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9TH EDITIONIntroduction toElectric CircuitsJames A. SvobodaClarkson UniversityRichard C. DorfUniversity of California

PUBLISHEREXECUTIVE EDITORCONTENT MANAGERPRODUCTION EDITOREXECUTIVE MARKETING MANAGERMARKETING ASSISTANTDESIGN DIRECTORPRODUCT DESIGNEREDITORIAL OPERATIONS MANAGEREDITORIAL OPERATIONS ASSISTANTSENIOR DESIGNERPHOTO EDITORSENIOR CONTENT EDITOREDITORIAL PROGRAM ASSISTANTCONTENT ASSISTANTPRODUCTION MANAGEMENT SERVICESDon FowleyDan SayreKevin HolmTim LindnerChris RuelMarissa CarrollHarry NolanJenny WelterMelissa EdwardsCourtney WelshMadelyn LesureSheena GoldsteinWendy AshenbergJessica KnechtHelen SeachristBruce Hobart/Laserwords MaineCover Photos: # Jivko Kazakov/iStockphoto.com; Alberto Pomares/Getty Images; # choicegraphx/iStockphoto.com;# mattjeacock/iStockphoto.comThis book was set in 10/12 pt in Times New Roman by Laserwords Maine, and printed and bound by RRD Jefferson City.The cover was printed by RRD Jefferson City.1This book is printed on acid-free paper. Copyright # 2014, 2010, 2006, 2004, 2001 John Wiley & Sons, Inc. All rights reserved. No part of this publication may bereproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying,recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act,without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to thePublisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., Ill River Street,Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website www.wiley.com/go/permissions.Evaluation copies are provided to qualiﬁed academics and professionals for review purposes only, for use in their courses duringthe next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of thereview period, please return the evaluation copy to Wiley. Return instructions and a free of charge return shipping label areavailable at www.wiley.com/go/returnlabel. Outside of the United States, please contact your local representative.ISBN-13:978-1-118-47750-2BRV ISBN: 978-1-118-52106-9Printed in the United States of America10 9 8 7 6 5 4 3 2 1

The scientiﬁc nature of the ordinary manIs to go on out and do the best he can.—John PrineBut, Captain, I cannot change the laws of physics.—Lt. Cmdr. Montogomery Scott (Scotty), USS EnterpriseDedicated to our grandchildren:Ian Christopher Boilard, Kyle Everett Schafer, and Graham Henry SchaferandHeather Lynn Svoboda, James Hugh Svoboda, Jacob Arthur Leis,Maxwell Andrew Leis, and Jack Mandlin Svoboda

About the AuthorsJames A. Svoboda is an associate professor of electrical and computer engineering at Clarkson University, where he teaches courses on topics such as circuits,electronics, and computer programming. He earned a PhD in electrical engineeringfrom the University of Wisconsin at Madison, an MS from the University of Colorado,and a BS from General Motors Institute.Sophomore Circuits is one of Professor Svoboda’s favorite courses. He hastaught this course to 6,500 undergraduates at Clarkson University over the past 35years. In 1986, he received Clarkson University’s Distinguished Teaching Award.Professor Svoboda has written several research papers describing the advantagesof using nullors to model electric circuits for computer analysis. He is interested in theway technology affects engineering education and has developed several softwarepackages for use in Sophomore Circuits.Richard C. Dorf, professor of electrical and computer engineeringat the University of California, Davis, teaches graduate and undergraduate courses in electrical engineering in the ﬁelds of circuits andcontrol systems. He earned a PhD in electrical engineering from theU.S. Naval Postgraduate School, an MS from the University ofColorado, and a BS from Clarkson University. Highly concernedwith the discipline of electrical engineering and its wide value tosocial and economic needs, he has written and lectured internationallyon the contributions and advances in electrical engineering.Professor Dorf has extensive experience with education andindustry and is professionally active in the ﬁelds of robotics, automation, electric circuits, and communications. He has served as a visitingprofessor at the University of Edinburgh, Scotland, the MassachusettsInstitute of Technology, Stanford University, and the University ofCalifornia at Berkeley.A Fellow of the Institute of Electrical and Electronic Engineers and the American Society forEngineering Education, Dr. Dorf is widely known to the profession for his Modern Control Systems,twelfth edition (Pearson, 2011) and The International Encyclopedia of Robotics (Wiley, 1988).Dr. Dorf is also the coauthor of Circuits, Devices and Systems (with Ralph Smith), ﬁfth edition(Wiley, 1992). Dr. Dorf edited the widely used Electrical Engineering Handbook, third edition (CRCPress and IEEE press), published in 2011. His latest work is Technology Ventures, fourth edition(McGraw-Hill 2013).ix

