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Electric Circuits
Electric Circuits
James W. Nilsson, Susan A. Riedel
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The fundamental goals of the bestselling Electric Circuits remain unchanged. The 11th Edition continues to motivate students to build new ideas based on concepts previously presented, to develop problemsolving skills that rely on a solid conceptual foundation, and to introduce realistic engineering experiences that challenge students to develop the insights of a practicing engineer. The 11th Edition represents the most extensive revision since the 5th Edition with every sentence, paragraph, subsection, and chapter examined and oftentimes rewritten to improve clarity, readability, and pedagogy—without sacrificing the breadth and depth of coverage that Electric Circuits is known for. Dr. Susan Riedel draws on her classroom experience to introduce the Analysis Methods feature, which gives students a stepbystep problemsolving approach.
Kategorije:
Godina:
2018
Izdanje:
11th
Izdavač:
Pearson
Jezik:
english
Strane:
816 / 4390
ISBN 13:
9780134746968
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PDF, 76,69 MB
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capacitor^{1278}
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terminals^{1155}
axis^{1109}
minus^{1096}
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left wire^{1001}
bottom wires^{927}
circuits^{901}
input^{858}
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independent voltage^{785}
circuit shows^{745}
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domain^{663}
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calculate^{640}
transform^{631}
two nodes^{626}
connecting^{613}
op amp^{584}
equations^{560}
impedance^{558}
axis plots^{546}
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circuit shown^{511}
voltages^{506}
currents^{493}
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rectangular^{458}
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4 comments
BIGSIAW
Electric Circuits, 11th2019_(James W. Nilsson and Susan Riedel).pdf
pages: 4390 (After converted from epub file)
pages: 4390 (After converted from epub file)
04 February 2019 (08:04)
office2020
Not recommended. This file is A VERY BAD version of an EPUB file converted to PDF with a too much pages. Indeed, I suggest to use the 10th version of this book with its correspondent Instructor's Solutions Manual. If I found an adequate version, I promise to upload it to this website.
18 May 2020 (18:29)
office2020
One more time: NOT recommended. It's no matter if the legal owner deleted the link. Don't waste your time connecting to TOR Network to download it!.
15 June 2020 (16:46)
jeyamani moses
it is very basic, i expected a good lot.
11 July 2021 (19:59)
Možete napisati recenziju za knjigu i podeliti svoje mišljenje. Ostale čitaoce će uvek zanimati vaše mišljenje o knjigama koje ste pročitali. Bez obzira da li vam se knjiga svidela ili ne, ako iskreno i detaljno izložite svoje misli, ljudi će pronaći nove knjige koje im odgovaraju.
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Table 4.3 Steps in the Node Voltage Method and the Mesh Current Method Analyzing a Circuit With an Ideal OP AMP 1. Check for a negative feedback path. If it exists, assume the op amp operates in its linear region. 2. Write a KCL equation at the inverting input terminal. 3. Solve the KCL equation and use the solution to find the op amp’s output voltage. 4. Compare the op amp’s output voltage to the power supply voltages to determine if the op amp is operating in its linear region or if it is saturated. General Method for Natural and Step Response of RL and RC Circuits 1. Identify the variable x(t), which is the inductor current for RL circuits and capacitor voltage for RC circuits. 2. Calculate the initial value X0, by analyzing the circuit to find x(t) for t<0 3. Calculate the time constant τ; for RL circuits τ=L/R and for RC circuits τ=RC, where R is the equivalent resistance connected to the inductor or capacitor for t≥0 4. Calculate the final value Xf, by analyzing the circuit to find x(t) as t→∞; for the natural response, Xf=0 5. Write the equation for x(t), x(t)=Xf+(X0−Xf) e−t/τ, for t≥0. 6. Calculate other quantities of interest using x(t). Natural Response of a Parallel RLC Circuit 1. Determine the initial capacitor voltage (V0) and inductor current (I0) from the circuit. 2. Determine the values of α and ω0 using the equations in Table 8.1. 3. If α2>ω02, the response is overdamped and v(t)=A1es1t+A2es2t,t≥0 4. If the response is overdamped, calculate s1 and s2 using the equations in Table 8.1. 5. If the response is overdamped, calculate A1 and A2 by simultaneously solving Eqs. 8.10 and 8.11. 