bird, j. (2001). electrical circuit theory and technology (2nd ed.)

Electrical Circuit Theory and Technology
John Bird
In Memory of Elizabeth
Electrical Circuit Theory and Technology
Revised second edition
John Bird, BSc(Hons), CEng, MIEE, FIEIE, CMath,
FIMA, FCollP
Newnes
OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS
SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Newnes
An imprint of Elsevier Science
Linacre House, Jordan Hill, Oxford OX2 8DP
200 Wheeler Rd, Burlington, MA 01803
First published 1997
Second edition 2001
Reprinted 2002
Revised second edition 2003
Copyright
 1997, 2001, John Bird. All rights reserved
The right of John Bird to be identified as the author of this work
has been asserted in accordance with the Copyright, Designs
and Patents Act 1988
No part of this publication may be reproduced in any material
form (including photocopying or storing in any medium by
electronic means and whether or not transiently or incidentally to some
other use of this publication) without the written permission of the
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England W1P 4LP. Applications for the copyright holder’s written

permission to reproduce any part of this publication should be addressed
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0 7506 5784 7
For information on all Newnes publications visit our website at
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Typeset by Laser Words, Madras, India
Printed and bound in Great Britain
Part 1 Basic Electrical Engineering Principles1
1 Units associated with basic electrical quantities 1
SI units 1
Charge 4
Force 4
Work 5
Power 5
Electrical potential and e. m. f. 6
Resistance and conductance 6
Electrical power and energy 7
Summary of terms, units and their symbols 8
Further problems on units associated with basic electrical quantities9
2 An introduction to electric circuits10
Standard symbols for electrical components10
Electric current and quantity of electricity 11
Potential difference and resistance 13
Basic electrical measuring instruments 13
Linear and non- linear devices 13
Ohms law 14
Multiples and sub- multiples 14
Conductors and insulators 16

Electrical power and energy 16
Main effects of electric current 20
Fuses 20
Further problems13
3 Resistance variation23
Resistance and resistivity23
Temperature coefficient of resistance 26
Further problems on resistance variation 29
4 Chemical effects of electricity31
Introduction31
Electrolysis31
Electroplating 32
The simple cell 32
Corrosion 33
E.m.f. and internal resistance of a cell 34
Primary cells 36
Secondary cells 37
Cell capacity 39
Further problems on the chemical effects of electricity 39
Assignment 141
5 Series and parallel networks42
Series circuits42
Potential divider 44
Parallel networks 45
Current division 48
Wiring lamps in series and in parallel 52
Further problems on series and parallel networks 53
6 Capacitors and capacitance55
Electrostatic field57
Electric field strength 57

Capacitance 57
Capacitors 57
Electric flux density 59
Permittivity 59
The parallel plate capacitor 61
Capacitors connected in parallel and series 63
Dielectric strength 67
Energy stored 68
Practical types of capacitor 69
Discharging capacitors 70
Further problems on capacitors and capacitance 70
7 Magnetic circuits74
Magnetic fields74
Magnetic flux and flux density 75
Magnetomotive force and magnetic field strength 76
Permeability and B  H curves 77
Reluctance 80
Composite series magnetic circuits 81
Comparison between electrical and magnetic quantities 84
Hysteresis and hysteresis loss 84
Further problems on magnetic circuits 85
Assignment 287
8 Electromagnetism89
Magnetic field due to an electric current89
Electromagnets 91
Force on a current- carrying conductor 92
Principle of operation of a simple d. c. motor 96
Principle of operation of a moving coil instrument 97
Force on a charge 98
Further problems on electromagnetism 98

