Hayt Engineering Circuit Analysis 8th Edition PDF

This page intentionally left blank  The Resistor Color Code Band color Black Brown Red Orange Yellow Green Blue Violet Gray White Numeric value...

This page intentionally left blank  The Resistor Color Code Band color Black Brown Red Orange Yellow Green Blue Violet Gray White Numeric value 0 1 2 3 4 5 6 7 8 9 1st number Multiplier 2nd number Tolerance band (e.g. gold = 5% silver = 10%, none = 20%) 1. Write down the numeric value corresponding to the first band on the left. 2. Write down the numeric value corresponding to the second band from the left. 3. Write down the number of zeros indicated by the multiplier band, which represents a power of 10 (black = no extra zeros, brown = 1 zero, etc.). A gold multiplier band indicates that the decimal is shifted one place to the left; a silver multiplier band indicates that the decimal is shifted two places to the left. 4. The tolerance band represents the precision. So, for example, we would not be surprised to find a 100  5 percent tolerance resistor that measures anywhere in the range of 95 to 105 . Example Red Red Orange Gold = 22,000 or 22 × 103 = 22 k, 5% tolerance Blue Gray Gold = 6.8 or 68 × 10−1 = 6.8 , 20% tolerance Standard 5 Percent Tolerance Resistor Values 1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1  10. 11. 12. 13. 15. 16. 18. 20. 22. 24. 27. 30. 33. 36. 39. 43. 47. 51. 56. 62. 68. 75. 82. 91.  100 110 120 130 150 160 180 200 220 240 270 300 330 360 390 430 470 510 560 620 680 750 820 910  1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 k 10. 11. 12. 13. 15. 16. 18. 20. 22. 24. 27. 30. 33. 36. 39. 43. 47. 51. 56. 62. 68. 75. 82. 91. k 100 110 120 130 150 160 180 200 220 240 270 300 330 360 390 430 470 510 560 620 680 750 820 910 k 1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 M TABLE 14.1 Laplace Transform Pairs f(t) = −1 {F(s)} F(s) = {f(t)} f(t) = −1 {F(s)} F(s) = {f(t)} 1 1 δ(t) 1 (e−αt − e−βt )u(t) β −α (s + α)(s + β) 1 ω u(t) sin ωt u(t) s s2 + ω2 1 s tu(t) cos ωt u(t) s2 s2 + ω2 t n−1 1 s sin θ + ω cos θ u(t) , n = 1, 2,... sin(ωt + θ) u(t) (n − 1)! sn s2 + ω2 1 s cos θ − ω sin θ e−αt u(t) cos(ωt + θ) u(t) s+α s2 + ω2 1 ω te−αt u(t) e−αt sin ωt u(t) (s + α)2 (s + α)2 + ω2 t n−1 −αt 1 s+α e u(t), n = 1, 2,... e−αt cos ωt u(t) (n − 1)! (s + α)n (s + α)2 + ω2 TABLE 6.1 Summary of Basic Op Amp Circuits Name Circuit Schematic Input-Output Relation Rf i Rf Inverting Amplifier vout = − vin R1 R1 – i + + + vout v in – –   Noninverting Amplifier Rf Rf vout = 1 + vin R1 R1 – + + vout + vin – – Voltage Follower vout = vin (also known as a – Unity Gain Amplifier) + + vout + v in – – Summing Amplifier Rf i Rf vout = − (v1 + v2 + v3 ) R R va – i1 R vb + + + v1 RL vout – i2 R v2 + – – i3 v3 + – Difference Amplifier R i vout = v2 − v1 i1 R va – vb + + i2 R + v1 + RL vout – v2 R – – ENGINEERING CIRCUIT ANALYSIS This page intentionally left blank ENGINEERING CIRCUIT ANALYSIS EIGHTH EDITION William H. Hayt, Jr. (deceased) Purdue University Jack E. Kemmerly (deceased) California State University Steven M. Durbin University at Buffalo The State University of New York ENGINEERING CIRCUIT ANALYSIS, EIGHTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2007, 2002, and 1993. Printed in the United States of America. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOW/DOW 1 0 9 8 7 6 5 4 3 2 1 ISBN 978-0-07-352957-8 MHID 0-07-352957-5 Vice President & Editor-in-Chief: Marty Lange Vice President & Director of Specialized Publishing: Janice M. Roerig-Blong Editorial Director: Michael Lange Global Publisher: Raghothaman Srinivasan Senior Marketing Manager: Curt Reynolds Developmental Editor: Darlene M. Schueller Lead Project Manager: Jane Mohr Buyer: Kara Kudronowicz Design Coordinator: Brenda A. Rolwes Senior Photo Research Coordinator: John C. Leland Senior Media Project Manager: Tammy Juran Compositor: MPS Limited, a Macmillan Company Typeface: 10/12 Times Roman Printer: R. R. Donnelley Cover Image: © Getty Images Cover Designer: Studio Montage, St. Louis, Missouri MATLAB is a registered trademark of The MathWorks, Inc. PSpice is a registered trademark of Cadence Design Systems, Inc. The following photos are courtesy of Steve Durbin: Page 5, Fig. 2.22a, 2.24a–c, 5.34, 6.1a, 7.2a–c, 7.11a–b, 13.15, 17.29 Library of Congress Cataloging-in-Publication Data Hayt, William Hart, 1920–1999 Engineering circuit analysis / William H. Hayt, Jr., Jack E. Kemmerly, Steven M. Durbin. — 8th ed. p. cm. Includes index. ISBN 978-0-07-352957-8 1. Electric circuit analysis. 2. Electric network analysis. I. Kemmerly, Jack E. (Jack Ellsworth), 1924–1998 II. Durbin, Steven M. III. Title. TK454.H4 2012 621.319'2—dc22 2011009912 www.mhhe.com  To Sean and Kristi. The best part of every day. This page intentionally left blank  ABOUT THE AUTHORS WILLIAM H. HAYT, Jr., received his B.S. and M.S. at Purdue University and his Ph.D. from the University of Illinois. After spending four years in industry, Professor Hayt joined the faculty of Purdue University, where he served as Professor and Head of the School of Electrical Engineering, and as Professor Emeritus after retiring in 1986. Besides Engineering Circuit Analysis, Professor Hayt authored three other texts, including Engineering Electromagnetics, now in its eighth edition with McGraw-Hill. Professor Hayt’s professional society memberships included Eta Kappa Nu, Tau Beta Pi, Sigma Xi, Sigma Delta Chi, Fellow of IEEE, ASEE, and NAEB. While at Purdue, he received numerous teaching awards, including the univer- sity’s Best Teacher Award. He is also listed in Purdue’s Book of Great Teachers, a permanent wall display in the Purdue Memorial Union, dedi- cated on April 23, 1999. The book bears the names of the inaugural group of 225 faculty members, past and present, who have devoted their lives to excellence in teaching and scholarship. They were chosen by their students and their peers as Purdue’s finest educators. JACK E. KEMMERLY received his B.S. magna cum laude from The Catholic University of America, M.S. from University of Denver, and Ph.D. from Purdue University. Professor Kemmerly first taught at Purdue University and later worked as principal engineer at the Aeronutronic Division of Ford Motor Company. He then joined California State University, Fullerton, where he served as Professor, Chairman of the Faculty of Electrical Engi- neering, Chairman of the Engineering Division, and Professor Emeritus. Professor Kemmerly’s professional society memberships included Eta Kappa Nu, Tau Beta Pi, Sigma Xi, ASEE, and IEEE (Senior Member). His pursuits outside of academe included being an officer in the Little League and a scoutmaster in the Boy Scouts. STEVEN M. DURBIN received the B.S., M.S. and Ph.D. degrees in Electrical Engineering from Purdue University, West Lafayette, Indiana. Subsequently, he was with the Department of Electrical Engineering at Florida State University and Florida A&M University before joining the University of Canterbury, New Zealand, in 2000. SinceAugust 2010, he has been with the University at Buffalo, The State University of New York, where he holds a joint appointment between the Departments of Electrical Engineering and Physics. His teaching interests include circuits, electronics, electromagnetics, solid-state electronics and nanotechnology. His research interests are primarily concerned with the development of new