6. Write the equation for v(t) from Step 3 using the results from Steps 4 and 5; find any desired branch currents. Table 8.2 Equations for analyzing the natural response of parallel RLC circuits (Note that the equations in the last three rows assume that the reference direction for the current in every component is in the direction of the reference voltage drop across th; at component.) Step Response of a Parallel RLC Circuit 1. Determine the initial capacitor voltage (V0), the initial inductor current (I0), and the final inductor current (If) from the circuit. 2. Determine the values of α and ω0 using the equations in Table 8.3. 3. If α2>ω02, the response is overdamped and iL(t)=If+A′1es1t+A′2es2t, t≥0+; If α2>ω02 the response is underdamped and iL(t)=If+B′1e −αtcosωdt+B′2e−αtsinωdt, t≥0+; If α2=ω02, the response is critically damped and iL(t)=If+D′1te−αt+D ′2e−αt, t≥0+ 4. If the response is overdamped, calculate s1 and s2 using the equations in Table 8.3; If the response is underdamped, calculate ωd using the equation in Table 8.3. 5. If the response is overdamped, calculate A1′ and A2′ by simultaneously solving the equations in Table 8.3; If the response is underdamped, calculate B1′ and B2′ by simultaneously solving the equations in Table 8.3; If the response is critically damped, calculate D1′ and D2′ by simultaneously solving the equations in Table 8.3. 6. Write the equation for iL(t) from Step 3 using the results from Steps 4 and 5; find the inductor voltage and any desired branch currents. Table 8.3 Equations for analyzing the step response of parallel RLC circuits (Note that the equations in the last three rows assume that the reference direction for the current in every component is in the direction of the reference voltage drop across that component.) Electric Circuits Eleventh Edition Electric Circuits Eleventh Edition James W. Nilsson Professor Emeritus Iowa State University Susan A. Riedel Marquette University 330 Hudson Street, NY NY 10013 Senior Vice President Courseware Portfolio Management, Engineering, Computer Science, Mathematics, Statistics, and Global Editions: Marcia J. Horton Director, Portfolio Management, Engineering, Computer Science, and Global Editions: Julian Partridge Specialist, Higher Ed Portfolio Management: Norrin Dias Portfolio Management Assistant: Emily Egan Managing Producer, ECS and Mathematics: Scott Disanno Senior Content Producer: Erin Ault Manager, Rights and Permissions: Ben Ferrini Operations Specialist: Maura ZaldivarGarcia Inventory Manager: Ann Lam Product Marketing Manager: Yvonne Vannatta Field Marketing Manager: Demetrius Hall Marketing Assistant: Jon Bryant Project Manager: Rose Kernan Cover Design: Black Horse Designs Cover Art: © Leonardo Ulian, Matrix board series 06  Resistance by abstraction, 2017. Composition: Integra Publishing Services Cover Printer: Phoenix Color/Hagerstown Printer/Binder: LSC Communications, Inc. Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Copyright © 2019, 2015, 2008, 2005 Pearson Education, Inc., Hoboken, NJ 07030. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/. MATLAB is a registered trademark of The MathWorks, Inc., 3 Apple Hill Road, Natick, MA. Library of Congress CataloginginPublication Data Names: Nilsson, James William, author.  Riedel, Susan A., author. Title: Electric circuits / James W. Nilsson, professor emeritus Iowa State University, Susan A. Riedel, Marquette University. Description: Eleventh edition.  Pearson, [2019]  Includes index. Identifiers: LCCN 2017025128  ISBN 9780134746968  ISBN 0134746961 Subjects: LCSH: Electric circuits. Classification: LCC TK454 .N54 2019  DDC 621.319/2—dc23 LC record available at https://lccn.loc.gov/2017025128 1 18 http://www.pearsoned.com/permissions/ https://lccn.loc.gov/2017025128 ISBN10: 0134746961 ISBN13: 9780134746968 Courtesy of Anna Nilsson In Memoriam We remember our beloved author, James W. Nilsson, for his lasting legacy to the electrical and computer engineering field. The first edition of Electric Circuits was published in 1983. As this book evolved over the years to better meet the needs of both students and their instructors, the underlying teaching methodologies Jim established remain relevant, even in the Eleventh Edition. Jim earned his bachelor’s degree at the University of Iowa (1948), and his master’s degree (1952) and Ph.D. (1958) at Iowa State University. He joined the ISU faculty in 1948 and taught electrical engineering there for 39 years. He became an IEEE fellow in 1990 and earned the prestigious IEEE Undergraduate Teaching Award in 1992. For Anna Brief Contents 1. List of Examples xii 2. List of Tables xvi 3. List of Analysis Methods xvii 4. Preface xx 1. Chapter 1 Circuit Variables 2 2. Chapter 2 Circuit Elements 26 3. Chapter 3 Simple Resistive Circuits 58 4. Chapter 4 Techniques of Circuit Analysis 92 5. Chapter 5 The Operational Amplifier 150 6. Chapter 6 Inductance, Capacitance, and Mutual Inductance 182 7. Chapter 7 Response of FirstOrder RL and RC Circuits 220 8. Chapter 8 Natural and Step Responses of RLC Circuits 272 9. Chapter 9 Sinusoidal SteadyState Analysis 318 10. Chapter 10 Sinusoidal SteadyState Power Calculations 374 11. Chapter 11 Balanced ThreePhase Circuits 412 12. Chapter 12 Introduction to the Laplace Transform 444 13. Chapter 13 The Laplace Transform in