use, larger units are more

convenient to use. • A kilowatt (kW) is equal to 1,000 watts.• The other common unit of power often seen

on electric motors is the horsepower.• One horsepower is 746 watts.

2.3 Power

P = VI Current (amps)Voltage (volts)

Power (watts)

2.3 Calculate power

• A light bulb with a resistance of 1.5Ω is connected to a 1.5-volt battery in the circuit shown at right.

• Calculate the power used by the light bulb.

2.3 Paying for electricity

• Electric companies charge for the number of kilowatt-hours used during a set period of time, often a month.

• One kilowatt-hour (kWh) means that a kilowatt of power has been used for one hour.

• Since power multiplied by time is energy, a kilowatt-hour is a unit of energy.

• One kilowatt-hour is 3.6 x 106 joules.

2.3 Calculate power

• Your electric company charges 14 cents per kilowatt-hour. Your coffee maker has a power rating of 1,050 watts.

• How much does it cost to use the coffee maker one hour per day for a month?

2.3 Alternating and direct current

• The current from a battery is always in the same direction.

• One end of the battery is positive and the other end is negative.

• The direction of current flows from positive to negative.

• This is called direct current, or DC.


• If voltage alternates, so does current.

• When the voltage is positive, the current in the circuit is clockwise.

• When the voltage is negative the current is the opposite direction.

• This type of current is called alternating current, or AC.


• AC current is used for almost all high-power applications because it is easier to generate and to transmit over long distances.

• The 220 volt AC (VAC) electricity used in homes and businesses

• AC electricity is usually identified by the average voltage, (220 VAC) not the peak voltage.

2.3 Power in AC circuits

• For a circuit containing a motor, the power calculation is a little different from that for a simple resistance like a light bulb.

• Because motors store energy and act like generators, the current and voltage are not in phase with each other.

• The current is always a little behind the voltage.

20.3 Power for AC circuits

• Electrical engineers use a power factor (pf) to calculate power for AC circuits with motors

P = VI x pf

Avg. current (amps)Avg. voltage (volts)

Power (watts)

power factor0-100%

Application: Wiring in Homes and Buildings

MAGNETISM & ELECTROMAGNETISM

Lecture 3

Magnets and Magnetic Fields

• This is sometimes a complicated subject, because although we use it every day in every motor, we don't really come in contact with magnetism.

• Also, the way the force of magnetism acts is unlike any we have come in contact with yet in our study of physical phenomena. It is a property that always requires three dimensions to describe.

• Because magnetism involves three dimensions, we often have to draw vectors into the plane of the paper or out of the plane of the paper. We represent vectors like that as arrows. But all we see is either the tip of the arrow , if the field is coming out of the page, or the tail of the arrow, , if the field is going into the page.

Permanent Magnets and Magnetic Fields

Magnetic Field of a Wire (Hans Christian Oersted – 1820)

• The field goes in circles around the wire. The direction is given by the right hand rule. Thumb is in direction of current.

• The fingers curl in the direction of the magnetic field. What is its magnitude? A drawing of the field lines shows they go in circles around the wire and are denser near the wire.

• Where the field lines are denser, the magnetic field is stronger.

• It is stronger near the wire.

• The magnitude is given by the formula

MAGNETISM AND CURRENT

Magnetic Field of a Wire Loop

• What about a loop of wire? Each section of the wire gives a magnetic field with the direction determined by the right hand rule.

• The magnetic field inside the wire is in a different direction from the magnetic field outside the wire. At the center of the loop

Magnetic Field of a Wire Loop

• N = number of turns. I = current in the wire. R is the radius of the wire

Ampere's Law

• There is a fundamental principle which allows us to calculate the magnetic field from any wire carrying a current.

• André Marie Ampere determined that if we take any closed path around a current carrying wire and looked only at the vector component of the magnetic field parallel to that closed path, you would find

Magnetic Field of a Solenoid

• If I now take many turns of wire, and pack them tightly, I get a solenoid. Inside the solenoid, the magnetic field is approximately constant and outside the solenoid the magnetic field is approximately zero. See Figure below. The direction of the field is given by the RHR and the magnitude can be determined using Ampere's law.

Magnetic Field of a Solenoid

• where n = number of turns per unit length and I is the current in the loop.

Magnetic Fields Exert a Force on a Moving Charge

Characteristics of the Force•A magnetic field can create a force on an object. However, for the object to feel a force, and the magnetic field to affect the object, three things must be true 1. The object must have an electric charge. 2. The charged object must be moving. 3. The velocity of the moving charged object must have a component that is perpendicular to the direction of the magnetic field. •A slightly different "Right Hand Rule" (RHR) is used to determine the direction of the force on a charged particle from a magnetic field. Index finger points in direction of the particle's velocity, the middle finger points in the direction of the magnetic field, and the thumb points in the direction of the force on a positive charge - the direction a positively charged particle will accelerate.

