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Contents xiii35 Maximum powertransfer theoremsand impedancematching36 Complex ctionThe general equation for a complex waveformHarmonic synthesisRms value, mean value and the form factorof a complex wavePower associated with complex wavesHarmonics in single-phase circuitsResonance due to harmonicsSources of harmonicsFurther problems on complex waveforms631632633IntroductionHarmonic analysis on data given intabular or graphical formComplex waveform considerationsFurther problems on a numerical method ofharmonic analysis678Revision of terms and units used with magnetic circuitsMagnetic properties of materialsHysteresis and hysteresis lossEddy current lossSeparation of hysteresis and eddy current lossesNonpermanent magnetic materialsPermanent magnetic materialsFurther problems on magnetic 8 Magnetic materials617623Assignment 1136.536.636.736.836.937 A numerical methodof harmonic analysisMaximum power transfer theoremsImpedance matchingFurther problems on maximum power transfertheorems and impedance 64666671678683685Assignment 1271039 Dielectrics anddielectric loss39.139.239.339.439.539.639.739.839.9Electric fields, capacitance and permittivityPolarizationDielectric strengthThermal effectsMechanical propertiesTypes of practical capacitorLiquid dielectrics and gas insulationDielectric loss and loss angleFurther problems on dielectric loss and loss angle71171171271471471571571571940 Field theory40.140.2Field plotting by curvilinear squaresCapacitance between concentric cylinders720725

xiv Contents41 Attenuators40.340.440.540.640.740.840.9Capacitance of an isolated twin lineEnergy stored in an electric fieldInduced e.m.f. and inductanceInductance of a concentric cylinder (or coaxial cable)Inductance of an isolated twin lineEnergy stored in an electromagnetic fieldFurther problems on field 641.741.841.9IntroductionCharacteristic impedanceLogarithmic ratiosSymmetrical T-and -attenuatorsInsertion lossAsymmetrical T- and -sectionsThe L-section attenuatorTwo-port networks in cascadeFurther problems on attenuators758759761764772775779782785Assignment 1378942.142.242.3IntroductionBasic types of filter sectionsThe characteristic impedance and the attenuation offilter sections42.4Ladder networks42.5Low-pass filter sections42.6High-pass filter sections42.7Propagation coefficient and time delay infilter sections42.8‘m-derived’ filter sections42.9Practical composite filters42.10 Further problems on filter networks79079143 Magnetically roductionSelf-inductanceMutual inductanceCoupling coefficientCoils connected in seriesCoupled circuitsDot rule for coupled circuitsFurther problems on magnetically coupled circuits84184184284384584985786444 Transmission lines44.144.244.344.444.5IntroductionTransmission line primary constantsPhase delay, wavelength and velocity of propagationCurrent and voltage relationshipsCharacteristic impedance and propagationcoefficient in terms of the primary constants86986987187342 Filter networks792795797807815825833837875

Contents xv44.644.744.844.945 Transients andLaplace transformsDistortion on transmission linesWave reflection and the reflection coefficientStanding waves and the standing wave ratioFurther problems on transmission ionResponse of R–C series circuit to a step inputResponse of R–L series circuit to a step inputL –R–L series circuit responseIntroduction to Laplace transformsInverse Laplace transforms and the solution ofdifferential equations45.7Laplace transform analysis directly from the circuitdiagram45.8L –R–C series circuit using Laplace transforms45.9Initial conditions45.10 Further problems on transients and Laplace transforms901901906910914Assignment 14958Main formulae for Part 3960921930944949952Part 4 General referenceStandard electrical quantities — their symbols and units968Greek alphabet971Common prefixes972Resistor colour coding and ohmic values973Index975

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Preface‘Electrical Circuit Theory and Technology, Revised second Edition’provides coverage for a wide range of courses that contain electricalprinciples, circuit theory and technology in their syllabuses, fromintroductory to degree level. The chapter ‘Transients and Laplacetransforms’, which had been removed from the second edition due to pagerestraints, 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 ElectricalEngineering Principles’ which any student wishing to progress inelectrical engineering would need to know. An introduction to electricalcircuits, resistance variation, chemical effects of electricity, seriesand parallel circuits, capacitors and capacitance, magnetic circuits,electromagnetism, electromagnetic induction, electrical measuringinstruments and measurements, semiconductor diodes and transistors areall included in this section.PART 2, involving chapters 13 to 22, contains ‘Electrical Principlesand Technology’ suitable for Advanced GNVQ, National Certificate,National Diploma and City and Guilds courses in electrical and electronicengineering. D.c. circuit theory, alternating voltages and currents,single-phase series and parallel circuits, d.c. transients, operationalamplifiers, three-phase systems, transformers, d.c. machines and threephase induction motors are all included in this section.PART 3, involving chapters 23 to 45, contains ‘Advanced CircuitTheory and Technology’ suitable for Degree, Higher NationalCertificate/Diploma and City and Guilds courses in electrical andelectronic/telecommunications engineering. The two earlier sections of thebook 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 andQ-factor, network analysis involving Kirchhoff’s laws, mesh and nodalanalysis, the superposition theorem, Thévenin’s and Norton’s theorems,delta-star and star-delta transforms, maximum power transfer theoremsand impedance matching, complex waveforms, harmonic analysis,magnetic materials, dielectrics and dielectric loss, field theory, attenuators,filter networks, magnetically coupled circuits, transmission line theory andtransients and Laplace transforms are all included in this section.PART 4 provides a short, ‘General Reference’ for standard electricalquantities — their symbols and units, the Greek alphabet, commonprefixes and resistor colour coding and ohmic values.At the beginning of each of the 45 chapters learning objectivesare listed.At the end of each of the first three parts of the text is a handy referenceof the main formulae used.