Circuit Analysis 482 14. Chapter 14 Introduction to Frequency Selective Circuits 536 15. Chapter 15 Active Filter Circuits 572 16. Chapter 16 Fourier Series 618 17. Chapter 17 The Fourier Transform 660 18. Chapter 18 TwoPort Circuits 692 1. Appendix A The Solution of Linear Simultaneous Equations 718 2. Appendix B Complex Numbers 727 3. Appendix C More on Magnetically Coupled Coils and Ideal Transformers 733 4. Appendix D The Decibel 741 5. Appendix E Bode Diagrams 743 6. Appendix F An Abbreviated Table of Trigonometric Identities 757 7. Appendix G An Abbreviated Table of Integrals 758 8. Appendix H Common Standard Component Values 760 9. Answers to Selected Problems 761 10. Index 771 Contents 1. List of Examples xii 2. List of Tables xvi 3. List of Analysis Methods xvii 4. Preface xx 1. Chapter 1 Circuit Variables 2 1. Practical Perspective: Balancing Power 3 1. 1.1 Electrical Engineering: An Overview 4 2. 1.2 The International System of Units 9 3. 1.3 Circuit Analysis: An Overview 11 4. 1.4 Voltage and Current 12 5. 1.5 The Ideal Basic Circuit Element 14 6. 1.6 Power and Energy 15 1. Practical Perspective: Balancing Power 18 2. Summary 19 3. Problems 20 2. Chapter 2 Circuit Elements 26 1. Practical Perspective: Heating with Electric Radiators 27 1. 2.1 Voltage and Current Sources 28 2. 2.2 Electrical Resistance (Ohm’s Law) 32 3. 2.3 Constructing a Circuit Model 36 4. 2.4 Kirchhoff’s Laws 39 5. 2.5 Analyzing a Circuit Containing Dependent Sources 45 1. Practical Perspective: Heating with Electric Radiators 48 2. Summary 50 3. Problems 50 3. Chapter 3 Simple Resistive Circuits 58 1. Practical Perspective: Resistive Touch Screens 59 1. 3.1 Resistors in Series 60 2. 3.2 Resistors in Parallel 61 3. 3.3 The VoltageDivider and CurrentDivider Circuits 64 4. 3.4 Voltage Division and Current Division 68 5. 3.5 Measuring Voltage and Current 70 6. 3.6 Measuring Resistance—The Wheatstone Bridge 73 7. 3.7 DeltatoWye (PitoTee) Equivalent Circuits 75 1. Practical Perspective: Resistive Touch Screens 78 2. Summary 79 3. Problems 80 4. Chapter 4 Techniques of Circuit Analysis 92 1. Practical Perspective: Circuits with Realistic Resistors 93 1. 4.1 Terminology 94 2. 4.2 Introduction to the NodeVoltage Method 96 3. 4.3 The NodeVoltage Method and Dependent Sources 98 4. 4.4 The NodeVoltage Method: Some Special Cases 100 5. 4.5 Introduction to the MeshCurrent Method 104 6. 4.6 The MeshCurrent Method and Dependent Sources 107 7. 4.7 The MeshCurrent Method: Some Special Cases 108 8. 4.8 The NodeVoltage Method Versus the MeshCurrent Method 112 9. 4.9 Source Transformations 115 10. 4.10 Thévenin and Norton Equivalents 118 11. 4.11 More on Deriving the Thévenin Equivalent 123 12. 4.12 Maximum Power Transfer 126 13. 4.13 Superposition 129 1. Practical Perspective: Circuits with Realistic Resistors 131 2. Summary 134 3. Problems 136 5. Chapter 5 The Operational Amplifier 150 1. Practical Perspective: Strain Gages 151 1. 5.1 Operational Amplifier Terminals 152 2. 5.2 Terminal Voltages and Currents 152 3. 5.3 The InvertingAmplifier Circuit 156 4. 5.4 The SummingAmplifier Circuit 158 5. 5.5 The NoninvertingAmplifier Circuit 160 6. 5.6 The DifferenceAmplifier Circuit 162 7. 5.7 A More Realistic Model for the Operational Amplifier 167 1. Practical Perspective: Strain Gages 171 2. Summary 172 3. Problems 173 6. Chapter 6 Inductance, Capacitance, and Mutual Inductance 182 1. Practical Perspective: Capacitive Touch Screens 183 1. 6.1 The Inductor 184 2. 6.2 The Capacitor 189 3. 6.3 SeriesParallel Combinations of Inductance and Capacitance 194 4. 6.4 Mutual Inductance 199 5. 6.5 A Closer Look at Mutual Inductance 203 1. Practical Perspective: Capacitive Touch Screens 209 2. Summary 211 3. Problems 212 7. Chapter 7 Response of FirstOrder RL and RC Circuits 220 1. Practical Perspective: Artificial Pacemaker 221 1. 7.1 The Natural Response of an RL Circuit 222 2. 7.2 The Natural Response of an RC Circuit 228 3. 7.3 The Step Response of RL and RC Circuits 233 4. 7.4 A General Solution for Step and Natural Responses 241 5. 7.5 Sequential Switching 246 6. 7.6 Unbounded Response 250 7. 7.7 The Integrating Amplifier 252 1. Practical Perspective: Artificial Pacemaker 255 2. Summary 256 3. Problems 256 8. Chapter 8 Natural and Step Responses of RLC Circuits 272 1. Practical Perspective: Clock for Computer Timing 273 1. 8.1 Introduction to the Natural Response of a Parallel RLC Circuit 274 2. 8.2 The Forms of the Natural Response of a Parallel RLC Circuit 278 3. 8.3 The Step Response of a Parallel RLC Circuit 289 4. 8.4 The Natural and Step Response of a Series RLC Circuit 296 5. 8.5 A Circuit with Two Integrating Amplifiers 303 1. Practical Perspective: Clock for Computer Timing 308 2. Summary 309 3. Problems 310 9. Chapter 9 Sinusoidal SteadyState Analysis 318 1. Practical Perspective: A Household Distribution Circuit 319 1. 9.1 The Sinusoidal Source 320 2. 9.2 The Sinusoidal Response 323 3. 9.3 The Phasor 324 4. 9.4 The Passive Circuit Elements in the Frequency Domain 327 5. 9.5 Kirchhoff’s Laws in the Frequency Domain 332 6. 