semiconductor materials—in particular those based on ox- ide and nitride compounds—as well as novel optoelectronic device structures. HeisafoundingprincipalinvestigatoroftheMacDiarmidInstituteforAdvanced Materials and Nanotechnology, a New Zealand National Centre of Research Excellence, and coauthor of over 100 technical publications. He is a senior mem- ber of the IEEE, and a member of Eta Kappa Nu, the Electron Devices Society, the Materials Research Society, the AVS (formerly the American Vacuum Society), theAmerican Physical Society, and the Royal Society of New Zealand. vii This page intentionally left blank  BRIEF CONTENTS PREFACE xv 1 INTRODUCTION 1 2 BASIC COMPONENTS AND ELECTRIC CIRCUITS 9 3 VOLTAGE AND CURRENT LAWS 39 4 BASIC NODAL AND MESH ANALYSIS 79 5 HANDY CIRCUIT ANALYSIS TECHNIQUES 123 6 THE OPERATIONAL AMPLIFIER 175 7 CAPACITORS AND INDUCTORS 217 8 BASIC RL AND RC CIRCUITS 261 9 THE RLC CIRCUIT 321 10 SINUSOIDAL STEADY-STATE ANALYSIS 371 11 AC CIRCUIT POWER ANALYSIS 421 12 POLYPHASE CIRCUITS 457 13 MAGNETICALLY COUPLED CIRCUITS 493 14 COMPLEX FREQUENCY AND THE LAPLACE TRANSFORM 533 15 CIRCUIT ANALYSIS IN THE s-DOMAIN 571 16 FREQUENCY RESPONSE 619 17 TWO-PORT NETWORKS 687 18 FOURIER CIRCUIT ANALYSIS 733 Appendix 1 AN INTRODUCTION TO NETWORK TOPOLOGY 791 Appendix 2 SOLUTION OF SIMULTANEOUS EQUATIONS 803 Appendix 3 A PROOF OF THÉVENIN’S THEOREM 811 Appendix 4 A PSPICE® TUTORIAL 813 Appendix 5 COMPLEX NUMBERS 817 Appendix 6 A BRIEF MATLAB® TUTORIAL 827 Appendix 7 ADDITIONAL LAPLACE TRANSFORM THEOREMS 833 INDEX 839 ix This page intentionally left blank  CONTENTS CHAPTER 1 4.5 Nodal vs. Mesh Analysis: A Comparison 101 INTRODUCTION 1 4.6 Computer-Aided Circuit Analysis 103 1.1 Overview of Text 2 SUMMARY AND REVIEW 107 1.2 Relationship of Circuit Analysis to Engineering 4 READING FURTHER 109 1.3 Analysis and Design 5 EXERCISES 109 1.4 Computer-Aided Analysis 6 1.5 Successful Problem-Solving Strategies 7 CHAPTER 5 READING FURTHER 8 HANDY CIRCUIT ANALYSIS TECHNIQUES 123 5.1 Linearity and Superposition 123 CHAPTER 2 5.2 Source Transformations 133 BASIC COMPONENTS AND ELECTRIC CIRCUITS 9 5.3 Thévenin and Norton Equivalent Circuits 141 2.1 Units and Scales 9 5.4 Maximum Power Transfer 152 2.2 Charge, Current, Voltage, and Power 11 5.5 Delta-Wye Conversion 154 2.3 Voltage and Current Sources 17 5.6 Selecting an Approach: A Summary of Various 2.4 Ohm’s Law 22 Techniques 157 SUMMARY AND REVIEW 28 SUMMARY AND REVIEW 158 READING FURTHER 29 READING FURTHER 159 EXERCISES 29 EXERCISES 159 CHAPTER 3 CHAPTER 6 VOLTAGE AND CURRENT LAWS 39 THE OPERATIONAL AMPLIFIER 175 3.1 Nodes, Paths, Loops, and Branches 39 6.1 Background 175 3.2 Kirchhoff’s Current Law 40 6.2 The Ideal Op Amp: A Cordial Introduction 176 3.3 Kirchhoff’s Voltage Law 42 6.3 Cascaded Stages 184 3.4 The Single-Loop Circuit 46 6.4 Circuits for Voltage and Current Sources 188 3.5 The Single-Node-Pair Circuit 49 6.5 Practical Considerations 192 3.6 Series and Parallel Connected Sources 51 6.6 Comparators and the Instrumentation Amplifier 203 3.7 Resistors in Series and Parallel 55 SUMMARY AND REVIEW 206 3.8 Voltage and Current Division 61 READING FURTHER 207 SUMMARY AND REVIEW 66 EXERCISES 208 READING FURTHER 67 EXERCISES 67 CHAPTER 7 CAPACITORS AND INDUCTORS 217 CHAPTER 4 7.1 The Capacitor 217 BASIC NODAL AND MESH ANALYSIS 79 7.2 The Inductor 225 4.1 Nodal Analysis 80 7.3 Inductance and Capacitance Combinations 235 4.2 The Supernode 89 7.4 Consequences of Linearity 238 4.3 Mesh Analysis 92 7.5 Simple Op Amp Circuits with Capacitors 240 4.4 The Supermesh 98 7.6 Duality 242 xi xii CONTENTS 7.7 Modeling Capacitors and Inductors SUMMARY AND REVIEW 409 with PSpice 245 READING FURTHER 410 SUMMARY AND REVIEW 247 EXERCISES 410 READING FURTHER 249 EXERCISES 249 CHAPTER 11 AC CIRCUIT POWER ANALYSIS 421 CHAPTER 8 11.1 Instantaneous Power 422 BASIC RL AND RC CIRCUITS 261 11.2 Average Power 424 8.1 The Source-Free RL Circuit 261 11.3 Effective Values of Current and Voltage 433 8.2 Properties of the Exponential Response 268 11.4 Apparent Power and Power Factor 438 8.3 The Source-Free RC Circuit 272 11.5 Complex Power 441 8.4 A More General Perspective 275 SUMMARY AND REVIEW 447 8.5 The Unit-Step Function 282 READING FURTHER 449 8.6 Driven RL Circuits 286 EXERCISES 449 8.7 Natural and Forced Response 289 8.8 Driven RC Circuits 295 CHAPTER 12 8.9 Predicting the Response of Sequentially Switched Circuits 300 POLYPHASE CIRCUITS 457 SUMMARY AND REVIEW 306 12.1 Polyphase Systems 458 READING FURTHER 308 12.2 Single-Phase Three-Wire Systems 460 EXERCISES 309 12.3 Three-Phase Y-Y Connection 464 12.4 The Delta () Connection 470 12.5 Power Measurement in Three-Phase Systems 476 CHAPTER 9 SUMMARY AND REVIEW 484 THE RLC CIRCUIT 321 READING FURTHER 486 9.1 The Source-Free Parallel Circuit 321 EXERCISES 486 9.2 The Overdamped Parallel RLC Circuit 326 9.3 Critical Damping 334 CHAPTER 13 9.4 The Underdamped Parallel RLC Circuit 338 9.5 The Source-Free Series RLC Circuit 345 MAGNETICALLY COUPLED CIRCUITS 493 9.6 The Complete Response of the RLC Circuit 351 13.1 Mutual Inductance 493 9.7 The Lossless LC Circuit 359 13.2 Energy Considerations 501 SUMMARY AND REVIEW 361 13.3 The Linear Transformer 505 READING FURTHER 363 13.4 The Ideal Transformer 512 EXERCISES 363 SUMMARY AND REVIEW 522 READING FURTHER 523 CHAPTER 10 EXERCISES 523 SINUSOIDAL STEADY-STATE ANALYSIS 371 10.1 Characteristics of Sinusoids 371 CHAPTER 14 10.2 Forced Response to Sinusoidal Functions 374 COMPLEX FREQUENCY AND THE LAPLACE 10.3 The Complex Forcing Function 378 TRANSFORM 533 10.4 The Phasor 383 14.1 Complex Frequency 533 10.5 Impedance and Admittance 389 14.2 The Damped Sinusoidal Forcing Function 537 10.6 Nodal and Mesh Analysis 394 14.3 Definition of the Laplace Transform 540 10.7 Superposition, Source Transformations and 14.4 Laplace Transforms of Simple Time Functions 543 Thévenin’s Theorem 397 14.5 Inverse Transform Techniques 546 10.8 Phasor Diagrams 406 14.6 Basic Theorems for the Laplace Transform 553  CONTENTS xiii 14.7 The Initial-Value and Final-Value Theorems 561 CHAPTER 18 SUMMARY AND REVIEW 564 FOURIER CIRCUIT ANALYSIS 733 READING FURTHER 565 18.1 Trigonometric Form of the Fourier Series 733 EXERCISES 565 18.2 The Use of Symmetry 743 18.3 Complete Response to Periodic Forcing CHAPTER 15 Functions 748 CIRCUIT ANALYSIS IN THE s-DOMAIN 571 18.4 Complex Form of the Fourier Series 750 15.1 Z(s) and Y(s) 571 18.5 Definition of the Fourier Transform 757 15.2 Nodal and Mesh Analysis in the s-Domain 578 18.6 Some Properties of the Fourier Transform 761 15.3 Additional Circuit Analysis Techniques 585 18.7 Fourier Transform Pairs for Some Simple Time 15.4 Poles, Zeros, and Transfer Functions 588 Functions 764 15.5 Convolution 589 18.8 The Fourier Transform of a General Periodic Time 15.6 The Complex-Frequency Plane 598 Function 769 15.7 Natural Response and the s Plane 602 18.9 The System Function and Response in the Frequency Domain 770 15.8 A Technique for Synthesizing the Voltage Ratio H(s) = Vout/Vin 606 18.10 The Physical Significance of the System Function 777 SUMMARY AND REVIEW 610 SUMMARY AND REVIEW 782 READING FURTHER 612 READING FURTHER 783 EXERCISES 612 EXERCISES 783 CHAPTER 16 FREQUENCY RESPONSE 619 APPENDIX 1 AN INTRODUCTION TO NETWORK 16.1 Parallel Resonance 619 TOPOLOGY 791 16.2 Bandwidth and High-Q Circuits 627 16.3 Series Resonance 633 APPENDIX 2 SOLUTION OF SIMULTANEOUS 