9 Electromagnetic induction100
Introduction to electromagnetic induction100
Laws of electromagnetic induction 101
Inductance 104
Inductors 106
Energy stored 107
Inductance of a coil 107
Mutual inductance 108
Further problems on electromagnetic induction 109
10 Electrical measuring instruments and measurements113
Introduction 113
Analogue instruments 113
Moving-iron instrument 113
The moving-coil rectifier instrument 114
Comparison of moving- coil, moving- iron and moving- coil rectifier instruments 114
Shunts and multipliers 115
Electronic instruments 117
The ohmmeter 117
Multimeters 118
Wattmeters 118
Instrument ˛ loading effect 118
The cathode ray oscilloscope 121
Waveform harmonics 124
Logarithmic ratios 126
Null method of measurement 129
Wheatstone bridge 129
D.c. potentiometer 130
A.c. bridges 130
Measurement errors 131
Further problems on electrical measuring instruments and measurements 133

11 Semiconductor diodes137
Types of materials137
Silicon and germanium 138
n-type and p-type materials 138
The p-n junction 139
Forward and reverse bias 140
Semiconductor diodes 140
Rectification 143
Further problems on semiconductor diodes 143
12 Transistors145
The bipolar junction transistor145
Transistor action 147
Transistor symbols 149
Transistor connections 149
Transistor characteristics 150
The transistor as an amplifier 152
The load line 154
Current and voltage gains 155
Thermal runaway 158
Further problems on transistors 159
Assignment 3162
Main formulae for Part 1164
General164
Capacitors and capacitance164
Magnetic circuits164
Electromagnetism164
Electromagnetic induction164
Measurements164
Part 2 Electrical Principles and Technology165
13 D.c. circuit theory167

Introduction167
Kirchhoffs laws167
The superposition theorem 171
General d.c. circuit theory 174
Th · evenins theorem 176
Constant-current source 181
Nortons theorem 181
Th · evenin and Norton equivalent networks 184
Maximum power transfer theorem187
Further problems on d. c. circuit theory189
14 Alternating voltages and currents193
Introduction193
The a.c. generator194
Waveforms 194
A.c. values 195
The equation of a sinusoidal waveform 200
Combination of waveforms 204
Rectification 208
Further problems on alternating voltages and currents 209
Assignment 4212
15 Single-phase series a.c. circuits213
Purely resistive a.c. circuit214
Purely inductive a.c. circuit 214
Purely capacitive a. c. circuit 214
R  L series a.c. circuit 215
R  C series a.c. circuit 220
R  L  C series a.c. circuit 221
Series resonance 225
Q-factor 227
Bandwidth and selectivity 229

Power in a.c. circuits 230
Power triangle and power factor 232
Further problems on single- phase series a. c. circuits 234
16 Single-phase parallel a. c. circuits238
Introduction238
R  L parallel a.c. circuit238
R  C parallel a.c. circuit 240
L  C parallel a.c. circuit 241
LR  C parallel a.c. circuit 243
Parallel resonance and Q- factor 247
Power factor improvement 252
Further problems on single- phase parallel a. c. circuits 256
17 D.c. transients259
Introduction259
Charging a capacitor 260
Time constant for a C  R circuit 260
Transient curves for a C  R circuit 261
Discharging a capacitor 266
Current growth in an L  R circuit 268
Time constant for an L  R circuit 269
Transient curves for an L  R circuit 269
Current decay in an L  R circuit 272
Switching inductive circuits 275
The effects of time constant on a rectangular waveform 275
Further problems on d. c. transients 276
18 Operational amplifiers278
Introduction to operational amplifiers278
Some op amp parameters 280
Op amp inverting amplifier 282
Op amp non- inverting amplifier 285

Op amp voltage- follower 286
Op amp summing amplifier 286
Op amp voltage comparator 288
Op amp integrator 288
Op amp differential amplifier 289
Digital to analogue ( D/ A) conversion 291
Analogue to digital ( A/ D) conversion 293
Further problems on operational amplifiers 294
Assignment 5296
19 Three phase systems297
Introduction297
Three-phase supply298
Star connection 298
Delta connection 302
Power in three- phase systems 303
Measurement of power in three- phase systems 306
Comparison of star and delta connections 312
Advantages of three- phase systems 312
Further problems on three- phase systems 312
20 Transformers315
Introduction315
Transformer principle of operation 316
Transformer no- load phasor diagram 319
E.m.f. equation of a transformer 320
Transformer on- load phasor diagram 324
Transformer construction 325
Equivalent circuit of a transformer 326
Regulation of a transformer 329
Transformer losses and efficiency 330
Resistance matching 334