9.6 Series, Parallel, and DeltatoWye Simplifications 333 7. 9.7 Source Transformations and Thévenin–Norton Equivalent Circuits 340 8. 9.8 The NodeVoltage Method 344 9. 9.9 The MeshCurrent Method 345 10. 9.10 The Transformer 347 11. 9.11 The Ideal Transformer 351 12. 9.12 Phasor Diagrams 357 1. Practical Perspective: A Household Distribution Circuit 359 2. Summary 361 3. Problems 362 10. Chapter 10 Sinusoidal SteadyState Power Calculations 374 1. Practical Perspective: Vampire Power 375 1. 10.1 Instantaneous Power 376 2. 10.2 Average and Reactive Power 377 3. 10.3 The rms Value and Power Calculations 382 4. 10.4 Complex Power 384 5. 10.5 Power Calculations 386 6. 10.6 Maximum Power Transfer 393 1. Practical Perspective: Vampire Power 399 2. Summary 401 3. Problems 401 11. Chapter 11 Balanced ThreePhase Circuits 412 1. Practical Perspective: Transmission and Distribution of Electric Power 413 1. 11.1 Balanced ThreePhase Voltages 414 2. 11.2 ThreePhase Voltage Sources 415 3. 11.3 Analysis of the WyeWye Circuit 416 4. 11.4 Analysis of the WyeDelta Circuit 422 5. 11.5 Power Calculations in Balanced ThreePhase Circuits 425 6. 11.6 Measuring Average Power in ThreePhase Circuits 430 1. Practical Perspective: Transmission and Distribution of Electric Power 433 2. Summary 435 3. Problems 436 12. Chapter 12 Introduction to the Laplace Transform 444 1. Practical Perspective: Transient Effects 445 1. 12.1 Definition of the Laplace Transform 446 2. 12.2 The Step Function 447 3. 12.3 The Impulse Function 449 4. 12.4 Functional Transforms 452 5. 12.5 Operational Transforms 453 6. 12.6 Applying the Laplace Transform 458 7. 12.7 Inverse Transforms 460 8. 12.8 Poles and Zeros of F(s) 470 9. 12.9 Initialand FinalValue Theorems 472 1. Practical Perspective: Transient Effects 474 2. Summary 476 3. Problems 477 13. Chapter 13 The Laplace Transform in Circuit Analysis 482 1. Practical Perspective: Surge Suppressors 483 1. 13.1 Circuit Elements in the s Domain 484 2. 13.2 Circuit Analysis in the s Domain 486 3. 13.3 Applications 488 4. 13.4 The Transfer Function 500 5. 13.5 The Transfer Function in Partial Fraction Expansions 502 6. 13.6 The Transfer Function and the Convolution Integral 505 7. 13.7 The Transfer Function and the SteadyState Sinusoidal Response 511 8. 13.8 The Impulse Function in Circuit Analysis 514 1. Practical Perspective: Surge Suppressors 520 2. Summary 521 3. Problems 522 14. Chapter 14 Introduction to Frequency Selective Circuits 536 1. Practical Perspective: Pushbutton Telephone Circuits 537 1. 14.1 Some Preliminaries 538 2. 14.2 LowPass Filters 539 3. 14.3 HighPass Filters 545 4. 14.4 Bandpass Filters 550 5. 14.5 Bandreject Filters 560 1. Practical Perspective: Pushbutton Telephone Circuits 564 2. Summary 564 3. Problems 565 15. Chapter 15 Active Filter Circuits 572 1. Practical Perspective: Bass Volume Control 573 1. 15.1 FirstOrder LowPass and HighPass Filters 574 2. 15.2 Scaling 577 3. 15.3 Op Amp Bandpass and Bandreject Filters 580 4. 15.4 HigherOrder Op Amp Filters 587 5. 15.5 Narrowband Bandpass and Bandreject Filters 600 1. Practical Perspective: Bass Volume Control 605 2. Summary 608 3. Problems 609 16. Chapter 16 Fourier Series 618 1. Practical Perspective: Active HighQ Filters 619 1. 16.1 Fourier Series Analysis: An Overview 621 2. 16.2 The Fourier Coefficients 622 3. 16.3 The Effect of Symmetry on the Fourier Coefficients 625 4. 16.4 An Alternative Trigonometric Form of the Fourier Series 631 5. 16.5 An Application 633 6. 16.6 AveragePower Calculations with Periodic Functions 639 7. 16.7 The rms Value of a Periodic Function 641 8. 16.8 The Exponential Form of the Fourier Series 642 9. 16.9 Amplitude and Phase Spectra 645 1. Practical Perspective: Active HighQ Filters 647 2. Summary 649 3. Problems 650 17. Chapter 17 The Fourier Transform 660 1. Practical Perspective: Filtering Digital Signals 661 1. 17.1 The Derivation of the Fourier Transform 662 2. 17.2 The Convergence of the Fourier Integral 664 3. 17.3 Using Laplace Transforms to Find Fourier Transforms 666 4. 17.4 Fourier Transforms in the Limit 668 5. 17.5 Some Mathematical Properties 671 6. 17.6 Operational Transforms 672 7. 17.7 Circuit Applications 677 8. 17.8 Parseval’s Theorem 679 1. Practical Perspective: Filtering Digital Signals 685 2. Summary 686 3. Problems 686 18. Chapter 18 TwoPort Circuits 692 1. Practical Perspective: Characterizing an Unknown Circuit 693 1. 18.1 The Terminal Equations 694 2. 18.2 The TwoPort Parameters 695 3. 18.3 Analysis of the Terminated TwoPort Circuit 703 4. 