16.4 Other Resonant Forms 637 EQUATIONS 803 16.5 Scaling 644 16.6 Bode Diagrams 648 APPENDIX 3 A PROOF OF THÉVENIN’S 16.7 Basic Filter Design 664 THEOREM 811 16.8 Advanced Filter Design 672 SUMMARY AND REVIEW 677 READING FURTHER 679 APPENDIX 4 A PSPICE® TUTORIAL 813 EXERCISES 679 APPENDIX 5 COMPLEX NUMBERS 817 CHAPTER 17 TWO-PORT NETWORKS 687 17.1 One-Port Networks 687 APPENDIX 6 A BRIEF MATLAB® TUTORIAL 827 17.2 Admittance Parameters 692 17.3 Some Equivalent Networks 699 APPENDIX 7 ADDITIONAL LAPLACE TRANSFORM 17.4 Impedance Parameters 708 THEOREMS 833 17.5 Hybrid Parameters 713 17.6 Transmission Parameters 716 SUMMARY AND REVIEW 720 INDEX 839 READING FURTHER 721 EXERCISES 722 This page intentionally left blank  PREFACE T he target audience colors everything about a book, being a major fac- tor in decisions big and small, particularly both the pace and the overall writing style. Consequently it is important to note that the au- thors have made the conscious decision to write this book to the student, and not to the instructor. Our underlying philosophy is that reading the book should be enjoyable, despite the level of technical detail that it must incor- porate. When we look back to the very first edition of Engineering Circuit Analysis, it’s clear that it was developed specifically to be more of a con- versation than a dry, dull discourse on a prescribed set of fundamental top- ics. To keep it conversational, we’ve had to work hard at updating the book so that it continues to speak to the increasingly diverse group of students using it all over the world. Although in many engineering programs the introductory circuits course is preceded or accompanied by an introductory physics course in which electricity and magnetism are introduced (typically from a fields perspec- tive), this is not required to use this book. After finishing the course, many students find themselves truly amazed that such a broad set of analytical tools have been derived from only three simple scientific laws—Ohm’s law and Kirchhoff’s voltage and current laws. The first six chapters assume only a familiarity with algebra and simultaneous equations; subsequent chapters assume a first course in calculus (derivatives and integrals) is being taken in tandem. Beyond that, we have tried to incorporate sufficient details to allow the book to be read on its own. So, what key features have been designed into this book with the student in mind? First, individual chapters are organized into relatively short sub- sections, each having a single primary topic. The language has been up- dated to remain informal and to flow smoothly. Color is used to highlight important information as opposed to merely improve the aesthetics of the page layout, and white space is provided for jotting down short notes and questions. New terms are defined as they are introduced, and examples are placed strategically to demonstrate not only basic concepts, but problem- solving approaches as well. Practice problems relevant to the examples are placed in proximity so that students can try out the techniques for them- selves before attempting the end-of-chapter exercises. The exercises repre- sent a broad range of difficulties, generally ordered from simpler to more complex, and grouped according to the relevant section of each chapter. Answers to selected odd-numbered end-of-chapter exercises are posted on the book’s website at www.mhhe.com/haytdurbin8e. Engineering is an intensive subject to study, and students often find them- selves faced with deadlines and serious workloads. This does not mean that textbooks have to be dry and pompous, however, or that coursework should never contain any element of fun. In fact, successfully solving a problem of- ten is fun, and learning how to do that can be fun as well. Determining how xv xvi PREFACE to best accomplish this within the context of a textbook is an ongoing process. The authors have always relied on the often very candid feedback received from our own students at Purdue University; the California State University, Fullerton; Fort Lewis College in Durango, the joint engineering program at Florida A&M University and Florida State University, the Uni- versity of Canterbury (New Zealand) and the University at Buffalo. We also rely on comments, corrections, and suggestions from instructors and students worldwide, and for this edition, consideration has been given to a new source of comments, namely, semianonymous postings on various websites. The first edition of Engineering Circuit Analysis was written by Bill Hayt and Jack Kemmerly, two engineering professors who very much en- joyed teaching, interacting with their students, and training generations of future engineers. It was well received due to its compact structure, “to the point” informal writing style, and logical organization. There is no timidity when it comes to presenting the theory underlying a specific topic, or pulling punches when developing mathematical expressions. Everything, however, was carefully designed to assist students in their learning, present things in a straightforward fashion, and leave theory for theory’s sake to other books. They clearly put a great deal of thought into writing the book, and their enthusiasm for the subject comes across to the reader. KEY FEATURES OF THE EIGHTH EDITION We have taken great care to retain key features from the seventh edition which were clearly working well. These include the general layout and se- quence of chapters, the basic style of both the text and line drawings, the use of four-color printing where appropriate, numerous worked examples and related practice problems, and grouping of end-of-chapter exercises accord- ing to section. Transformers continue to merit their own chapter, and com- plex frequency is briefly introduced through a student-friendly extension of the phasor technique, instead of indirectly by merely stating the Laplace transform integral. We also have retained the use of icons, an idea first in- troduced in the sixth edition: Provides a heads-up to common mistakes; Indicates a point that’s worth noting; Denotes a design problem to which there is no unique answer; Indicates a problem which requires computer-aided analysis. The introduction of engineering-oriented analysis and design software in the book has been done with the mind-set that it should assist, not replace, the learning process. Consequently, the computer icon denotes problems that are typically phrased such that the software is used to verify answers, and not simply provide them. Both MATLAB® and PSpice® are used in this context.  