PrefaceThe central theme of Introduction to Electric Circuits is the concept that electric circuits are partof the basic fabric of modern technology. Given this theme, we endeavor to show how theanalysis and design of electric circuits are inseparably intertwined with the ability of the engineerto design complex electronic, communication, computer, and control systems as well as consumerproducts.Approach and OrganizationThis book is designed for a one- to three-term course in electric circuits or linear circuit analysis and isstructured for maximum ﬂexibility. The ﬂowchart in Figure 1 demonstrates alternative chapterorganizations that can accommodate different course outlines without disrupting continuity.The presentation is geared to readers who are being exposed to the basic concepts of electriccircuits for the ﬁrst time, and the scope of the work is broad. Students should come to the course with thebasic knowledge of differential and integral calculus.This book endeavors to prepare the reader to solve realistic problems involving electric circuits.Thus, circuits are shown to be the results of real inventions and the answers to real needs in industry, theofﬁce, and the home. Although the tools of electric circuit analysis may be partially abstract, electriccircuits are the building blocks of modern society. The analysis and design of electric circuits are criticalskills for all engineers.What’s New in the 9th EditionRevisions to Improve ClarityChapter 10, covering AC circuits, has been largely rewritten to improve clarity of exposition.In addition, revisions have been made through the text to improve clarity. Sometimes these revisionsare small, involving sentences or paragraphs. Other larger revisions involved pages or even entiresections. Often these revisions involve examples. Consequently, the 9th edition contains 36 newexamples.More ProblemsThe 9th edition contains 180 new problems, bringing the total number of problems to more than 1,400.This edition uses a variety of problem types and they range in difﬁculty from simple to challenging,including: Straightforward analysis problems. Analysis of complicated circuits.Simple design problems. (For example, given a circuit and the speciﬁed response, determine therequired RLC values.) Compare and contrast, multipart problems that draw attention to similarities or differences betweentwo situations. MATLAB and PSpice problems. Design problems. (Given some speciﬁcations, devise a circuit that satisﬁes those speciﬁcations.)How Can We Check . . . ? (Verify that a solution is indeed correct.)xi

TSMETHODS OFANALYSIS OFRESISTIVECIRCUITSComplexNumbersB, C, D9101112THE COMPLETERESPONSE OFCIRCUITS WITHTWO ENERGYSTORAGE ELEMENTSSINUSOIDALSTEADY-STATEANALYSISAC STEADY-STATEPOWERTHREE-PHASECIRCUITSFIGURE 1 Flow chart showing alternative paths through the topics in this textbook.Features Retained from Previous EditionsIntroductionEach chapter begins with an introduction that motivates consideration of the material of that chapter.ExamplesBecause this book is oriented toward providing expertise in problem solving, we have included morethan 260 illustrative examples. Also, each example has a title that directs the student to exactly what isbeing illustrated in that particular example.Various methods of solving problems are incorporated into select examples. These cases showstudents that multiple methods can be used to derive similar solutions or, in some cases, that multiplesolutions can be correct. This helps students build the critical thinking skills necessary to discern thebest choice between multiple outcomes.Much attention has been given to using PSpice and MATLAB to solve circuits problems. Twoappendices, one introducing PSpice and the other introducing MATLAB, brieﬂy describe thecapabilities of the programs and illustrate the steps needed to get started using them. Next, PSpice