18.4 Interconnected TwoPort Circuits 708 1. Practical Perspective: Characterizing an Unknown Circuit 711 2. Summary 712 3. Problems 713 1. Appendix A The Solution of Linear Simultaneous Equations 718 1. A.1 Preliminary Steps 718 2. A.2 Calculator and Computer Methods 719 3. A.3 PaperandPencil Methods 721 4. A.4 Applications 723 2. Appendix B Complex Numbers 727 1. B.1 Notation 727 2. B.2 The Graphical Representation of a Complex Number 728 3. B.3 Arithmetic Operations 729 4. B.4 Useful Identities 730 5. B.5 The Integer Power of a Complex Number 731 6. B.6 The Roots of a Complex Number 731 3. Appendix C More on Magnetically Coupled Coils and Ideal Transformers 733 1. C.1 Equivalent Circuits for Magnetically Coupled Coils 733 2. C.2 The Need for Ideal Transformers in the Equivalent Circuits 737 4. Appendix D The Decibel 741 5. Appendix E Bode Diagrams 743 1. E.1 Real, FirstOrder Poles and Zeros 743 2. E.2 StraightLine Amplitude Plots 744 3. E.3 More Accurate Amplitude Plots 747 4. E.4 StraightLine Phase Angle Plots 748 5. E.5 Bode Diagrams: Complex Poles and Zeros 750 6. E.6 StraightLine Amplitude Plots for Complex Poles 751 7. E.7 Correcting StraightLine Amplitude Plots for Complex Poles 752 8. E.8 Phase Angle Plots for Complex Poles 754 6. Appendix F An Abbreviated Table of Trigonometric Identities 757 7. Appendix G An Abbreviated Table of Integrals 758 8. Appendix H Common Standard Component Values 760 9. Answers to Selected Problems 761 10. Index 771 List of Examples 1. Chapter 1 1. 1.1 Using SI Units and Prefixes for Powers of 10 11 2. 1.2 Relating Current and Charge 15 3. 1.3 Using the Passive Sign Convention 17 4. 1.4 Relating Voltage, Current, Power, and Energy 17 2. Chapter 2 1. 2.1 Testing Interconnections of Ideal Sources 30 2. 2.2 Testing Interconnections of Ideal Independent and Dependent Sources 31 3. 2.3 Calculating Voltage, Current, and Power for a Simple Resistive Circuit 34 4. 2.4 Constructing a Circuit Model of a Flashlight 36 5. 2.5 Constructing a Circuit Model Based on Terminal Measurements 38 6. 2.6 Using Kirchhoff’s Current Law 41 7. 2.7 Using Kirchhoff’s Voltage Law 42 8. 2.8 Applying Ohm’s Law and Kirchhoff’s Laws to Find an Unknown Current 42 9. 2.9 Constructing a Circuit Model Based on Terminal Measurements 43 10. 2.10 Analyzing a Circuit with a Dependent Source 45 11. 2.11 Applying Ohm’s Law and Kirchhoff’s Laws to Find an Unknown Voltage 46 12. 2.12 Applying Ohm’s Law and Kirchhoff’s Law in an Amplifier Circuit 47 3. Chapter 3 1. 3.1 Applying SeriesParallel Simplification 62 2. 3.2 Solving a Circuit Using SeriesParallel Simplification 63 3. 3.3 Designing a Simple Voltage Divider 65 4. 3.4 Adding a Resistive Load to a Voltage Divider 65 5. 3.5 The Effect of Resistor Tolerance on the VoltageDivider Circuit 66 6. 3.6 Designing a CurrentDivider Circuit 67 7. 3.7 Using Voltage Division and Current Division to Solve a Circuit 69 8. 3.8 Using a d’Arsonval Ammeter 71 9. 3.9 Using a d’Arsonval Voltmeter 72 10. 3.10 Using a Wheatstone Bridge to Measure Resistance 75 11. 3.11 Applying a DeltatoWye Transform 77 4. Chapter 4 1. 4.1 Identifying Node, Branch, Mesh, and Loop in a Circuit 94 2. 4.2 Using Essential Nodes and Essential Branches to Write Simultaneous Equations 95 3. 4.3 Using the NodeVoltage Method 97 4. 4.4 Using the NodeVoltage Method with Dependent Sources 99 5. 4.5 NodeVoltage Analysis of the Amplifier Circuit 102 6. 4.6 Using the MeshCurrent Method 106 7. 4.7 Using the MeshCurrent Method with Dependent Sources 107 8. 4.8 A Special Case in the MeshCurrent Method 108 9. 4.9 MeshCurrent Analysis of the Amplifier Circuit 111 10. 4.10 Understanding the NodeVoltage Method Versus Mesh Current Method 113 11. 4.11 Comparing the NodeVoltage and MeshCurrent Methods 114 12. 4.12 Using Source Transformations to Solve a Circuit 116 13. 4.13 Using Special Source Transformation Techniques 117 14. 4.14 Finding a Thévenin Equivalent 120 15. 4.15 Finding a Norton Equivalent 121 16. 4.16 Finding the Thévenin Equivalent of a Circuit with a Dependent Source 122 17. 4.17 Finding the Thévenin Equivalent Resistance Directly from the Circuit 123 18. 4.18 Finding the Thévenin Equivalent Resistance Using a Test Source 124 19. 4.19 Finding the Thévenin Equivalent of a Circuit with Dependent Sources and Resistors 124 20. 4.20 Using a Thévenin Equivalent to Analyze the Amplifier Circuit 125 21. 4.21 Calculating the Condition for Maximum Power Transfer 127 22. 4.22 Using Superposition to Solve a Circuit 129 23. 4.23 Using Superposition to Solve a Circuit with Dependent Sources 130 5. Chapter 5 1. 5.1 Analyzing an Op Amp Circuit 155 2. 5.2 Designing an Inverting Amplifier 157 3. 5.3 Designing a Summing Amplifier 159 4. 5.4 Designing a Noninverting Amplifier 161 5. 5.5 Designing a Difference Amplifier 163 6. 5.6 Calculating the CMRR 167 7. 5.7 Analyzing a NoninvertingAmplifier Circuit using a Realistic Op Amp Model 169 6. Chapter 6 1. 6.1 Determining the Voltage, Given the Current, at the Terminals of an Inductor 184 2. 6.2 Determining the Current, Given the Voltage, at the Terminals of an Inductor 186 3. 6.3 Determining the Current, Voltage, Power, and Energy for an Inductor 187 4. 6.4 Determining Current, Voltage, Power, and Energy for a Capacitor 191 5. 6.5 Finding v, p, and w Induced by a Triangular Current Pulse for a Capacitor 192 6. 6.6 Finding the Equivalent Inductance 196 7. 6.7 Finding the Equivalent Capacitance 197 8. 6.8 Finding MeshCurrent Equations for a Circuit with Magnetically Coupled Coils 201 9. 6.9 Calculating the Coupling Coefficient and Stored Energy for Magnetically Coupled Coils 209 7. Chapter 7 1. 