Definition of Magnetic Field

• Remember that there was a relationship between the electric field and the force that a charged particle felt. That relationship was qE=F. Similarly, there is a relationship between a magnetic field and the force a charged particle feels. It is

• Remember that force is a vector, and there is a direction to this force. The direction is given by the RHR as explained above. If we look at this equation we can see four different ways to increase the force a particle feels from a magnetic field? Increase B. Increase q. Increase v. Maximize sin theta. The sign of q must be used.

Magnetic Fields Exert a Force on a Current in a Wire

• What is a current in a wire? Moving charges. What does a magnetic field do to moving charges? Exerts a force. What does a magnetic field do to a wire. Exerts a force.

Magnetic Fields Exert a Force on a Current in a Wire

• A stereo speaker works by using this principle. If current increases the force increases. The direction is given by RHR.

Magnetic Fields Exert a Torque on a Current in a Coil

• Now put a current carrying loop of wire in an already present magnetic field.

• There is a force on the loop due to the current in the wires and the force on all the wires creates a net torque.

• The torque is given by force multiplied by the length of the lever arm:

Force Between Two Wires

• Okay, what do we know about currents in wires.

• They produce a magnetic field. • They feel a force from magnetic fields

ELECTROMAGNETISM

Introduction • The main emphasis of this chapter can be

summed up in one sentence. A Changing Magnetic Flux induces an emf (electromotive force, or voltage difference). This statement immediately brings up three questions that we need to answer?

• What is a magnetic flux? • How do you change it? • What are the consequences of the induced emf

and what is its polarity?

Magnetic Flux

• Definition: What is Magnetic Flux

ELECTROMAGNETISM

APPLICATIONS:•Electric generator•Electric motor•Transformers

Electrical machines

Transformers

AC Circuits lecture 4Objectives:

Understanding AC circuits and their use in electric networkRLC series and parallel circuitsPower factorEconomic power factor improvement

Phasors

A phasor is a vector whose magnitude is the maximum value of a quantity (eg V or I) and which rotates counterclockwise in a 2-d plane with angular velocity . Recall uniform circular motion:

The projections of r (on the vertical y axis) execute sinusoidal oscillation.

iL

tLm

cos

i C tC m cos

iR

tRm sin

x r t cosy r t sin

V Ri tR R m sin• R: V in phase with i

V QC

tC m sin• C: V lags i by 90

V Ldidt

tLL

m sin• L: V leads i by 90

x

y y

Phasors for L,C,R i

t

VR

it

VL

it

VC

Suppose:

V Ri tR m sin

VCi tC m 1

cos

V Li tL m cos

t

iVR0

VC

0

i

i0

VL

Phasors: LCR

From these equations, we can draw the phasor diagram to the right.

• Assume:

imR

imL

imC

m

LC

R• Given: m tsin

This picture corresponds to a snapshot at t=0. The projections of these phasors along the vertical axis are the actual values of the voltages at the given time.

Phasors: LCR

• The phasor diagram has been relabeled in terms of the reactances defined from:

imR

m

imXC

imXL

LC

R

XCC 1

X LL

The unknowns (im,) can now be solved for graphically since the vector sum of the voltages VL + VC + VR must sum to the driving emf.

Phasors:LCR

imR

m

im(XL-X C)

imR

m

imXC

imXL

XCC 1

X LL

Z R X XL C 2 2

tan X XR

L C

m m L Ci R X X2 2 2 2

i

R X X Zmm

L C

m

2 2

Phasors:Tips• This phasor diagram was drawn as a snapshot of time t=0 with the voltages being given as the projections along the y-axis.

imR

m

imXC

imXLy

x

imR

imXL

imXC

m

“Full Phasor Diagram”

From this diagram, we can also create a triangle which allows us to calculate the impedance Z:

X XL C

Z

R

“ Impedance Triangle”

• Sometimes, in working problems, it is easier to draw the diagram at a time when the current is along the x-axis (when i=0).

Phasors:LCRWe have found the general solution for the driven LCR circuit:

X LL

XCC 1

Z R X XL C 2 2

R

XL

XC

tan X XR

L C

iZmm

i Zm

the loop

eqn

XL - XC

i i tm sin( )

imR

imXL

imXC

m

Lagging & LeadingThe phase between the current and the driving emf depends on the relative magnitudes of the inductive and capacitive reactances.

R

XL

XC

tan X XR

L CiZmm X LL

XCC 1

XL > XC > 0 current LAGS applied voltage

R

XL

XC

XL < XC < 0 current LEADSapplied voltage

XL = XC = 0 current IN PHASE applied voltage

R

XL

XC

Parallel RLC Circuit Discussions and exercises on parallel RLC Circuits during the lecture will be conducted

Power in RLC circuits both in // and Series

• Discussed in class• Exercises • Assignments

Electrical engineering, students notes

Engineering

Transcript of Electrical engineering, students notes