Auto transformers 337
Isolating transformers 340
Three-phase transformers 340
Current transformers 342
Voltage transformers 343
Further problems on transformers 344
Assignment 6349
21 D.c. machines350
Introduction350
The action of a commutator 351
D.c. machine construction 352
Shunt, series and compound windings 353
E.m.f. generated in an armature winding 353
D.c. generators 356
Types of d.c. generator and their characteristics 356
D.c. machine losses 362
Efficiency of a d.c. generator 363
D.c. motors 364
Torque of a d.c. machine 365
Types of d.c. motor and their characteristics 368
The efficiency of a d. c. motor 373
D.c. motor starter 376
Speed control of d. c. motors 377
Motor cooling 381
Further problems on d. c. machines 381
22 Three-phase induction motors386
Introduction386
Production of a rotating magnetic field 387
Synchronous speed 388
Construction of a three- phase induction motor 390

Principle of operation of a three- phase induction motor 390
Slip 391
Rotor e.m.f. and frequency 393
Rotor impedance and current 394
Rotor copper loss 395
Induction motor losses and efficiency 395
Torque equation for an induction motor 397
Induction motor torque - speed characteristics 401
Starting methods for induction motors 403
Advantages of squirrel- cage induction motors 404
Advantages of wound rotor induction motor 405
Double cage induction motor 405
Uses of three-phase induction motors 405
Further problems on three- phase induction motors 406
Assignment 7408
Main formulae for Part 2409
A.c. theory:409
Single-phase circuits:410
D.c. transients:410
Operational amplifiers 411
Three-phase systems:411
Transformers:411
D.c. machines:411
Three-phase induction motors:411
Part 3 Advanced Circuit Theory and Technology413
23 Revision of complex numbers415
Introduction415
Operations involving Cartesian complex numbers 417
Complex equations419
The polar form of a complex number 421

Multiplication and division using complex numbers in polar form 421
De Moivres theorem  powers and roots of complex numbers 423
Further problems on complex numbers 424
24 Application of complex numbers to series a. c. circuits429
Introduction429
Series a.c. circuits429
Further problems on series a. c. circuits 440
25 Application of complex numbers to parallel a. c. networks 25
Introduction 25
Admittance, conductance and susceptance 25
Parallel a.c. networks 448
Further problems on parallel a. c. networks 454
26 Power in a.c. circuits459
Introduction459
Determination of power in a. c. circuits459
Power triangle and power factor 464
Use of complex numbers for determination of power 465
Power factor improvement 470
Further problems on power in a. c. circuits 472
Assignment 8475
27 A.c. bridges476
Introduction476
Balance conditions for an a. c. bridge476
Types of a.c. bridge circuit 478
Further problems on a. c. bridges 488
28 Series resonance and Q- factor491
Introduction491
Series resonance491
Q-factor 495
Voltage magnification 498

Q-factors in series 502
Bandwidth 504
Small deviations from the resonant frequency 509
Further problems on series resonance and Q- factor 512
29 Parallel resonance and Q- factor515
Introduction516
The LR  C parallel network 516
Dynamic resistance 517
The LR  CR parallel network 517
Q-factor in a parallel network 519
Further problems on parallel resonance and Q- factor 527
Assignment 9530
30 Introduction to network analysis531
Introduction531
Solution of simultaneous equations using determinants 532
Network analysis using Kirchhoffs laws 535
Further problems on Kirchhoffs laws 542
31 Mesh-current and nodal analysis545
Mesh-current analysis545
Nodal analysis 550
Further problems on mesh- current and nodal analysis 559
32 The superposition theorem562
Introduction562
Using the superposition theorem562
Further problems on the superposition theorem 573
33 Thevenins and Nortons theorems5755
Introduction575
Thevenins theorem575
Nortons theorem 587
Thevenin and Norton equivalent networks 593