7.1 Determining the Natural Response of an RL Circuit 224 2. 7.2 Determining the Natural Response of an RL Circuit with Parallel Inductors 227 3. 7.3 Determining the Natural Response of an RC Circuit 230 4. 7.4 Determining the Natural Response of an RC Circuit with Series Capacitors 231 5. 7.5 Determining the Step Response of an RL Circuit 234 6. 7.6 Determining the Step Response of an RC Circuit 239 7. 7.7 Using the General Solution Method to Find an RL Circuit’s Natural Response 242 8. 7.8 Using the General Solution Method to Find an RC Circuit’s Step Response 243 9. 7.9 Using the General Solution Method to Find an RL Circuit’s Step Response 244 10. 7.10 Determining the Step Response of a Circuit with Magnetically Coupled Coils 245 11. 7.11 Analyzing an RL Circuit that has Sequential Switching 247 12. 7.12 Analyzing an RC Circuit that has Sequential Switching 249 13. 7.13 Finding the Unbounded Response in an RC Circuit 251 14. 7.14 Analyzing an Integrating Amplifier 253 15. 7.15 Analyzing an Integrating Amplifier that has Sequential Switching 253 8. Chapter 8 1. 8.1 Finding the Roots of the Characteristic Equation of a Parallel RLC Circuit 277 2. 8.2 Finding the Overdamped Natural Response of a Parallel RLC Circuit 280 3. 8.3 Calculating Branch Currents in the Natural Response of a Parallel RLC Circuit 281 4. 8.4 Finding the Underdamped Natural Response of a Parallel RLC Circuit 284 5. 8.5 Finding the Critically Damped Natural Response of a Parallel RLC Circuit 288 6. 8.6 Finding the Overdamped Step Response of a Parallel RLC Circuit 293 7. 8.7 Finding the Underdamped Step Response of a Parallel RLC Circuit 294 8. 8.8 Finding the Critically Damped Step Response of a Parallel RLC Circuit 294 9. 8.9 Comparing the ThreeStep Response Forms 295 10. 8.10 Finding Step Response of a Parallel RLC Circuit with Initial Stored Energy 295 11. 8.11 Finding the Natural Response of a Series RLC Circuit 302 12. 8.12 Finding the Step Response of a Series RLC Circuit 302 13. 8.13 Analyzing Two Cascaded Integrating Amplifiers 305 14. 8.14 Analyzing Two Cascaded Integrating Amplifiers with Feedback Resistors 307 9. Chapter 9 1. 9.1 Finding the Characteristics of a Sinusoidal Current 321 2. 9.2 Finding the Characteristics of a Sinusoidal Voltage 322 3. 9.3 Translating a Sine Expression to a Cosine Expression 322 4. 9.4 Calculating the rms Value of a Triangular Waveform 322 5. 9.5 Adding Cosines Using Phasors 326 6. 9.6 Calculating Component Voltages Using Phasor Techniques 331 7. 9.7 Using KVL in the Frequency Domain 333 8. 9.8 Combining Impedances in Series 334 9. 9.9 Combining Impedances in Series and in Parallel 337 10. 9.10 Using a DeltatoWye Transform in the Frequency Domain 339 11. 9.11 Performing Source Transformations in the Frequency Domain 341 12. 9.12 Finding a Thévenin Equivalent in the Frequency Domain 342 13. 9.13 Using the NodeVoltage Method in the Frequency Domain 344 14. 9.14 Using the MeshCurrent Method in the Frequency Domain 346 15. 9.15 Analyzing a Linear Transformer in the Frequency Domain 349 16. 9.16 Analyzing an Ideal Transformer Circuit in the Frequency Domain 355 17. 9.17 Using Phasor Diagrams to Analyze a Circuit 357 18. 9.18 Using Phasor Diagrams to Analyze Capacitive Loading Effects 358 10. Chapter 10 1. 10.1 Calculating Average and Reactive Power 380 2. 10.2 Making Power Calculations Involving Household Appliances 382 3. 10.3 Determining Average Power Delivered to a Resistor by a Sinusoidal Voltage 384 4. 10.4 Calculating Complex Power 385 5. 10.5 Calculating Power Using Phasor Voltage and Current 387 6. 10.6 Calculating Average and Reactive Power 389 7. 10.7 Calculating Power in Parallel Loads 390 8. 10.8 Balancing Power Delivered with Power Absorbed in an AC Circuit 391 9. 10.9 Determining Maximum Power Transfer without Load Restrictions 395 10. 10.10 Determining Maximum Power Transfer with Load Impedance Restriction 396 11. 10.11 Finding Maximum Power Transfer with Impedance Angle Restrictions 396 12. 10.12 Finding Maximum Power Transfer in a Circuit with an Ideal Transformer 397 11. Chapter 11 1. 11.1 Analyzing a WyeWye Circuit 420 2. 11.2 Analyzing a WyeDelta Circuit 423 3. 11.3 Calculating Power in a ThreePhase WyeWye Circuit 428 4. 11.4 Calculating Power in a ThreePhase WyeDelta Circuit 428 5. 11.5 Calculating ThreePhase Power with an Unspecified Load 429 6. 11.6 Computing Wattmeter Readings in ThreePhase Circuits 432 12. Chapter 12 1. 12.1 Using Step Functions to Represent a Function of Finite Duration 448 2. 12.2 Using Laplace Transforms to Predict a Circuit’s Response 460 3. 12.3 Finding the Inverse Laplace Transform when F(s) has Distinct Real Roots 462 4. 12.4 Finding the Inverse Laplace Transform when F(s) has Distinct Complex Roots 465 5. 12.5 Finding the Inverse Laplace Transform when F(s) has Repeated Real Roots 467 6. 12.6 Finding the Inverse Laplace Transform when F(s) has Repeated Complex Roots 468 7. 12.7 Finding the Inverse Laplace Transform of an Improper Rational Function 470 8. 