PREFACE xvii SPECIFIC CHANGES FOR THE EIGHTH EDITION INCLUDE: A new section in Chapter 16 on the analysis and design of multistage Butterworth filters Over 1000 new and revised end-of-chapter exercises A new overarching philosophy on end-of-chapter exercises, with each section containing problems similar to those solved in worked examples and practice problems, before proceeding to more complex problems to test the reader’s skills Introduction of Chapter-Integrating Exercises at the end of each chapter. For the convenience of instructors and students, end-of- chapter exercises are grouped by section. To provide the opportunity for assigning exercises with less emphasis on an explicit solution method (for example, mesh or nodal analysis), as well as to give a broader perspective on key topics within each chapter, a select number of Chapter-Integrating Exercises appear at the end of each chapter. New photos, many in full color, to provide connection to the real world Updated screen captures and text descriptions of computer-aided analysis software New worked examples and practice problems Updates to the Practical Application feature, introduced to help students connect material in each chapter to broader concepts in engineering. Topics include distortion in amplifiers, modeling automotive suspension systems, practical aspects of grounding, the relationship of poles to stability, resistivity, and the memristor, sometimes called “the missing element” Streamlining of text, especially in the worked examples, to get to the point faster Answers to selected odd-numbered end-of-chapter exercises are posted on the book’s website at www.mhhe.com/haytdurbin8e. I joined the book in 1999, and sadly never had the opportunity to speak to either Bill or Jack about the revision process, although I count myself lucky to have taken a circuits course from Bill Hayt while I was a student at Purdue. It is a distinct privilege to serve as a coauthor to Engineering Circuit Analysis, and in working on this book I give its fundamental philos- ophy and target audience the highest priority. I greatly appreciate the many people who have already provided feedback—both positive and negative— on aspects of previous editions, and welcome others to do so as well, either through the publishers (McGraw-Hill Higher Education) or to me directly ([email protected]). Of course, this project has been a team effort, as is the case with every modern textbook. In particular I would like to thank Raghu Srinivasan (Global Publisher), Peter Massar (Sponsoring Editor), Curt Reynolds (Mar- keting Manager), Jane Mohr (Project Manager), Brittney-Corrigan- McElroy (Project Manager), Brenda Rolwes (Designer), Tammy Juran (Media Project Manager), and most importantly, Developmental Editor Darlene Schueller, who helped me with many, many details, issues, deadlines, xviii PREFACE and questions. She is absolutely the best, and I’m very grateful for all the support from the team at McGraw-Hill. I would also like to thank various McGraw-Hill representatives, especially Nazier Hassan, who dropped by whenever on campus to just say hello and ask how things were going. Spe- cial thanks are also due to Catherine Shultz and Michael Hackett, former editors who continue to keep in contact. Cadence® and The MathWorks kindly provided assistance with software-aided analysis software, which was much appreciated. Several colleagues have generously supplied or helped with photographs and technical details, for which I’m very grateful: Prof. Masakazu Kobayashi of Waseda University; Dr. Wade Enright, Prof. Pat Bodger, Prof. Rick Millane, Mr. Gary Turner, and Prof. Richard Blaikie of the University of Canterbury; and Prof. Reginald Perry and Prof. Jim Zheng of Florida A&M University and the Florida State University. For the eighth edition, the following individuals deserve acknowledgment and a debt of gratitude for taking the time to review various versions of the manuscript: Chong Koo An, The University of Ulsan Mark S. Andersland, The University of Iowa Marc Cahay, University of Cincinnati Claudio Canizares, University of Waterloo Teerapon Dachokiatawan, King Mongkut’s University of Technology North Bangkok John Durkin, The University of Akron Lauren M. Fuentes, Durham College Lalit Goel, Nanyang Technological University Rudy Hofer, Conestoga College ITAL Mark Jerabek, West Virginia University Michael Kelley, Cornell University Hua Lee, University of California, Santa Barbara Georges Livanos, Humber College Institute of Technology Ahmad Nafisi, Cal Poly State University Arnost Neugroschel, University of Florida Pravin Patel, Durham College Jamie Phillips, The University of Michigan Daryl Reynolds, West Virginia University G.V.K.R. Sastry, Andhra University Michael Scordilis, University of Miami Yu Sun, University of Toronto, Canada Chanchana Tangwongsan, Chulalongkorn University Edward Wheeler, Rose-Hulman Institute of Technology Xiao-Bang Xu, Clemson University Tianyu Yang, Embry-Riddle Aeronautical University Zivan Zabar, Polytechnic Institute of NYU  PREFACE xix I would also like to thank Susan Lord, University of San Diego, Archie L. Holmes, Jr., University of Virginia, Arnost Neugroschel, University of Florida, and Michael Scordilis, University of Miami, for their assistance in accuracy checking answers to selected end-of-chapter exercises. Finally, I would like to briefly thank a number of other people who have contributed both directly and indirectly to the eighth edition. First and fore- most, my wife, Kristi, and our son, Sean, for their patience, understanding, support, welcome distractions, and helpful advice. Throughout the day it has always been a pleasure to talk to friends and colleagues about what should be taught, how it should be taught, and how to measure learning. In particular, Martin Allen, Richard Blaikie, Alex Cartwright, Peter Cottrell, Wade Enright, Jeff Gray, Mike Hayes, Bill Kennedy, Susan Lord, Philippa Martin, Theresa Mayer, Chris McConville, Reginald Perry, Joan Redwing, Roger Reeves, Dick Schwartz, Leonard Tung, Jim Zheng, and many others have provided me with many useful insights, as has my father, Jesse Durbin, an electrical engineering graduate of the Indiana Institute of Technology. Steven M. Durbin Buffalo, New York xx PREFACE McGRAW-HILL DIGITAL OFFERINGS INCLUDE: McGraw-Hill Connect™ Engineering McGraw-Hill Connect Engineering is a web-based assignment and assess- ment platform that gives students the means to better connect with their coursework, with their instructors, and with the important concepts that they will need to know for success now and in the future. With Connect Engineering, instructors can deliver assignments, quizzes, and tests easily online. 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To learn more about CourseSmart options, contact your sales representative or visit www.CourseSmart.com. This page intentionally left blank CHAPTER 1 Introduction KEY CONCEPTS Linear versus Nonlinear PREAMBLE Circuits Although there are clear specialties within the field of engineering, all engineers share a considerable amount of common ground, Four Main Categories of particularly when it comes to problem solving. In fact, many prac- Circuit Analysis: ticing engineers find it is possible to work in a large variety of DC Analysis settings and even outside their traditional specialty, as their skill set is often transferrable to other environments. Today’s engineering Transient Analysis graduates are employed in a broad range of jobs, from design of Sinusoidal Analysis individual components and systems, to assisting in solving socio- Frequency Response economic problems such as air and water pollution, urban planning, communication, mass transportation, power generation and distribu- Circuit Analysis Beyond tion, and efficient use and conservation of natural resources. Circuits Circuit analysis has long been a traditional introduction to the art of problem solving from an engineering perspective, even for Analysis and Design those whose interests lie outside electrical engineering. There are many reasons for this, but one of the best is that in today’s world Use of Engineering Software it’s