PrefacexiiiPSpiceF, TORAGEELEMENTSTHE COMPLETERESPONSE OFRL AND :Primary flowChapterAppendixOptional flowand MATLAB are used throughout the text to solve various circuit analysis and design problems. Forexample, PSpice is used in Chapter 5 to ﬁnd a Th evenin equivalent circuit and in Chapter 15 to representcircuit inputs and outputs as Fourier series. MATLAB is frequently used to obtain plots of circuit inputsand outputs that help us to see what our equations are telling us. MALAB also helps us with some longand tedious arithmetic. For example, in Chapter 10, MATLAB helps us do the complex arithmetic thatwe must do in order to analyze ac circuits, and in Chapter 14, MATLAB helps with the partial fractionrequired to ﬁnd inverse Laplace transforms.

xivPrefaceOf course, there’s more to using PSpice and MATLAB than simply running the programs. Wepay particular attention to interpreting the output of these computer programs and checking it to makesure that it is correct. Frequently, this is done in the section called “How Can We Check . . . ?” that isincluded in every chapter. For example, Section 8.9 shows how to interpret and check a PSpice“Transient Response,” and Section 13.7 shows how to interpret and check a frequency responseproduced using MATLAB or PSpice.Design Examples, a Problem-Solving Method, and“How Can We Check . . . ?” SectionsEach chapter concludes with a design example that uses the methods of that chapter to solve a designproblem. A formal ﬁve-step problem-solving method is introduced in Chapter 1 and then used in eachof the design examples. An important step in the problem-solving method requires you to checkyour results to verify that they are correct. Each chapter includes a section entitled “How Can WeCheck . . . ? ” that illustrates how the kind of results obtained in that chapter can be checked to ensurecorrectness.Key Equations and FormulasYou will ﬁnd that key equations, formulas, and important notes have been called out in a shaded box tohelp you pinpoint critical information.Summarizing Tables and FiguresThe procedures and methods developed in this text have been summarized in certain key tables andﬁgures. Students will ﬁnd these to be an important problem-solving resource. Table 1.5-1. The passive convention. Figure 2.7-1 and Table 2.7-1. Dependent sources. Table 3.10-1. Series and parallel sources.Table 3.10-1. Series and parallel elements. Voltage and current division. Figure 4.2-3. Node voltages versus element currents and voltages. Figure 4.5-4. Mesh currents versus element currents and voltages.Figures 5.4-3 and 5.4-4. Thévenin equivalent circuits. Figure 6.3-1. The ideal op amp.Figure 6.5-1. A catalog of popular op amp circuits. Table 7.8-1. Capacitors and inductors. Table 7.13-2. Series and parallel capacitors and inductors.Table 8.11-1. First-order circuits. Tables 9.13-1, 2, and 3. Second-order circuits. Table 10.5-1. Voltage and current division for AC circuits. Table 10.16-1. AC circuits in the frequency domain (phasors and impedances). Table 11.5-1. Power formulas for AC circuits. Tables 11.13-1 and 11.13-2. Coupled inductors and ideal transformers. Table 13.4-1. Resonant circuits.Tables 14.2-1 and 14.2-2. Laplace transform tables.

Preface Table 14.7-1. s-domain models of circuit elements. Table 15.4-1. Fourier series of selected periodic waveforms.Introduction to Signal ProcessingSignal processing is an important application of electric circuits. This book introduces signal processingin two ways. First, two sections (Sections 6.6 and 7.9) describe methods to design electric circuits thatimplement algebraic and differential equations. Second, numerous examples and problems throughoutthis book illustrate signal processing. The input and output signals of an electric circuit are explicitlyidentiﬁed in each of these examples and problems. These examples and problems investigate therelationship between the input and output signals that is imposed by the circuit.Interactive Examples and ExercisesNumerous examples throughout this book are labeled as interactive examples. This label indicates thatcomputerized versions of that example are available at the textbook’s companion site, www.wiley.com/svoboda. Figure 2 illustrates the relationship between the textbook example and the computerizedexample available on the Web site. Figure 2a shows an example from Chapter 3. The problem presentedby the interactive example shown in Figure 2