Further problems on Thevenins and Nortons theorem 598
Assignment 10602
34 Delta-star and star-delta transformations603
Introduction603
Delta and star connections603
Delta-star transformation603
Star-delta transformation 611
Further problems on delta-star and star-delta transformations 614
35 Maximum power transfer theorems and impedance matching617
Maximum power transfer theorems617
Impedance matching 623
Further problems on maximum power transfer theorems and impedance matching 626
Assignment 11629
36 Complex Waveforms631
Introduction631
The general equation for a complex waveform 632
Harmonic synthesis 633
Rms value, mean value and the form factor of a complex wave 645
Power associated with complex waves 650
Harmonics in single- phase circuits 653
Resonance due to harmonics 664
Sources of harmonics 666
Further problems on complex waveforms 671
37 A numerical method of harmonic analysis678
Introduction678
Harmonic analysis on data given in tabular or graphical form683
Complex waveform considerations 683
Further problems on a numerical method of harmonic analysis 685
38 Magnetic materials688
Revision of terms and units used with magnetic circuits688

Magnetic properties of materials 690
Hysteresis and hysteresis loss 692
Eddy current loss 696
Separation of hysteresis and eddy current losses 701
Nonpermanent magnetic materials 704
Permanent magnetic materials 706
Further problems on magnetic materials 707
Assignment 12710
39 Dielectrics and dielectric loss711
Electric fields, capacitance and permittivity711
Polarization711
Dielectric strength 712
Thermal effects 714
Mechanical properties 714
Types of practical capacitor 715
Liquid dielectrics and gas insulation 715
Dielectric loss and loss angle 715
Further problems on dielectric loss and loss angle719
40 Field theory720
Field plotting by curvilinear squares720
Capacitance between concentric cylinders 725
Capacitance of an isolated twin line 733
Energy stored in an electric field 737
Induced e.m.f. and inductance 741
Inductance of a concentric cylinder ( or coaxial cable) 741
Inductance of an isolated twin line 746
Energy stored in an electromagnetic field 750
Further problems on field theory 753
41 Attenuators758
Introduction758

Characteristic impedance 759
Logarithmic ratios 761
Symmetrical T-and p- attenuators 764
Insertion loss 772
Asymmetrical Tand p- sections 775
The L-section attenuator 779
Two-port networks in cascade 782
Further problems on attenuators 785
Assignment 13789
42 Filter networks790
Introduction791
Basic types of filter sections 791
The characteristic impedance and the attenuation of filter sections 792
Ladder networks 795
Low-pass filter sections 797
High-pass filter sections 807
Propagation coefficient and time delay in filter sections 815
˛m-derived filter sections 825
Practical composite filters 833
Further problems on filter networks 837
43 Magnetically coupled circuits841
Introduction841
Self-inductance841
Mutual inductance 842
Coupling coefficient 843
Coils connected in series 845
Coupled circuits 849
Dot rule for coupled circuits 857
Further problems on magnetically coupled circuits 864
44 Transmission lines869

Introduction869
Transmission line primary constants869
Phase delay, wavelength and velocity of propagation 871
Current and voltage relationships 873
Characteristic impedance and propagation coefficient in terms of the primary
constants 875
Distortion on transmission lines 882
Wave reflection and the reflection coefficient 885
Standing waves and the standing wave ratio 890
Further problems on transmission lines 897
45 Transients and Laplace transforms901
Introduction901
Response of R  C series circuit to a step input901
Response of R  L series circuit to a step input 906
L  R  C series circuit response 910
Introduction to Laplace transforms 914
Inverse Laplace transforms and the solution of differential equations921
Laplace transform analysis directly from the circuit diagram 930
L  R  C series circuit using Laplace transforms 944
Initial conditions 949
Further problems on transients and Laplace transforms 952
Assignment 14958
Main formulae for part 3 advanced circuit theory and technology960
Complex numbers:960
General:960
R  L  C series circuit:9600
LR  C network: 961
LR  CR network: 961
Determinants: 961
Delta-star: 961

