Bird J. Electrical Circuit Theory and Technology

Подождите немного. Документ загружается.

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 j.Blackfond@Elsevier.com with the following

details: course title, number of students, your job title and work

postal address.

To download the Instructor’s Manual visit

http://www.newnespress.com

and enter the book title in the search box, or use the following

direct URL:

http://www.bh.com/manuals/0750657847/

For up-to-date information on all Newnes textbooks visit our

websites:

www.newnespress.com

www.bh.com/engineering

If you have any suggestions for how we could improve this book

in future editions, corrections, or ideas for our future publishing

programme please e-mail Newnes at:

newnes@Elsevier.com

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

)

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 1000000 (i.e. ð10

)

k kilo multiply by 1000 (i.e. ð10

)

m milli divide by 1000 (i.e. ð10

3

)

 micro divide by 1 000 000 (i.e. ð10

6

)

n nano divide by 1000000000 (i.e. ð10

9

)

p pico divide by 1000000000000 (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

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