extremely unlikely for any engineer to encounter a system that does not in some way include electrical circuitry. As circuits be- A Problem-Solving Strategy come smaller and require less power, and power sources become smaller and cheaper, embedded circuits are seemingly everywhere. Since most engineering situations require a team effort at some stage, having a working knowledge of circuit analysis therefore helps to provide everyone on a project with the background needed for effective communication. Consequently, this book is not just about “circuit analysis” from an engineering perspective, but is also about developing basic problem-solving skills as they apply to situations an engineer is likely to encounter. As part of this, we also find that we’re develop- ing an intuitive understanding at a general level, and often we can 1 2 CHAPTER 1 INTRODUCTION Not all electrical engineers routinely make use of circuit analysis, but they often bring to bear analytical and problem-solving skills learned early on in their careers. A circuit analysis course is one of the first exposures to such concepts. (Solar Mirrors: © Corbis; Skyline: © Getty Images/PhotoLink; Oil Rig: © Getty Images; Dish: © Getty Images/J. Luke/PhotoLink) understand a complex system by its analogy to an electrical circuit. Before launching into all this, however, we’ll begin with a quick preview of the topics found in the remainder of the book, pausing briefly to ponder the difference between analysis and design, and the evolving role computer tools play in modern engineering. 1.1 OVERVIEW OF TEXT The fundamental subject of this text is linear circuit analysis, which some- times prompts a few readers to ask, “Is there ever any nonlinear circuit analysis?” Sure! We encounter nonlinear circuits every day: they capture and decode signals for our TVs and radios, perform calculations millions of times a second inside microprocessors, convert speech into electrical signals for transmission over phone lines, and execute many other functions outside our field of view. In designing, testing, and implementing such nonlinear circuits, detailed analysis is unavoidable. “Then why study linear circuit analysis?” Television sets include many nonlinear circuits. A great deal of them, however, can be understood and analyzed you might ask. An excellent question. The simple fact of the matter is that with the assistance of linear models. (© Sony Electronics, no physical system (including electrical circuits) is ever perfectly linear. Inc.) Fortunately for us, however, a great many systems behave in a reasonably  SECTION 1.1 OVERVIEW OF TEXT 3 linear fashion over a limited range—allowing us to model them as linear systems if we keep the range limitations in mind. For example, consider the common function f (x) = e x A linear approximation to this function is f (x) ≈ 1 + x Let’s test this out. Table 1.1 shows both the exact value and the approx- imate value of f (x) for a range of x. Interestingly, the linear approximation is exceptionally accurate up to about x = 0.1, when the relative error is still less than 1%. Although many engineers are rather quick on a calculator, it’s hard to argue that any approach is faster than just adding 1. TABLE 1.1 Comparison of a Linear Model for e x to Exact Value x f(x)* 1+x Relative error** 0.0001 1.0001 1.0001 0.0000005% 0.001 1.0010 1.001 0.00005% 0.01 1.0101 1.01 0.005% 0.1 1.1052 1.1 0.5% 1.0 2.7183 2.0 26% *Quoted to four significant figures.     e x − (1 + x)  **Relative error  100 ×  ex Linear problems are inherently more easily solved than their nonlinear counterparts. For this reason, we often seek reasonably accurate linear ap- proximations (or models) to physical situations. Furthermore, the linear models are more easily manipulated and understood—making design a more straightforward process. The circuits we will encounter in subsequent chapters all represent linear approximations to physical electric circuits. Where appropriate, brief discus- sions of potential inaccuracies or limitations to these models are provided, but generally speaking we find them to be suitably accurate for most applications. When greater accuracy is required in practice, nonlinear models are em- ployed, but with a considerable increase in solution complexity. A detailed dis- cussion of what constitutes a linear electric circuit can be found in Chap. 2. Linear circuit analysis can be separated into four broad categories: (1) dc analysis, where the energy sources do not change with time; (2) transient analysis, where things often change quickly; (3) sinusoidal analysis, which applies to both ac power and signals; and (4) frequency response, which is the most general of the four categories, but typically assumes something is changing with time. We begin our journey with the topic of resistive cir- cuits, which may include simple examples such as a flashlight or a toaster. This provides us with a perfect opportunity to learn a number of very pow- erful engineering circuit analysis techniques, such as nodal analysis, mesh analysis, superposition, source transformation, Thévenin’s theorem, Norton’s 4 CHAPTER 1 INTRODUCTION theorem, and several methods for simplifying networks of components con- nected in series or parallel. The single most redeeming feature of resistive circuits is that the time dependence of any quantity of interest does not affect our analysis procedure. In other words, if asked for an electrical quan- tity of a resistive circuit at several specific instants in time, we do not need to analyze the circuit more than once. As a result, we will spend most of our effort early on considering only dc circuits—those circuits whose electrical parameters do not vary with time. Although dc circuits such as flashlights or automotive rear window de- foggers are undeniably important in everyday life, things are often much more interesting when something happens suddenly. In circuit analysis Modern trains are powered by electric motors. Their parlance, we refer to transient analysis as the suite of techniques used to electrical systems are best analyzed using ac or phasor analysis techniques. (Used with permission. Image study circuits which are suddenly energized or de-energized. To make such copyright © 2010 M. Kobayashi. All rights reserved.) circuits interesting, we need to add elements that respond to the rate of change of electrical quantities, leading to circuit equations which include derivatives and integrals. Fortunately, we can obtain such equations using the simple techniques learned in the first part of our study. Still, not all time-varying circuits are turned on and off suddenly. Air conditioners, fans, and fluorescent lights are only a few of the many exam- ples we may see daily. In such situations, a calculus-based approach for every analysis can become tedious and time-consuming. Fortunately, there is a better alternative for situations where equipment has been allowed to run long enough for transient effects to die out, and this is commonly referred to as ac or sinusoidal analysis, or sometimes phasor analysis. The final leg of our journey deals with a subject known as frequency response. Working directly with the differential equations obtained in time- domain analysis helps us develop an intuitive understanding of the opera- tion of circuits containing energy storage elements (e.g., capacitors and