Star-delta: 961
Impedance matching: 961
Complex waveforms: 961
Harmonic analysis: 961
Hysteresis and Eddy current: 961
Dielectric loss: 962
Field theory: 962
Attenuators: 962
Filter networks 963
Magnetically coupled circuits 963
Transmission lines: 964
Transients: 964
Part 4 General Reference966
Standard electrical quantities  their symbols and units968
Greek alphabet971
Common prefixes972
Resistor colour coding and ohmic values973
Colour code for fixed resistors973
Letter and digit code for resistors973
Index975
Preface
‘Electrical Circuit Theory and Technology, Revised second Edition’
provides coverage for a wide range of courses that contain electrical
principles, circuit theory and technology in their syllabuses, from
introductory to degree level. The chapter ‘Transients and Laplace
transforms’, which had been removed from the second edition due to page
restraints, has been included in this edition in response to popular demand.
The text is set out in four parts as follows:
PART 1, involving chapters 1 to 12, contains ‘Basic Electrical
Engineering Principles’ which any student wishing to progress in

electrical engineering would need to know. An introduction to electrical
circuits, resistance variation, chemical effects of electricity, series
and parallel circuits, capacitors and capacitance, magnetic circuits,
electromagnetism, electromagnetic induction, electrical measuring
instruments and measurements, semiconductor diodes and transistors are
all included in this section.
PART 2, involving chapters 13 to 22, contains ‘Electrical Principles
and Technology’ suitable for Advanced GNVQ, National Certificate,
National Diploma and City and Guilds courses in electrical and electronic
engineering. D.c. circuit theory, alternating voltages and currents,
single-phase series and parallel circuits, d.c. transients, operational
amplifiers, three-phase systems, transformers, d.c. machines and three-
phase induction motors are all included in this section.
PART 3, involving chapters 23 to 45, contains ‘Advanced Circuit
Theory and Technology’ suitable for Degree, Higher National
Certificate/Diploma and City and Guilds courses in electrical and
electronic/telecommunications engineering. The two earlier sections of the
book will provide a valuable reference/revision for students at this level.
Complex numbers and their application to series and parallel networks,
power in a.c. circuits, a.c. bridges, series and parallel resonance and
Q-factor, network analysis involving Kirchhoff’s laws, mesh and nodal
analysis, the superposition theorem, Th
´
evenin’s and Norton’s theorems,
delta-star and star-delta transforms, maximum power transfer theorems
and impedance matching, complex waveforms, harmonic analysis,
magnetic materials, dielectrics and dielectric loss, field theory, attenuators,
filter networks, magnetically coupled circuits, transmission line theory and
transients and Laplace transforms are all included in this section.
PART 4 provides a short, ‘General Reference’ for standard electrical

quantities —their symbols and units, the Greek alphabet, common
prefixes and resistor colour coding and ohmic values.
At the beginning of each of the 45 chapters learning objectives
are listed.
At the end of each of the first three parts of the text is a handy reference
of the main formulae used.
xviii Electrical Circuit Theory and Technology
It is not possible to acquire a thorough understanding of electrical
principles, circuit theory and technology without working through a large
number of numerical problems. It is for this reason that ‘Electrical Circuit
Theory and Technology, Revised second Edition’ contains some 740
detailed worked problems, together with over 1100 further problems,
all with answers in brackets immediately following each question. Over
1100 line diagrams further enhance the understanding of the theory.
Fourteen Assignments have been included, interspersed within the
text every few chapters. For example, Assignment 1 tests understanding
of chapters 1 to 4, Assignment 2 tests understanding of chapters 5 to 7,
Assignment 3 tests understanding of chapters 8 to 12, and so on. These
Assignments do not have answers given since it is envisaged that lecturers
could set the Assignments for students to attempt as part of their course
structure. Lecturers’ may obtain a complimentary set of solutions of the
Assignments in an Instructor’s Manual available from the publishers
via the internet —see below.
‘Learning by Example’ is at the heart of ‘Electrical Circuit Theory
and Technology, Revised second Edition’.
JOHN BIRD
University of Portsmouth
Free web downloads
Instructor’s Manual
Full worked solutions and mark scheme for all the Assignments in

this book.
This material is available to lecturers only. To obtain a password
please e-mail with the following
details: course title, number of students, your job title and work
postal address.
To download the Instructor’s Manual visit

