Electric CircuitsLecture 1:

Introduction

By Sheharyar Zahid

Course Outline & Book List

• Course outline is provided separately• The officially recommended book is

“Fundamentals of Electric Circuits” By Sergio Franco

• You are also advised to consult the reference books mentioned in the course outline, for selective reading.

Assessment Weightages

• Theory (75%) • Practical (25%)

Quizzes (10%)Assignment(2%) Sessional Examination I & II (25%) Final Examination (38%)

A minimum class ATTENDANCE of 75% is required to be eligible for appearing in the final examination.

The basics• What is current? • What is a charge?• Atoms can be negatively or positively charged

(based on the borrowing or lending of electrons)

• Charge(Q) is measured in Coulombs (C) as a standard convention

• Current(I) is measured in Amperes(A) as a standard convention

• 1 ampere is defined as a 1 coulomb charge passing a point in a circuit in 1 second

• An electron carries a charge of 1.60 x 10-19 C• Therefore 6.24 x 1018 electrons constitute a 1 Coulomb charge

Charge Flow and Conduction

• Having defined charge, it can be said that current is the flow of charge

• Materials can either be electrical conductors, insulators or semiconductors

• Electrical current requires free electrons for mobility (i.e. the charge is physically carried via “borrowed” free electrons)

• Conductors have more free electrons whereas insulators have less free electrons

• What makes Copper a good conductor of electricity?• At room temperature, Copper has free electrons of the order of

1023 electrons/Cm3 • This makes Copper a very good conductor of electricity

Coulombs Law

Coulombs LawStatement: The force between 2 charges Q1 and Q2 is directly proportional to the product of their charges and inversely proportional to their distance apart

Mathematical Notation: F = (k Q1 Q2)/(r2)Where F = force

Q1 & Q2 = charges

r = distance between Q1 and Q2

k = 1/(4 π ε0)

Coulombs Law and Conduction

• As coulombs law indicates, within an atom, the least tightly bound electrons will be the valence electrons

• These valance electrons have an energy threshold ( overcome by applying sufficient energy) in order to break free and become “mobile” electrons and hence “carry” charge

• The amount of energy required depends on the number of valance electrons present in the atom

• If the valance shell is full (or nearly full), electrons are more tightly bound and there are lesser free electrons

Speed of Electric Charge

• Within all metals, electrons are able to move• The speed of this electron flow (drift velocity) is actually very

slow (order of mm/s in copper wire)• Electron speed in a wire depends on

– Value of electric current (Amperes) [Directly proportional]– Diameter of the wire [Inversely proportional]– What is the conducting material i.e. how dense is the electron sea?

• Now that we have established that the drift velocity of electrons within a conducting medium can be quite slow, the obvious question arises, why does electrical energy seem to travel almost instantaneously in a circuit?

• Imagine a bulb connected in series with a battery(voltage source) and a switch

• When the switch is closed it sets up an electric potential difference (thanks to the battery) across the circuit

• This electric field signal travels nearly at the speed of light (the exact value depends on conducting medium and such)

• That is why the bulb turns on almost instantaneously• In other words, when the switch is flipped, it generates an

electric field (nearly comparable to the speed of light) which causes the electrons throughout the circuit to almost instantaneously gain energy and become mobile– NOTE that this electron movement is for the case of DC current, in AC

current the electrons vibrate rather than flow

Resistance and Conductance

• Resistance(R) is the opposition offered to current flow, measured in Ohms(Ω)

• Conductance (G) measured in Siemens(S) can be defined as the reciprocal of resistance

• G = 1/R • As a general standard, resistors are color coded as the heat

they dissipate tends to burn away any physical writing on the device

• As an electronic/electrical/telecom engineer it would be very useful to memorize the resistor color code

Resi

stor

Col

or C

ode

Ohms Law• Suppose a battery is connected to provide 1 volt (V), connected with copper

wire to a 1 Ω load

• Ohms law: I = V/R• The current set up in this circuit (ignoring wiring/internal resistances) will

amount to an Ampere• Notice that this law states that current is directly proportional to voltage and

inversely proportional to resistance

Resistive circuits

• Circuits may employ resistances in series or in parallel

Mathematically, the total resistance RT :-Series case- -Parallel case-

RT = R1 + R2 1/RT = 1/R1 + 1/R2

Kirchhoff’s Laws

• Kirchhoff’s Current Law (KCL):– Statement: Current entering a junction equals the current

leaving that junction

I1 + I3 = I4 + I5 + I2

[2]

• Kirchhoff’s Voltage Law (KVL):– Statement: The sum of the EMF sources around any closed loop is

equivalent to the sum of potential drops in that loop

Kirchhoff’s Laws

See example on page 32, Franco

[2]

Power dissipation

• When a voltage is applied across a resistor and current flows through it, power is dissipated in the resistor as heat energy.