inductors). As we shall see, however, circuits with even a relatively small number of components can be somewhat onerous to analyze, and so much more straightforward methods have been developed. These methods, which include Laplace and Fourier analysis, allow us to transform differential equations into algebraic equations. Such methods also enable us to design circuits to respond in specific ways to particular frequencies. We make use Frequency-dependent circuits lie at the heart of many of frequency-dependent circuits every day when we dial a telephone, select electronic devices, and they can be a great deal of fun our favorite radio station, or connect to the Internet. to design. (© The McGraw-Hill Companies, Inc.) 1.2 RELATIONSHIP OF CIRCUIT ANALYSIS TO ENGINEERING Whether we intend to pursue further circuit analysis at the completion of this course or not, it is worth noting that there are several layers to the con- cepts under study. Beyond the nuts and bolts of circuit analysis techniques lies the opportunity to develop a methodical approach to problem solving, the ability to determine the goal or goals of a particular problem, skill at collecting the information needed to effect a solution, and, perhaps equally importantly, opportunities for practice at verifying solution accuracy. Students familiar with the study of other engineering topics such as fluid flow, automotive suspension systems, bridge design, supply chain manage- ment, or process control will recognize the general form of many of the  SECTION 1.3 ANALYSIS AND DESIGN 5 A molecular beam epitaxy crystal growth facility. The equations governing its operation closely resemble those used to describe simple linear circuits. equations we develop to describe the behavior of various circuits. We simply need to learn how to “translate” the relevant variables (for example, replacing voltage with force, charge with distance, resistance with friction coefficient, etc.) to find that we already know how to work a new type of problem. Very often, if we have previous experience in solving a similar or related problem, our intuition can guide us through the solution of a totally new problem. What we are about to learn regarding linear circuit analysis forms the basis for many subsequent electrical engineering courses. The study of elec- tronics relies on the analysis of circuits with devices known as diodes and transistors, which are used to construct power supplies, amplifiers, and dig- ital circuits. The skills which we will develop are typically applied in a rapid, methodical fashion by electronics engineers, who sometimes can analyze a complicated circuit without even reaching for a pencil! The time-domain and frequency-domain chapters of this text lead directly into discussions of signal processing, power transmission, control theory, and communications. We find that frequency-domain analysis in particular is an extremely powerful technique, easily applied to any physical system subjected to time-varying excitation, and particularly helpful in the design of filters. An example of a robotic manipulator. The feedback control 1.3 ANALYSIS AND DESIGN system can be modeled using linear circuit elements to determine situations in which the operation may become Engineers take a fundamental understanding of scientific principles, com- unstable. (NASA Marshall Space Flight Center.) bine this with practical knowledge often expressed in mathematical terms, and (frequently with considerable creativity) arrive at a solution to a given problem. Analysis is the process through which we determine the scope of a problem, obtain the information required to understand it, and compute the parameters of interest. Design is the process by which we synthesize something new as part of the solution to a problem. Generally speaking, there is an expectation that a problem requiring design will have no unique solution, whereas the analysis phase typically will. Thus, the last step in designing is always analyzing the result to see if it meets specifications. 6 CHAPTER 1 INTRODUCTION This text is focused on developing our ability to analyze and solve problems because it is the starting point in every engineering situation. The philosophy of this book is that we need clear explanations, well-placed ex- amples, and plenty of practice to develop such an ability. Therefore, elements of design are integrated into end-of-chapter problems and later chapters so as to be enjoyable rather than distracting. 1.4 COMPUTER-AIDED ANALYSIS Solving the types of equations that result from circuit analysis can often be- come notably cumbersome for even moderately complex circuits. This of course introduces an increased probability that errors will be made, in addi- tion to considerable time in performing the calculations. The desire to find a tool to help with this process actually predates electronic computers, with purely mechanical computers such as the Analytical Engine designed by Charles Babbage in the 1880s proposed as possible solutions. Perhaps the earliest successful electronic computer designed for solution of differential equations was the 1940s-era ENIAC, whose vacuum tubes filled a large room. With the advent of low-cost desktop computers, however, computer- aided circuit analysis has developed into an invaluable everyday tool which has become an integral part of not only analysis but design as well. One of the most powerful aspects of computer-aided design is the rela- Two proposed designs for a next-generation space shuttle. tively recent integration of multiple programs in a fashion transparent to the Although both contain similar elements, each is unique. (NASA Dryden Flight Research Center.) user. This allows the circuit to be drawn schematically on the screen, re- duced automatically to the format required by an analysis program (such as SPICE, introduced in Chap. 4), and the resulting output smoothly trans- ferred to a third program capable of plotting various electrical quantities of Charles Babbage’s “Difference Engine Number 2,” as completed by the Science Museum (London) in 1991. (© Science Museum/Science & Society Picture Library.)  SECTION 1.5 SUCCESSFUL PROBLEM-SOLVING STRATEGIES 7 An amplifier circuit drawn using a commercial schematic capture software package. interest that describe the operation of the circuit. Once the engineer is satis- fied with the simulated performance of the design, the same software can generate the printed circuit board layout using geometrical parameters in the components library. This level of integration is continually increasing, to the point where soon an engineer will be able to draw a schematic, click a few buttons, and walk to the other side of the table to pick up a manufac- tured version of the circuit, ready to test! The reader should be wary, however, of one thing. Circuit analysis soft- ware, although fun to use, is by no means a replacement for good old- fashioned paper-and-pencil analysis. We need to have a solid understanding of how circuits work in order to develop an ability to design them. Simply going through the motions of running a particular software package is a little like playing the lottery: with user-generated entry errors, hidden default parame- ters in the myriad of menu choices, and the occasional shortcoming of human- written code, there is no substitute for having at least an approximate idea of the expected behavior of a circuit. Then, if the simulation result does not agree with expectations, we can find the error early, rather than after it’s too late. Still, computer-aided analysis is a powerful tool. It allows us to vary pa- rameter values and evaluate the change in circuit performance, and to con- sider several variations to a design in a straightforward manner. The result is a reduction of repetitive tasks, and more time to concentrate on engineer- ing details. 