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Part1BasicElectrical
Engineering
Principles
1 Units associated with
basic electrical quantities
At the end of this chapter you should be able to:
ž state the basic SI units
ž recognize derived SI units
ž understand prefixes denoting multiplication and division
ž state the units of charge, force, work and power and perform
simple calculations involving these units
ž state the units of electrical potential, e.m.f., resistance,

conductance, power and energy and perform simple
calculations involving these units
1.1 SI units
The system of units used in engineering and science is the Syst
`
eme Inter-
nationale d’Unit
´
es (International system of units), usually abbreviated to
SI units, and is based on the metric system. This was introduced in 1960
and is now adopted by the majority of countries as the official system of
measurement.
The basic units in the SI system are listed with their symbols, in
Table 1.1.
TABLE 1.1 Basic SI Units
Quantity Unit
length metre, m
mass kilogram, kg
time second, s
electric current ampere, A
thermodynamic temperature kelvin, K
luminous intensity candela, cd
amount of substance mole, mol
Derived SI units use combinations of basic units and there are many of
them. Two examples are:
ž Velocity —metres per second (m/s)
ž Acceleration— metres per second squared (m/s
2
)
4 Electrical Circuit Theory and Technology

SI units may be made larger or smaller by using prefixes which denote
multiplication or division by a particular amount. The six most common
multiples, with their meaning, are listed in Table 1.2.
TABLE 1.2
Prefix Name Meaning
M mega multiply by 1 000000 (i.e. ð10
6
)
k kilo multiply by 1000 (i.e. ð10
3
)
m milli divide by 1000 (i.e. ð10
3
)
 micro divide by 1 000000 (i.e. ð10
6
)
n nano divide by 1 000000 000 (i.e. ð10
9
)
p pico divide by 1 000000 000 000 (i.e. ð10
12
)
1.2 Charge
The unit of charge is the coulomb (C) where one coulomb is one ampere
second. (1 coulomb D 6.24 ð 10
18
electrons). The coulomb is defined as
the quantity of electricity which flows past a given point in an electric
circuit when a current of one ampere is maintained for one second. Thus,

charge, in coulombs
Q = It
where I is the current in amperes and t is the time in seconds.
Problem 1. If a current of 5 A flows for 2 minutes, find the quan-
tity of electricity transferred.
Quantity of electricity Q D It coulombs
I D 5A,t D 2 ð60 D 120 s
Hence Q D 5 ð 120 D 600 C
1.3 Force
The unit of force is the newton (N) where one newton is one kilogram
metre per second squared. The newton is defined as the force which, when
applied to a mass of one kilogram, gives it an acceleration of one metre
per second squared. Thus,
force, in newtons
F = ma
where m is the mass in kilograms and a is the acceleration in metres
per second squared. Gravitational force, or weight, is mg, where g D
9.81 m/s
2
Units associated with basic electrical quantities 5
Problem 2. A mass of 5000 g is accelerated at 2 m/s
2
by a force.
Determine the force needed.
Force D mass ðacceleration
D 5kgð2 m/s
2
D 10
kg m
s

2
D 10 N
Problem 3. Find the force acting vertically downwards on a mass
of 200 g attached to a wire.
Mass D 200 g D 0.2 kg and acceleration due to gravity, g D 9.81 m/s
2
Force acting downwards D weight D mass ð acceleration
D 0.2kgð 9.81 m/s
2
D 1.962 N
1.4 Work
The unit of work or energy is the joule (J) where one joule is one newton
metre. The joule is defined as the work done or energy transferred when
a force of one newton is exerted through a distance of one metre in the
direction of the force. Thus
work done on a body, in joules
W = Fs
where F is the force in newtons and s is the distance in metres moved
by the body in the direction of the force. Energy is the capacity for
doing work.
1.5 Power
The unit of power is the watt (W) where one watt is one joule per second.
Power is defined as the rate of doing work or transferring energy. Thus,
power in watts,
P =
W
t
where W is the work done or energy transferred in joules and t is the
time in seconds. Thus
energy, in joules,

