Bird J. Electrical Circuit Theory and Technology

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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

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

Designs and Patents Act 1988 or under the terms of a licence issued by the

England W1P 4LP. Applications for the copyright holder’s written

permission to reproduce any part of this publication should be addressed

to the publisher

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

www.newnespress.com

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.........................................................................................................