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`EXHIBIT 1019
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`EXHIBIT 1019
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`Library of Congress Cataloging in Publication Data
`Johnson, David E
`Basic electric circuit analysis.
`Includes index,
`1, Electric circuits,
`I. Hilburn, John L., 1938-
`joint author,
`Il. Johnson, Johnny Ray, joint
`author.
`IIT. Title,
`421,319’2
`TR454,356
`77-24210
`ISBN 0-13-060137-a
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`© 1978 by Prentice-Hall, Inc., Englewood Cliffs, N.J.
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`07632
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`All rights reserved. No part ofthis book
`may be reproduced in any form or
`by any means without permission in writing
`fromthe publisher,
`
`Printed in the United States of America
`1098765 4
`3
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`PRENTICE-HALLINTERNATIONAL, INC., London
`PRENTICE-HALL OF AUSTRALIA Pry, Limitep, Sydney
`PRENTICE-HALL OF CANADA, Lip., Toronto
`PRENTICE-HALL OF INDIA PRIVATE LiMiTED, New Delhi
`PRENTICE-HALL OF JAPAN, INc., Tokyo
`PRENTICE-HALL OF SOUTHEAST AsIA Pre. Ltp., Singapore
`WHITEHALL BooxKs LIMITED, Wellington, New Zealand
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`Sinusoidal Excitation and Phasors
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`EXERCISES
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`Using phasors,find the ac steady-state current if » = 12 cos (10007 + 30°) V
`in (a) Fig. 10.9(a) for R = 4kQ, (b) Fig. 10.11(a) for £ = 20 mH, and (c)
`Fig. 10.13(a) for C = 1 uF,
`Ans,(a) 3 cos (1000r + 30°) mA,(b) 0.6 cos (10002 — 60°) A,
`(6) 12 cos (1000¢ + 120°) mA
`In Ex,10.6.1, find 7 in each case at ¢ = 1 ms.
`Ans, (a) 0.142 mA,(b) 0.599 A,(c) —11.987 mA
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`10.7 IMPEDANCE AND ADMITTANCE
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`Let us now consider a general phasorcircuit with two accessible terminals, as shown in
`Fig. 10.15. If the time-domain voltage and current at the terminals are given by
`(10.38), then the phasor quantities at the terminals are
`V=V,/0
`T= 1,/6
`‘Wedefine theratio of the phasor voltage to the phasor current as the impedance of
`the circuit, which we denote by Z. Thatis,
`_v¥
`-4.
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`which by (10.46) is
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`Chap.
`ap. 10
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`generally denoted by
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`tereni
`Sinusoidal Excitation and Phasors
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`265
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`“7
`(10.49)
`ZR jx
`where R= Re Zisthe resistive component, or simply resistance, and X = Im Z is the
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`reactive component, or reactance. In general, Z = Z(jaa)is a compl, OF ce if plex function ofjeo,
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`i je
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`but R= R@) and X=X@) are real functions of @. Both R and X,like Z, are
`measuredin ohms, Evidently, comparing (10.48) and (10.49} we may write
`[Z| = SRF?
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`62 = tan? +
`R=|Z|cos 6,
`X=|Z|sin6,
`Theserelations are shown graphically in Fig. 10.16.
`we have
`As an example, supposein Fig. 10.15 that V — 10/56.1° V and I = 2/20° A. Then
`Z= Se ~ 5/36.1° 0
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`In rectangular form thisis
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`Z = S(cos 36.1° + j sin 36.1°)
`=44730
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`The impedances ofresistors, inductors, and capacitors are readily found from their
`V-I relations of (10.40), (10.43), and (10.45), Distinguishing their impedances with
`subscripts R, L, and C, respectively, we have, from these equations and (10.47),
`Zp=R
`Zz, = joL ~ wL/90°—
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`(10.50)
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`PHASOR
`CIRCUIT
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`FIGURE 10.15 Generalphasor citcuit
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`FIGURE 10.16 Graphical representation
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`ofimpedance
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`Z=|Z\0. = "ajo —¢
`where| Z| is the magnitude and 8, the angle of Z. Evidently,
`=n,
`|Z|= 78
`Impedance,asis seen from (10.47), plays the role, in a general circuit, of resistance in
`resistive circuits, Indeed, (10.47) looks very muchlike Ohm’s law; alsolike resistance,
`impedance is measured in ohms, being a ratio of volts to amperes.
`It is importantto stress that impedanceis a complex number, being the ratio of two
`complex numbers, butit is not a phasor. Thatis, it has no corresponding sinusoidal
`time-domain function of any physical meaning, as current and voltage phasors have.
`The impedance Z is written in polar form in (10.48); in rectangular form it is
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`(10.46)
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`(10.47)
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`(10.48)
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