xviii Electrical Circuit Theory and TechnologyIt is not possible to acquire a thorough understanding of electricalprinciples, circuit theory and technology without working through a largenumber of numerical problems. It is for this reason that ‘Electrical CircuitTheory and Technology, Revised second Edition’ contains some 740detailed worked problems, together with over 1100 further problems,all with answers in brackets immediately following each question. Over1100 line diagrams further enhance the understanding of the theory.Fourteen Assignments have been included, interspersed within thetext every few chapters. For example, Assignment 1 tests understandingof 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. TheseAssignments do not have answers given since it is envisaged that lecturerscould set the Assignments for students to attempt as part of their coursestructure. Lecturers’ may obtain a complimentary set of solutions of theAssignments in an Instructor’s Manual available from the publishersvia the internet — see below.‘Learning by Example’ is at the heart of ‘Electrical Circuit Theoryand Technology, Revised second Edition’.JOHN BIRDUniversity of Portsmouth

Free web downloadsInstructor’s ManualFull worked solutions and mark scheme for all the Assignments inthis book.This material is available to lecturers only. To obtain a passwordplease e-mail j.Blackfond@Elsevier.com with the followingdetails: course title, number of students, your job title and workpostal address.To download the Instructor’s Manual visithttp://www.newnespress.comand enter the book title in the search box, or use the followingdirect URL:http://www.bh.com/manuals/0750657847/For up-to-date information on all Newnes textbooks visit ingRegister as a user to receive regular e-mail bulletins.If you have any suggestions for how we could improve this bookin future editions, corrections, or ideas for our future publishingprogramme please e-mail Newnes at:newnes@Elsevier.com

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Part 1 Basic ElectricalEngineeringPrinciples

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1Units associated withbasic electrical quantitiesAt the end of this chapter you should be able to:žžžžstate the basic SI unitsrecognize derived SI unitsunderstand prefixes denoting multiplication and divisionstate the units of charge, force, work and power and performsimple calculations involving these unitsž state the units of electrical potential, e.m.f., resistance,conductance, power and energy and perform simplecalculations involving these units1.1 SI unitsThe system of units used in engineering and science is the Système Internationale d’Unités (International system of units), usually abbreviated toSI units, and is based on the metric system. This was introduced in 1960and is now adopted by the majority of countries as the official system ofmeasurement.The basic units in the SI system are listed with their symbols, inTable 1.1.TABLE 1.1Basic SI UnitsQuantityUnitlengthmasstimeelectric currentthermodynamic temperatureluminous intensityamount of substancemetre, mkilogram, kgsecond, sampere, Akelvin, Kcandela, cdmole, molDerived SI units use combinations of basic units and there are many ofthem. Two examples are:žžVelocity — metres per second (m/s)Acceleration — metres per second squared (m/s2 )

4 Electrical Circuit Theory and TechnologySI units may be made larger or smaller by using prefixes which denotemultiplication or division by a particular amount. The six most commonmultiples, with their meaning, are listed in Table 1.2.TABLE 1.21.2 ChargePrefixNameMeaningMkm npmegakilomillimicronanopicomultiply by 1 000 000multiply by 1000divide by 1000divide by 1 000 000divide by 1 000 000 000divide by 1 000 000 000 000(i.e.(i.e.(i.e.(i.e.(i.e.(i.e.ð106 )ð103 )ð10 3 )ð10 6 )ð10 9 )ð10 12 )The unit of charge is the coulomb (C) where one coulomb is one amperesecond. (1 coulomb D 6.24 ð 1018 electrons). The coulomb is defined asthe quantity of electricity which flows past a given point in an electriccircuit when a current of one ampere is maintained for one second. Thus,charge, in coulombs Q Itwhere 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 quantity of electricity transferred.Quantity of electricity Q D It coulombsI D 5 A, t D 2 ð 60 D 120 sHence Q D 5 ð 120 D 600 C1.3ForceThe unit of force is the newton (N) where one newton is one kilogrammetre per second squared. The newton is defined as the force which, whenapplied to a mass of one kilogram, gives it an acceleration of one metreper second squared. Thus,force, in newtons F mawhere m is the mass in kilograms and a is the acceleration in metresper second squared. Gravitational force, or weight, is mg, where g D9.81 m/s2

