Engineering Circuit Analysis
`
`Second Edition
`
`William H. Hayt, Jr.
`Professor of Electrical Engineering
`Purdue University
`
`Jack E. Kemmerly
`Professor of Engineering
`California State College, Fullerton
`
`McGraw-Hili Book Company
`
`New York
`St. Louis
`San Francisco
`Dusseldorf
`Johannesburg
`Kuala Lumpur
`London
`Mexico
`Montreal
`New Delhi
`Panama
`Rio de Janeiro
`Singapore
`Sydney
`Toronto
`
`

`
`Engineering Circuit Analysis
`
`Copyright © 1962, 1971 by McGraw-Hill, Inc. All rights reserved.
`'Printed in the United States of America. No part of this
`publication may be reproduced, stored in a retrieval system,
`or transmitted, in any form or by any means, electronic,
`mechanical, photocopying, recording, or otherwise, without
`the prior written permission of the publisher.
`
`Library of Congress Catalog Card Number 70-141920
`
`07-027382-0
`
`234567890 HDBP 7987654321
`
`This book was set in Laurel by York Graphic Services, Inc., printed on
`permanent paper by Halliday Lithograph Corporation, and bound by
`The Book Press, Inc. The designer was Merrill Haber; the drawings
`were done by John Cordes, J. & R. Technical Services, Inc. The
`editors were Michael Elia and Madelaine Eichberg. Robert R.
`Lamer ~upervised production.
`
`

`
`1 2 2 The Transient Circuit
`
`currents. However, circuit analysiS is not concerned with this internal
`displacement current, and since it is fortunately equal to the conduction
`current, we may consider Maxwell's hypotheSiS as relating the conduction
`current to the changing voltage across the capacitor. The relationship is
`linear, and the constant of proportionality is obViously the capacitance C;
`. C av
`.
`Idisp = I = dt
`
`A capacitor constructed of two parallel conducting plates of area A,
`separated a distance d, has a capacitance C = fA/d, where f is the permit­
`tivity, a constant of the insulating material between the plates, and where
`the linear dimensions of the conducting plates are all very much greater
`than d. For air or vacuum, f = fO = 8.854 pf/m == (1/3671") nF/m.
`The concepts of the electric field, displacement current, and the gener­
`alized form of Kirchhoff's current law are more appropriate subjects for
`courses in physics and electromagnetic field theory, as is the determination
`of a suitable mathematical model to represent a specific physical capacitor.
`Several important characteristics of our new mathematical model can
`be discovered from the defining equation (8). A constant voltage across
`a capacitor requires zero current passing through it; a capacitor is thus
`an "open circuit to dc." This fact is certainly represented by the capacitor
`symbol. It is also apparent that a sudden jump in the voltage requires an
`infinite current. lust as we outlawed abrupt changes in inductor currents
`and the associated infinite voltages on physical grounds, we shall not permit
`« abrupt changes in capacitor voltage; the infinite current (and infinite power)
`which results is nonphysical. We shall remove this restriction at the time
`we assume the existence of the current impulse.
`The capacitor voltage may be expressed in terms of the current by
`integrating (8). We first obtain
`
`dv = lidt
`C
`
`and then integrate between the times to and t and between the corre­
`sponding voltages v(to) and v(t),
`v(t) = cf i dt + v(to)
`
`to
`
`Equation (9) may also be written as an indefinite integral plus a constant
`of integration,
`'
`
`v(t) =C1 J'tdt + k
`
`(10)
`
`1
`
`!
`
`(9)