• This power can be calculated by using the equation• P=VI• Measured in Watts

• Also note that the power is conserved in a circuit

• Having talked about voltage, remember that it is actually a potential difference between two points. Therefore to find out the “voltage” at any point in the circuit we need a reference point to compare it to. This reference point is often called “Ground” or “Earth”, and is said to be at zero voltage

• Often depicted in circuit diagrams as follows:

• Sometimes also referred to as the reference node (or datum node)

Electrical Ground

Direction of and current and charge• We have talked about the flow of charge but we have not yet

talked about the direction of this flow. • Conventional current is defined as the “flow of positive

charge” and it flows from the positive terminal to the negative terminal since opposite charges attract

• Positive charge is the “absence of an electron”, in semiconductor theory we call it a ‘hole’

• But the flow of electrons and ‘negative charge’ is from the negative terminal to the positive one

• In fact to some degree you could even say that the direction of flow is irrelevant

• Just follow these rules and conventions and it will help you not only in this module but others as well throughout your course

Relation between charge and current

• Recall the formal definition of an ampere• If we can take a point in a circuit and somehow

– Know the amount of charge on each particle– Measure the number of particles passing through that point per unit

time

• We can then measure the current in amperes when we know how many coulombs are passing through that point per second

Difference between EMF and Voltage

EMF is the electromotive force and typically refers to the source voltage on zero load

Voltage on the other hand is a more general term and can be used to describe the potential difference between any two points in a closed circuit

Note that practical EMF sources do have an internal resistance and hence an internal voltage drop. However, if you would consider this trivial difference then the EMF would always be greater than the voltage of a source

Signals

• An electrical signal can be defined as “a function that conveys information about the behavior or attributes of some phenomenon” [3]

• A direct current (DC) signal is one that remains constant with respect to time. A constant voltage is required to bring this about so do not be confused when you hear the term “DC voltage”.

• A time varying signal on the other hand is a bit more complicated and changes its value with time as the name implies

• Read more about signals in Franco pg.16. Background reading is essential for success,

Equivalent steady state average DC current for a time varying signal:

[1]

[1]

AC Signal

• Another elementary signal you must know about is the alternating current signal

• It is a periodic signal i.e. it repeats itself after a defined period (one time period equals the reciprocal of signal frequency)

• An AC signal alternates between the positive maximum peak (+Xm) and the negative one (-Xm) forming a sinusoidal wave

• Another important value is the peak to peak value of the current (Xpk-pk) which would be twice Xm

• The root mean square value is given by[1]

AC Sine Wave

[1]

Instantaneous value can be calculated from:

[1]

Loops and Meshes

• A loop is a closed path such that no node is traversed more than once

How many loops exist here?

• A mesh is a loop that contains no other loops• A Node is a point where the connections of 2 or more

elements meet

How many meshes exist here?

[1]

Loops and Meshes

• Six loops are present. Can you guess which ones?

[1]

These are all loops according to the definition of a loop

Which ones are the meshes then?

The answer is …. First 3 loops are also meshes!

[1]

Current and Voltage sources• A voltage source enforces a specified voltage across its’

terminals, irrespective of the current• A current source enforces a specified current irrespective of

the voltage across its’ terminals• Sources can release power therefore they are active elements

[1] [1]

Sources

• Voltage sources may be connected in series and their overall voltage will add up as described in KVL

• However differing voltage sources connected in parallel would violate KVL, a load resistance is required to manage this configuration

• Current sources work in a different way though, they add up in parallel

• For an in-depth understanding see Franco pg. 44

Resistivity• A copper wire also has a resistance associated with it and it

happens to be• Elements have a parameter known as resistivity• This parameter, in combination with the dimensional

description of the object/surface in question can be used to calculate the resistance

• A copper wire of 0.1mm diameter would have a resistance of 0.0213Ω/m

• Resistance of a wire Rw =(ρ*l)/A– Where

• l = length• A= Cross-sectional area• ρ = resistivity constant (material dependent property)

Some instructions/information:You are expected to maintain a primary email account that you

will monitor regularly.Lecture slides, announcements, problem sheets and other

learning materials will be regularly emailed outQuizzes will be not be announced and will (usually) examine your

understanding of a preceding lecture. (this is not a promise, hence the use of the word ‘usually’)

This module is very important as it is elementary material and is a pre-requisite for many of your other courses, so do yourself a favor and do well!

References[1]Franco, S 1995, Electric circuit fundamentals, 2nd Edn, Saunders College Publishing[2]Kirchhoff’s circuit laws, Wikipedia, viewed 10th September 2012, ‘en.Wikipedia.org/wiki/kirchhoff’s_circuit_laws’[3]Ronald, P 1991 ’Introductory signal processing’ World Scientific. p1