12.8 Finding and Plotting the Poles and Zeros of an sDomain Function 471 9. 12.9 Applying the Initialand FinalValue Theorems 474 13. Chapter 13 1. 13.1 Transforming a Circuit into the s Domain 488 2. 13.2 The Natural Response of an RC Circuit 489 3. 13.3 The Step Response of an RLC Circuit 489 4. 13.4 Analyzing a Circuit with a Sinusoidal Source 491 5. 13.5 Analyzing a Circuit with Multiple Meshes 493 6. 13.6 Creating a Thévenin Equivalent in the s Domain 495 7. 13.7 Analyzing a Circuit with Mutual Inductance 497 8. 13.8 Applying Superposition in the s Domain 499 9. 13.9 Deriving the Transfer Function of a Circuit 501 10. 13.10 Analyzing the Transfer Function of a Circuit 503 11. 13.11 Using the Convolution Integral to Find an Output Signal 509 12. 13.12 Using the Transfer Function to Find the SteadyState Sinusoidal Response 513 13. 13.13 A Series Inductor Circuit with an Impulsive Response 515 14. 13.14 A Circuit with Both Internally Generated and Externally Applied Impulses 518 14. Chapter 14 1. 14.1 Designing a LowPass Filter 543 2. 14.2 Designing a Series RC LowPass Filter 544 3. 14.3 Designing a Series RL HighPass Filter 547 4. 14.4 Loading the Series RL HighPass Filter 548 5. 14.5 Designing a Bandpass Filter 555 6. 14.6 Designing a Parallel RLC Bandpass Filter 555 7. 14.7 Determining Effect of a Nonideal Voltage Source on a RLC Bandpass Filter 557 8. 14.8 Designing a Series RLC Bandreject Filter 562 15. Chapter 15 1. 15.1 Designing a LowPass Op Amp Filter 575 2. 15.2 Designing a HighPass Op Amp Filter 576 3. 15.3 Scaling a Series RLC Filter 578 4. 15.4 Scaling a Prototype LowPass Op Amp Filter 579 5. 15.5 Designing a Broadband Bandpass Op Amp Filter 583 6. 15.6 Designing a Broadband Bandreject Op Amp Filter 586 7. 15.7 Designing a FourthOrder LowPass Active Filter 589 8. 15.8 Calculating Butterworth Transfer Functions 592 9. 15.9 Designing a FourthOrder LowPass Butterworth Filter 594 10. 15.10 Determining the Order of a Butterworth Filter 597 11. 15.11 An Alternate Approach to Determining the Order of a Butterworth Filter 597 12. 15.12 Designing a Butterworth Bandpass Filter 599 13. 15.13 Designing a HighQ Bandpass Filter 602 14. 15.14 Designing a HighQ Bandreject Filter 604 16. Chapter 16 1. 16.1 Finding the Fourier Series of a Triangular Waveform 623 2. 16.2 Finding the Fourier Series of a Periodic Function with Symmetry 630 3. 16.3 Calculating Forms of the Trigonometric Fourier Series for Periodic Voltage 632 4. 16.4 Finding the Response of an RLC Circuit to a SquareWave Voltage 637 5. 16.5 Calculating Average Power for a Circuit with a Periodic Voltage Source 640 6. 16.6 Estimating the rms Value of a Periodic Function 642 7. 16.7 Finding the Exponential Form of the Fourier Series 644 8. 16.8 Plotting the Amplitude and Phase Spectra for a Periodic Voltage 646 17. Chapter 17 1. 17.1 Finding the Fourier Transform of a Constant 665 2. 17.2 Finding the Fourier Transform from the Laplace Transform 667 3. 17.3 Deriving an Operational Fourier Transform 675 4. 17.4 Using the Fourier Transform to Find the Transient Response 677 5. 17.5 Using the Fourier Transform to Find the Sinusoidal Steady State Response 678 6. 17.6 Applying Parseval’s Theorem 681 7. 17.7 Applying Parseval’s Theorem to an Ideal Bandpass Filter 682 8. 17.8 Applying Parseval’s Theorem to a LowPass Filter 683 9. 17.9 Calculating Energy Contained in a Rectangular Voltage Pulse 684 18. Chapter 18 1. 18.1 Finding the z Parameters of a TwoPort Circuit 696 2. 18.2 Finding the a Parameters from Measurements 697 3. 18.3 Finding h Parameters from Measurements and Table 18.1 700 4. 18.4 Determining Whether a Circuit Is Reciprocal and Symmetric 701 5. 18.5 Analyzing a Terminated TwoPort Circuit 707 6. 18.6 Analyzing Cascaded TwoPort Circuits 710 List of Tables 1. 1.1 The International System of Units (SI) 10 2. 1.2 Derived Units in SI 10 3. 1.3 Standardized Prefixes to Signify Powers of 10 10 4. 1.4 Interpretation of Reference Directions in Fig. 1.5 14 5. 1.5 Voltage and Current Values for the Circuit in Fig. 1.7 19 6. 4.1 Terms for Describing Circuits 95 7. 4.2 PSpice Sensitivity Analysis Results 133 8. 4.3 Steps in the NodeVoltage Method and the MeshCurrent Method 135 9. 6.1 Inductor and Capacitor Duality 198 10. 7.1 Value of e−t/τ For t Equal to Integral Multiples of τ 226 11. 8.1 NaturalResponse Parameters of the Parallel RLC Circuit 276 12. 8.2 Equations for Analyzing the Natural Response of Parallel RLC Circuits 288 13. 8.3 Equations for Analyzing the Step Response of Parallel RLC Circuits 293 14. 8.4 Equations for Analyzing the Natural Response of Series RLC Circuits 299 15. 8.5 Equations for Analyzing the Step Response of Series RLC Circuits 301 16. 9.1 Impedance and Reactance Values 331 17. 9.2 Admittance and Susceptance Values 336 18. 9.3 Impedance and Related Values 361 19. 10.1 Annual Energy Requirements of Electric Household Appliances 381 20. 10.2 Three Power Quantities and Their Units 385 21. 10.3 Average Power Consumption of Common Electrical Devices 399 22. 12.1 An Abbreviated List of Laplace Transform Pairs 453 23. 