W = Pt
6 Electrical Circuit Theory and Technology
Problem 4. A portable machine requires a force of 200 N to move
it. How much work is done if the machine is moved 20 m and what
average power is utilized if the movement takes 25 s?
Work done D force ð distance D 200 N ð 20 m D 4000 Nm or 4 kJ
Power D
work done
time taken
D
4000 J
25 s
D 160 J=s
= 160 W
Problem 5. A mass of 1000 kg is raised through a height of 10 m
in 20 s. What is (a) the work done and (b) the power developed?
(a) Work done D force ðdistance and force D mass ð acceleration
Hence, work done D 1000 kg ð9.81 m/s
2
 ð10 m
D 98 100 Nm D 98.1 kNm or 98.1 kJ
(b) Power D
work done
time taken
D
98100 J
20 s
D 4905 J/s
D 4905 W or 4.905 kW
1.6 Electrical potential

and e.m.f.
The unit of electric potential is the volt (V) where one volt is one joule
per coulomb. One volt is defined as the difference in potential between
two points in a conductor which, when carrying a current of one ampere,
dissipates a power of one watt, i.e.
volts D
watts
amperes
D
joules/second
amperes
D
joules
ampere seconds
D
joules
coulombs
A change in electric potential between two points in an electric circuit is
called a potential difference. The electromotive force (e.m.f.) provided
by a source of energy such as a battery or a generator is measured in volts.
1.7 Resistance and
conductance
The unit of electric resistance is the ohm (Z) where one ohm is one
volt per ampere. It is defined as the resistance between two points in a
conductor when a constant electric potential of one volt applied at the
two points produces a current flow of one ampere in the conductor. Thus,
resistance, in ohms
R =
V
I

Units associated with basic electrical quantities 7
where V is the potential difference across the two points in volts and I is
the current flowing between the two points in amperes.
The reciprocal of resistance is called conductance and is measured in
siemens (S). Thus,
conductance, in siemens
G =
1
R
where R is the resistance in ohms.
Problem 6. Find the conductance of a conductor of resistance
(a) 10 ,(b)5k and (c) 100 m
(a) Conductance G D
1
R
D
1
10
siemen D 0.1 s
(b) G D
1
R
D
1
5 ð10
3
S D 0.2 ð10
3
S D 0.2 mS
(c) G D

1
R
D
1
100 ð10
3
S D
10
3
100
S D 10 S
1.8 Electrical power and
energy
When a direct current of I amperes is flowing in an electric circuit and
the voltage across the circuit is V volts, then
power, in watts
P = VI
Electrical energy D Power ð time
D VIt Joules
Although the unit of energy is the joule, when dealing with large amounts
of energy, the unit used is the kilowatt hour (kWh) where
1kWhD 1000 watt hour
D 1000 ð3600 watt seconds or joules
D 3 600000 J
Problem 7. A source e.m.f. of 5 V supplies a current of 3 A for
10 minutes. How much energy is provided in this time?
Energy D power ðtime and power D voltage ð current. Hence
8 Electrical Circuit Theory and Technology
Energy D VIt D 5 ð3 ð10 ð 60 D 9000WsorJ
D 9kJ

Problem 8. An electric heater consumes 1.8 MJ when connected
to a 250 V supply for 30 minutes. Find the power rating of the
heater and the current taken from the supply.
i.e. Power rating of heater = 1kW
Power P D VI, thus I D
P
V
D
1000
250
D 4A
Hence the current taken from the supply is 4 A
1.9 Summary of terms,
units and their symbols
Quantity Quantity Unit Unit symbol
Symbol
Length l metre m
Mass m kilogram kg
Time t second s
Velocity
v metres per second m/s or m s
1
Acceleration a metres per
second squared m/s
2
orms
2
Force F newton N
Electrical charge coulomb C
or quantity Q