Units associated with basic electrical quantities 5Problem 2. A mass of 5000 g is accelerated at 2 m/s2 by a force.Determine the force needed.Force D mass ð accelerationD 5 kg ð 2 m/s2 D 10kg mD 10 Ns2Problem 3. Find the force acting vertically downwards on a massof 200 g attached to a wire.Mass D 200 g D 0.2 kg and acceleration due to gravity, g D 9.81 m/s2Force acting downwards D weight D mass ð accelerationD 0.2 kg ð 9.81 m/s2D 1.962 N1.4 WorkThe unit of work or energy is the joule (J) where one joule is one newtonmetre. The joule is defined as the work done or energy transferred whena force of one newton is exerted through a distance of one metre in thedirection of the force. Thuswork done on a body, in joules W Fswhere F is the force in newtons and s is the distance in metres movedby the body in the direction of the force. Energy is the capacity fordoing work.1.5 PowerThe 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 Wtwhere W is the work done or energy transferred in joules and t is thetime in seconds. Thusenergy, in joules, W Pt

6 Electrical Circuit Theory and TechnologyProblem 4. A portable machine requires a force of 200 N to moveit. How much work is done if the machine is moved 20 m and whataverage 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 kJPower Dwork done4000 JDD 160 J s 160 Wtime taken25 sProblem 5. A mass of 1000 kg is raised through a height of 10 min 20 s. What is (a) the work done and (b) the power developed?(a)Work done D force ð distance and force D mass ð accelerationHence, work done D 1000 kg ð 9.81 m/s2 ð 10 m D 98 100 Nm D 98.1 kNm or 98.1 kJ(b)1.6 Electrical potentialand e.m.f.Power D98100 Jwork doneDD 4905 J/stime taken20 sD 4905 W or 4.905 kWThe unit of electric potential is the volt (V) where one volt is one jouleper coulomb. One volt is defined as the difference in potential betweentwo points in a conductor which, when carrying a current of one ampere,dissipates a power of one watt, i.e.volts pere secondscoulombsA change in electric potential between two points in an electric circuit iscalled a potential difference. The electromotive force (e.m.f.) providedby a source of energy such as a battery or a generator is measured in volts.1.7 Resistance andconductanceThe unit of electric resistance is the ohm (Z) where one ohm is onevolt per ampere. It is defined as the resistance between two points in aconductor when a constant electric potential of one volt applied at thetwo points produces a current flow of one ampere in the conductor. Thus,resistance, in ohms R VI

Units associated with basic electrical quantities 7where V is the potential difference across the two points in volts and I isthe current flowing between the two points in amperes.The reciprocal of resistance is called conductance and is measured insiemens (S). Thus,conductance, in siemensG 1Rwhere R is the resistance in ohms.Problem 6. Find the conductance of a conductor of resistance(a) 10 , (b) 5 k and (c) 100 m 1.8 Electrical power andenergy11Dsiemen D 0.1 sR10(a)Conductance G D(b)GD11DS D 0.2 ð 10 3 S D 0.2 mSR5 ð 103(c)GD10311SDDS D 10 S 3R100 ð 10100When a direct current of I amperes is flowing in an electric circuit andthe voltage across the circuit is V volts, thenpower, in watts P VIElectrical energy D Power ð timeD VIt JoulesAlthough the unit of energy is the joule, when dealing with large amountsof energy, the unit used is the kilowatt hour (kWh) where1 kWh D 1000 watt hourD 1000 ð 3600 watt seconds or joulesD 3 600 000 JProblem 7. A source e.m.f. of 5 V supplies a current of 3 A for10 minutes. How much energy is provided in this time?Energy D power ð time and power D voltage ð current. Hence

8 Electrical Circuit Theory and TechnologyEnergy D VIt D 5 ð 3 ð 10 ð 60 D 9000 Ws or JD 9 kJProblem 8. An electric heater consumes 1.8 MJ when connectedto a 250 V supply for 30 minutes. Find the power rating of theheater and the current taken from the supply.i.e. Power rating of heater 1 kWPower P D VI, thus I D1000PDD4AV250Hence the current taken from the supply is 4 A1.9 Summary of terms,units and their yAccelerationlmtvaForceElectrical chargeor quantityElectric ntialdifferenceWorkEnergyPowerFQIRGUnitUnit symbolmetrekilogramsecondmetres per secondmetres persecond squarednewtoncoulombmkgsm/s or m s 1m/s2 or m s 2NCampereohmsiemenvoltA SVvoltVjoulejoulewattJJWEVWE (or W)PAs progress is made through Electrical Circuit Theory and Technologymany more terms will be met. A full list of electrical quantities, togetherwith their symbols and units are given in Part 4, page 968.

Units associated with basic electrical quantities 91.10 Further problemson units associated withbasic electrical

20.5 Transformer on-load phasor diagram 20.6 Transformer construction 20.7 Equivalent circuit of a transformer 20.8 Regulation of a transformer 20.9 Transformer losses and efficiency 20.10 Resistance matching 20.11 Auto transformers 20.12 Isolating transformers 20.13 Three-phase transformers 20.14