1.5 SUCCESSFUL PROBLEM-SOLVING STRATEGIES As the reader might have picked up, this book is just as much about problem solving as it is about circuit analysis. As a result, the expectation is that during your time as an engineering student, you are learning how to solve problems— so just at this moment, those skills are not yet fully developed. As you proceed 8 CHAPTER 1 INTRODUCTION Read the problem statement through your course of study, you will pick up techniques that work for you, slowly and carefully. and likely continue to do so as a practicing engineer. At this stage, then, we should spend a few moments discussing some basic points. The first point is that by far, the most common difficulty encountered by Identify the goal of the problem. engineering students is not knowing how to start a problem. This improves with experience, but early on that’s of no help. The best advice we can give is to adopt a methodical approach, beginning with reading the problem Collect the known information. statement slowly and carefully (and more than once, if needed). Since experience usually gives us some type of insight into how to deal with a specific problem, worked examples appear throughout the book. Rather than just read them, however, it might be helpful to work through them with a pencil and a piece of paper. Devise a plan. Once we’ve read through the problem, and feel we might have some use- ful experience, the next step is to identify the goal of the problem—perhaps to calculate a voltage or a power, or to select a component value. Knowing where we’re going is a big help. The next step is to collect as much infor- Construct an appropriate set of equations. mation as we can, and to organize it somehow. At this point we’re still not ready to reach for the calculator. It’s best first to devise a plan, perhaps based on experience, perhaps based simply on our intuition. Sometimes plans work, and sometimes they don’t. Starting Determine Yes if additional information with our initial plan, it’s time to construct an initial set of equations. If they is required. appear complete, we can solve them. If not, we need to either locate more information, modify our plan, or both. No Once we have what appears to be a working solution, we should not Attempt a solution. stop, even if exhausted and ready for a break. No engineering problem is solved unless the solution is tested somehow. We might do this by per- forming a computer simulation, or solving the problem a different way, or perhaps even just estimating what answer might be reasonable. Verify the solution. Is it reasonable No Since not everyone likes to read to learn, these steps are summarized in or expected? the adjacent flowchart. This is just one particular problem-solving strategy, and the reader of course should feel free to modify it as necessary. The real Yes key, however, is to try and learn in a relaxed, low-stress environment free of distractions. Experience is the best teacher, and learning from our own mis- End. takes will always be part of the process of becoming a skilled engineer. READING FURTHER This relatively inexpensive, best-selling book teaches the reader how to develop winning strategies in the face of seemingly impossible problems: G. Polya, How to Solve It. Princeton, N.J.: Princeton University Press, 1971. CHAPTER Basic Components 2 and Electric Circuits KEY CONCEPTS Basic Electrical Quantities INTRODUCTION and Associated Units: In conducting circuit analysis, we often find ourselves seeking spe- Charge, Current, Voltage, cific currents, voltages, or powers, so here we begin with a brief de- and Power scription of these quantities. In terms of components that can be used to build electrical circuits, we have quite a few from which to Current Direction and choose. We initially focus on the resistor, a simple passive compo- Voltage Polarity nent, and a range of idealized active sources of voltage and current. As we move forward, new components will be added to the inven- The Passive Sign Convention for Calculating Power tory to allow more complex (and useful) circuits to be considered. A quick word of advice before we begin: Pay close attention to Ideal Voltage and Current the role of “+” and “−” signs when labeling voltages, and the sig- Sources nificance of the arrow in defining current; they often make the difference between wrong and right answers. Dependent Sources 2.1 UNITS AND SCALES Resistance and Ohm’s Law In order to state the value of some measurable quantity, we must give both a number and a unit, such as “3 meters.” Fortunately, we all use the same number system. This is not true for units, and a lit- tle time must be spent in becoming familiar with a suitable system. We must agree on a standard unit and be assured of its permanence and its general acceptability. The standard unit of length, for exam- ple, should not be defined in terms of the distance between two marks on a certain rubber band; this is not permanent, and further- more everybody else is using another standard. The most frequently used system of units is the one adopted by the National Bureau of Standards in 1964; it is used by all major professional engineering societies and is the language in which to- day’s textbooks are written. This is the International System of Units (abbreviated SI in all languages), adopted by the General 9 10 CHAPTER 2 BASIC COMPONENTS AND ELECTRIC CIRCUITS Conference on Weights and Measures in 1960. Modified several times since, the SI is built upon seven basic units: the meter, kilogram, second, ampere, kelvin, mole, and candela (see Table 2.1). This is a “metric system,” some form of which is now in common use in most countries of the world, although it is not yet widely used in the United States. Units for other quan- tities such as volume, force, energy, etc., are derived from these seven base units. TABLE 2.1 SI Base Units Base Quantity Name Symbol There is some inconsistency regarding whether units length meter m named after a person should be capitalized. Here, we mass kilogram kg will adopt the most contemporary convention,1,2 where time second s such units are written out in lowercase (e.g., watt, joule), electric current ampere A but abbreviated with an uppercase symbol (e.g., W, J). thermodynamic temperature kelvin K _______________________________________ (1) H. Barrell, Nature 220, 1968, p. 651. amount of substance mole mol (2) V. N. Krutikov, T. K. Kanishcheva, S. A. Kononogov, L. K. Isaev, luminous intensity candela cd and N. I. Khanov, Measurement Techniques 51, 2008, p. 1045. The fundamental unit of work or energy is the joule (J). One joule (a kg m2 s−2 in SI base units) is equivalent to 0.7376 foot pound-force The “calorie” used with food, drink, and exercise is (ft · lbf). Other energy units include the calorie (cal), equal to 4.187 J; really a kilocalorie, 4.187 J. the British thermal unit (Btu), which is 1055 J; and the