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 copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, 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 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 [...]... 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... 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 threephase induction... ‘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. .. electrical circuits P D VI D I2 R D ž ž ž ž ž 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 An introduction to electric circuits 11 Figure 2.1 2.2 Electric current and quantity of electricity All atoms consist of protons, neutrons and electrons The protons, which have positive electrical. .. 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... found in Section 2.12, problems 4 to 7, page 21 16 Electrical Circuit Theory and Technology 2.8 Conductors and insulators 2.9 Electrical power and energy A conductor is a material having a low resistance which allows electric current to flow in it All metals are conductors and some examples include copper, aluminium, brass, platinum, silver, gold and carbon An insulator is a material having a high... volt 1 A J J W E V W E (or W) P 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/s2 where appropriate)... 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... shells are nearer the nucleus 12 Electrical Circuit Theory and Technology It is possible for an atom to lose an electron; the atom, which is now called an ion, is not now electrically balanced, but is positively charged and is thus able to attract an electron to itself from another atom Electrons that move from one atom to another are called free electrons and such random motion can continue indefinitely... symbols and units Greek alphabet Common prefixes Resistor colour coding and ohmic values 968 971 972 973 Colour code for fixed resistors Letter and digit code for resistors 973 973 Index 975 Preface Electrical Circuit Theory and Technology, Revised second Edition’ provides coverage for a wide range of courses that contain electrical . 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,. 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, . 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