Electric current I ampere A
Resistance R ohm 
Conductance G siemen S
Electromotive volt V
force E
Potential volt V
difference V
Work W joule J
Energy E (or W) joule J
Power P watt W
As progress is made through Electrical Circuit Theory and Technology
many more terms will be met. A full list of electrical quantities, together
with their symbols and units are given in Part 4, page 968.
Units associated with basic electrical quantities 9
1.10 Further problems
on units associated with
basic electrical quantities
(Take g = 9.81 m/s
2
where
appropriate)
1 What force is required to give a mass of 20 kg an acceleration of
30 m/s
2
? [600 N]
2 Find the accelerating force when a car having a mass of 1.7 Mg
increases its speed with a constant acceleration of 3 m/s
2
[5.1 kN]
3 A force of 40 N accelerates a mass at 5 m/s

2
. Determine the mass.
[8 kg]
4 Determine the force acting downwards on a mass of 1500 g
suspended on a string. [14.72 N]
5 A force of 4 N moves an object 200 cm in the direction of the force.
What amount of work is done? [8 J]
6 A force of 2.5 kN is required to lift a load. How much work is done
if the load is lifted through 500 cm? [12.5 kJ]
7 An electromagnet exerts a force of 12 N and moves a soft iron
armature through a distance of 1.5 cm in 40 ms. Find the power
consumed. [4.5 W]
8 A mass of 500 kg is raised to a height of 6 m in 30 s. Find (a) the
work done and (b) the power developed.
[(a) 29.43 kNm (b) 981 W]
9 What quantity of electricity is carried by 6.24 ð 10
21
electrons?
[1000 C]
10 In what time would a current of 1 A transfer a charge of 30 C? [30 s]
11 A current o
f 3 A flows for 5 minutes. What charge is transferred?
[900 C]
12 How long must a current of 0.1 A flow so as to transfer a charge of
30 C? [5 minutes]
13 Find the conductance of a resistor of resistance (a) 10Z (b)2kZ
(c) 2 mZ [(a) 0.1 S (b) 0.5 mS (c) 500 S]
14 A conductor has a conductance of 50
µS. What is its resistance?
[20 k]

15 An e.m.f. of 250 V is connected across a resistance and the current
flowing through the resistance is 4 A. What is the power developed?
[1 kW]
16 450 J of energy are converted into heat in 1 minute. What power is
dissipated? [7.5 W]
17 A current of 10 A flows through a conductor and 10 W is dissipated.
What p.d. exists across the ends of the conductor? [1 V]
18 A battery of e.m.f. 12 V supplies a current of 5 A for 2 minutes.
How much energy is supplied in this time? [7.2 kJ]
19 A dc electric motor consumes 36 MJ when connected to a 250 V
supply for 1 hour. Find the power rating of the motor and the current
taken from the supply. [10 kW, 40 A]
2 An introduction to
electric circuits
At the end of this chapter you should be able to:
ž recognize common electrical circuit diagram symbols
ž understand that electric current is the rate of movement of
charge and is measured in amperes
ž appreciate that the unit of charge is the coulomb
ž calculate charge or quantity of electricity Q from Q D It
ž understand that a potential difference between two points in a
circuit is required for current to flow
ž appreciate that the unit of p.d. is the volt
ž understand that resistance opposes current flow and is
measured in ohms
ž appreciate what an ammeter, a voltmeter, an ohmmeter, a
multimeter and a C.R.O. measure
ž distinguish between linear and non-linear devices
ž state Ohm’s law as V D IR or I D
V

R
or R D
V
I
ž use Ohm’s law in calculations, including multiples and
sub-multiples of units
ž describe a conductor and an insulator, giving examples of each
ž appreciate that electrical power P is given by
P D VI D I
2
R D
V
2
R
watts
ž calculate electrical power
ž define electrical energy and state its unit
ž calculate electrical energy
ž state the three main effects of an electric current, giving
practical examples of each
ž explain the importance of fuses in electrical circuits
2.1 Standard symbols for
electrical components
Symbols are used for components in electrical circuit diagrams and some
of the more common ones are shown in Figure 2.1.