kilowatthour (kWh), equal to 3.6 × 106 J. Power is defined as the rate at which work is done or energy is expended. The fundamental unit of power is the watt (W), defined as 1 J/s. One watt is equivalent to 0.7376 ft · lbf/s or, equivalently, 1/745.7 horsepower (hp). The SI uses the decimal system to relate larger and smaller units to the basic unit, and employs prefixes to signify the various powers of 10. A list of prefixes and their symbols is given in Table 2.2; the ones most commonly encountered in engineering are highlighted. TABLE 2.2 SI Prefixes Factor Name Symbol Factor Name Symbol 10−24 yocto y 1024 yotta Y 10−21 zepto z 1021 zetta Z 10−18 atto a 1018 exa E 10−15 femto f 1015 peta P 10−12 pico p 1012 tera T 10−9 nano n 109 giga G 10−6 micro μ 106 mega M 10−3 milli m 103 kilo k 10−2 centi c 102 hecto h 10−1 deci d 101 deka da  SECTION 2.2 CHARGE, CURRENT, VOLTAGE, AND POWER 11 These prefixes are worth memorizing, for they will appear often both in this text and in other technical work. Combinations of several prefixes, such as the millimicrosecond, are unacceptable. It is worth noting that in terms of distance, it is common to see “micron (μm)” as opposed to “microme- ter,” and often the angstrom (Å) is used for 10−10 meter. Also, in circuit analysis and engineering in general, it is fairly common to see numbers ex- pressed in what are frequently termed “engineering units.” In engineering notation, a quantity is represented by a number between 1 and 999 and an appropriate metric unit using a power divisible by 3. So, for example, it is preferable to express the quantity 0.048 W as 48 mW, instead of 4.8 cW, 4.8 × 10−2 W, or 48,000 μW. P R ACTICE 2.1 A krypton fluoride laser emits light at a wavelength of 248 nm. This is the same as: (a) 0.0248 mm; (b) 2.48 μm; (c) 0.248 μm; (d) 24,800 Å. 2.2 A single logic gate in a prototype integrated circuit is found to be capable of switching from the “on” state to the “off” state in 12 ps. This corresponds to: (a) 1.2 ns; (b) 120 ns; (c) 1200 ns; (d) 12,000 ns. 2.3 A typical incandescent reading lamp runs at 60 W. If it is left on constantly, how much energy (J) is consumed per day, and what is the weekly cost if energy is charged at a rate of 12.5 cents per kilowatthour? Ans: 2.1 (c); 2.2 (d); 2.3 5.18 MJ, $1.26. 2.2 CHARGE, CURRENT, VOLTAGE, AND POWER Charge One of the most fundamental concepts in electric circuit analysis is that of As seen in Table 2.1, the base units of the SI are not charge conservation. We know from basic physics that there are two types derived from fundamental physical quantities. Instead, of charge: positive (corresponding to a proton) and negative (corresponding they represent historically agreed upon measurements, to an electron). For the most part, this text is concerned with circuits in leading to definitions which occasionally seem which only electron flow is relevant. There are many devices (such as bat- backward. For example, it would make more sense teries, diodes, and transistors) in which positive charge motion is important physically to define the ampere based on electronic to understanding internal operation, but external to the device we typically charge. concentrate on the electrons which flow through the connecting wires. Although we continuously transfer charges between different parts of a cir- cuit, we do nothing to change the total amount of charge. In other words, we Cross section neither create nor destroy electrons (or protons) when running electric circuits.1 Charge in motion represents a current. In the SI system, the fundamental unit of charge is the coulomb (C). Direction of charge motion It is defined in terms of the ampere by counting the total charge that passes through an arbitrary cross section of a wire during an interval of one second; one coulomb is measured each second for a wire carrying a current Individual charges of 1 ampere (Fig. 2.1). In this system of units, a single electron has a charge FIGURE 2.1 The definition of current illustrated of −1.602 × 10−19 C and a single proton has a charge of +1.602 × 10−19 C. using current flowing through a wire; 1 ampere corresponds to 1 coulomb of charge passing through (1) Although the occasional appearance of smoke may seem to suggest otherwise... the arbitrarily chosen cross section in 1 second. 12 CHAPTER 2 BASIC COMPONENTS AND ELECTRIC CIRCUITS A quantity of charge that does not change with time is typically repre- sented by Q. The instantaneous amount of charge (which may or may not be time-invariant) is commonly represented by q(t), or simply q. This conven- tion is used throughout the remainder of the text: capital letters are reserved for constant (time-invariant) quantities, whereas lowercase letters represent the more general case. Thus, a constant charge may be represented by either Q or q, but an amount of charge that changes over time must be represented by the lowercase letter q. Current The idea of “transfer of charge” or “charge in motion” is of vital importance to us in studying electric circuits because, in moving a charge from place to q(t) (C) place, we may also transfer energy from one point to another. The familiar cross-country power-transmission line is a practical example of a device 6 that transfers energy. Of equal importance is the possibility of varying the 5 rate at which the charge is transferred in order to communicate or transfer 4 information. This process is the basis of communication systems such as radio, television, and telemetry. 3 The current present in a discrete path, such as a metallic wire, has both a 2 numerical value and a direction associated with it; it is a measure of the rate 1 at which charge is moving past a given reference point in a specified direction. 0 t(s) Once we have specified a reference direction, we may then let q(t) be the 1 2 3 4 5 6 7 8 –1 total charge that has passed the reference point since an arbitrary time t = 0, moving in the defined direction. A contribution to this total charge will be –2 negative if negative charge is moving in the reference direction, or if posi- FIGURE 2.2 A graph of the instantaneous value of tive charge is moving in the opposite direction. As an example, Fig. 2.2 the total charge q(t) that has passed a given reference shows a history of the total charge q(t) that has passed a given reference point since t  0. point in a wire (such as the one shown in Fig. 2.1). We define the current at a specific point and flowing in a specified direc- tion as the instantaneous rate at which net positive charge is moving past that point in the specified direction. This, unfortunately, is the historical de- finition, which came into popular use before it was appreciated that current in wires is actually due to negative, not positive, charge motion. Current is symbolized by I or i, and so dq i= dt i(t) (A) The unit of current is the ampere (A), named afterA. M.Ampère, a French 1.5 physicist. It is commonly abbreviated as an “amp,” although this is unofficial and somewhat informal. One ampere equals 1 coulomb per second. 1 Using Eq. , we compute the instantaneous current and obtain Fig. 2.3. 0.5 The use of the lowercase letter i is again to be associated with an instantaneous 0 t(s) value; an uppercase I would denote a constant (i.e., time-invariant) quantity. 1 2 3 4 5 6 7 8 The charge transferred between time t0 and t may be expressed as a –0.5 definite integral: