Electric Circuit Theory. Applied Electricity and Electronics

340 Pages·1981·3.89 MB·English

APPLIED ELECTRICITY AND ELECTRONICS
General Editor: P. HAMMOND
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ELECTRIC CIRCUIT
THEORY
By
R. YORKE,
B.Eng., B.Sc, Ph.D., M.I.E.E.
Department of Electrical Engineering,
The University of Southampton
PERGAMON PRESS
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FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg-Taunus,
OF GERMANY Hammerweg 6, Federal Republic of Germany
Copyright © 1981 R. Yorke
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system or transmitted in
any form or by any means: electronic, electrostatic, magnetic
tape, mechanical, photocopying, recording or otherwise,
without permission in writing from the publishers.
First edition 1981
British Library Cataloguing in Publication Data
Yorke, R
Electric circuit theory.
- (Applied electricity and electronics). - (Pergamon
international library).
1. Electric circuits
I. Title II. Series
621.319.2 TK454 80-41323
ISBN 0-08-026133-7 (Hard)
0-08-026132-9 (Flexi)
Computer typeset by Page Bros (Norwich) Ltd.
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
TO MY WIFE
PREFACE
THE aim of this book is to provide the first-year student of Electrical,
Electronic or Control Engineering with a Circuit Theory text of modest
complexity and length, which nevertheless does not shrink from intro-
ducing him to some of the relatively sophisticated concepts which are
essential, ultimately, for a complete understanding of the subject. The
only prerequisites are Mathematics to A-level (or possibly Scholarship)
standard, some slight background knowledge of Engineering and a desire
to learn.
Some of the concepts involved in the modern approach to Electrical
Engineering have to be pondered upon for a considerable length of time
before their full significance becomes apparent, and for this reason the
author believes that the sooner the student is made aware of them the
better. This is not to say that, on first acquaintance, an exhaustive study
should be undertaken, but merely that he should "rub shoulders" with
the ideas so as to be prepared for deeper study at a later stage.
An example is the distinction between the time- and frequency-domain
descriptions of signals, and, accordingly, this has been introduced at an
early stage in the book. This helps, later, in understanding the Laplace
Transformation—which itself has been included because it is so widely
used now in the study of all linear systems that a student would feel
inadequate without some knowledge of it. Notwithstanding this, how-
ever, it may be omitted on first reading, if the reader so wishes, with
no loss of continuity. The simpler exponential transform is dealt with
first and is considered by many to be an adequate introduction to the
transform technique.
Likewise, network topology is touched upon without delving too far
into its complexities, and several techniques for discovering the fre-
quency characteristics of networks should provide a useful insight for
vii
viii PREFACE
those going on, in later years, to study communications or control
engineering.
The book is based on a 1 hour per week, first-year Circuits course for
Electrical Engineers which has been taught for many years at Southamp-
ton University, although several of the topics have been expanded to
provide enough material for use in other universities and colleges where
such courses might occupy 2 hours per week.
There is no substitute, in the author's view, for worked examples as
a teaching aid and so they appear in abundance both in the text, where
full solutions are given, and at the end of each chapter, where they are
graded in order of difficulty, in the main, and for which answers only
are provided. Well over 200 problems are used altogether—most of
them original—though the scope for exhibiting originality in a problem
based on Ohm's Law is somewhat limited!
S.I. units have been used throughout and standard symbols and
abbreviations strictly adhered to—with one exception. The author felt
that the recommended abbreviation for the second—the single lower-
case s—would be too readily confused with the complex variable associ-
ated with the exponential and Laplace transformations. Consequently
he has preferred to use the abbreviation sec. His apologies to the purists.
Finally, his sincere thanks are offered, with enthusiasm, to Miss Gina
Lott, Miss Joan Sutton and Miss Susan Makin for their accurate and
painstaking typing from the manuscript, and with respect to the Senate
of Southampton University for their permission to use problems from
some past examination papers.
EDITOR'S PREFACE
ELECTRIC circuit theory provides the framework of electrical engineering
and is therefore central to all courses for future electrical engineers.
Such a central subject makes great demands on the teacher, particularly
in laying foundations which can give adequate support to later advanced
work. No amount of computational skill, useful though it is, can com-
pensate for a lack of physical understanding of circuit parameters, circuit
response and circuit topology. In this book Dr. Yorke, out of his long
experience as a university teacher, lays a foundation which will serve
his readers well. His emphasis throughout is on physical processes rather
than on abstract mathematics and the book has a real engineering
flavour, which sustains interest and meets the needs of those who want
to apply their knowledge to the practice of the profession of electrical
engineering.
P. HAMMOND
ix
SYMBOLS, UNITS AND ABBREVIATIONS
1. Standard symbols for electrical parameters
R Resistance
X Reactance
Z Impedance
G Conductance
B Susceptance
Y Admittance
C Capacitance
L Inductance (self)
M Inductance (mutual)
P Power
Q Q-factor (of resonant circuit); Imaginary compt. of com-
plex power
q Electric charge
hi Current
V, v Voltage
1
V I Peak voltage or current
V' *m,y I .*'•> ! Conjugate complex of V, I
pi Potential difference
E, e Electromotive force
e.m.f. Electromotive force
VA Volt-amperes
VAr Reactive volt-amperes
P.F., p.f. Power factor
S = P + ]Q Complex power = real 4- imaginary compts.
2. Units
A Amperes (pA, |iA, mA)
C Coulomb (mC, \iC)
XV
xvi SYMBOLS, UNITS AND ABBREVIATIONS
F Farad (nF, |iF, pF)
g Gram (mg, kg)
H Henry (mH, |iH)
Hz Hertz (cycles per second) (kHz, MHz)
J Joule (kJ, MJ)
min minute
m Metre (mm, cm, km)
rad radian
S Siemens (reciprocal ohms)
sec Second (msec, jisec)
V Volt GAV, mV, kV, MV)
W Watt (|iW, mW, kW, MW)
Q Ohm (M-Q, mQ, kQ, MQ)
3. General abbreviations
A, a A constant
or, /3 Constants
a Damping constant, — in series R, L, C, circuit
b A constant
B Number of branches (in a network)
a Ratio of frequencies ]
/5 Ratio of inductances V in a resonant circuit
6 Ratio of capacitances J
dB Decibel
e Base of Naperian logarithms (2.71828)
CO
— (ratio of any radian frequency: resonant radian
(DO
frequency)
Efficiency
F(s),2L. Laplace transform of
/ Frequency (Hz)
/ Function
Gain function
G(s),G(jo>)
Constant
J
K k
y
SYMBOLS, UNITS AND ABBREVIATIONS xvii
A
2
A 5 _ ,
T
log Logarithm to base 10
In Logarithm to base e
L Number of link branches in a network
N Number of nodes in a network
P Phasor
P(s)
Polynomial in 5
r Ratio of wattmeter readings
2fte, Re Real part
r.m.s. Root-mean-square
s Complex variable
a Real part of s
T, t Time
T(s), T(ja>) Transfer function
r(0"+) Instant just before t = 0
r(0 ) Instant just after t = 0
r Time constant
U(i) Unit step function
W, w Energy
coo Undamped natural frequency
(co o)\ . .
0
y for a resonant circuit
fl = y2 (G = G-factor)
Any frequency; imaginary part of s
<f>, <t> Function
0 Phase angle
Y(s), Y(ja>) Admittance function
Z(s), Z(jeo) Impedance function
damping constant a
£ Damping ratio ^ =
critical damping constant oc
Ct
ECT - B