12.2 An Abbreviated List of Operational Transforms 458 24. 12.3 Four Useful Transform Pairs 469 25. 13.1 Summary of the sDomain Equivalent Circuits 486 26. 14.1 Input and Output Voltage Magnitudes for Several Frequencies 543 27. 15.1 Normalized (so that ωc=1 rad/s ) Butterworth Polynomials up to the Eighth Order 593 28. 17.1 Fourier Transforms of Elementary Functions 670 29. 17.2 Operational Transforms 675 30. 18.1 Parameter Conversion Table 699 31. 18.2 TwoPort Parameter Relationships for Reciprocal Circuits 701 32. 18.3 Terminated TwoPort Equations 704 List of Analysis Methods 1. Analysis Method 4.1: The Basic Version of the NodeVoltage Method 97 2. Analysis Method 4.2: Modified Step 3 for the NodeVoltage Method 99 3. Analysis Method 4.3: Complete Form of the NodeVoltage Method 102 4. Analysis Method 4.4: The Basic Version of the MeshCurrent Method 105 5. Analysis Method 4.5: Modified Step 3 for the MeshCurrent Method 107 6. Analysis Method 4.6: Complete Form of the MeshCurrent Method 110 7. Analysis Method 5.1: Analyzing an Ideal Op Amp Circuit with a Negative Feedback Path 154 8. Analysis Method 7.1: Finding the RL Natural Response 224 9. Analysis Method 7.2: Finding the RC Natural Response 230 10. Analysis Method 7.3: Finding the RL Step Response 234 11. Analysis Method 7.4: Finding the RC Step Response 238 12. Analysis Method 7.5: Finding the RL and RC Natural and Step Response 242 13. Analysis Method 8.1: The Natural Response of an Overdamped Parallel Rlc Circuit 280 14. Analysis Method 8.2: The Natural Response of an Overdamped or Underdamped Parallel RLC Circuit 283 15. Analysis Method 8.3: The Natural Response of Parallel RLC Circuits 287 16. Analysis Method 8.4: The Step Response of Parallel RLC Circuits 292 17. Analysis Method 8.5: The Natural Response of Series RLC Circuits 299 18. Analysis Method 8.6: The Step Response of Series RLC Circuits 301 19. Analysis Method 13.1: LaplaceTransform Circuit Analysis Method 487 Combine this... With the Power of Mastering Engineering for Electric Circuits 11/e Mastering is the teaching and learning platform that empowers every student. By combining trusted authors’ content with digital tools developed to engage students and emulate the office hours experience, Mastering personalizes learning and improves results for each student. Empower each learner Each student learns at a different pace. Personalized learning, including adaptive tools and wronganswer feedback, pinpoints the precise areas where each student needs practice, giving all students the support they need — when and where they need it — to be successful. Learn more at www.pearson.com/mastering/engineering http://www.pearson.com/mastering/engineering Preface The Eleventh Edition of Electric Circuits represents the most extensive revision to the text since the Fifth Edition, published in 1996. Every sentence, paragraph, subsection, and chapter has been examined to improve clarity, readability, and pedagogy. Yet the fundamental goals of the text are unchanged. These goals are: To build new concepts and ideas on concepts previously presented. This challenges students to see the explicit connections among the many circuit analysis tools and methods. To develop problemsolving skills that rely on a solid conceptual foundation. This challenges students to examine many different approaches to solving a problem before writing a single equation. To introduce realistic engineering experiences at every opportunity. This challenges students to develop the insights of a practicing engineer and exposes them to practice of engineering. Why This Edition? The Eleventh Edition of Electric Circuits incorporates the following new and revised elements: Analysis Methods – This new feature identifies the steps needed to apply a particular circuit analysis technique. Many students struggle just to get started when analyzing a circuit, and the analysis methods will reduce that struggle. Some of the analysis methods that are used most often can be found inside the book’s covers for easy reference. Examples – Many students rely on examples when developing and refining their problemsolving skills. We identified many places in the text that needed additional examples, and as a result the number of examples has increased by nearly 35% to 200. Endofchapter problems – Problem solving is fundamental to the study of circuit analysis. Having a wide variety of problems to assign and work is a key to success in any circuits course. Therefore, some existing endofchapter problems were revised, and some new endofchapter problems were added. Approximately 30% of the problems in the Eleventh Edition were rewritten. Fundamental equations and concepts – These important elements in the text were previously identified with margin notes. In this edition, the margin notes have been replaced by a secondcolor background, enlarged fonts, and a descriptive title for each fundamental equation and concept. In additional, many equation numbers have been eliminated to make it easier to distinguish fundamental equations from the many other equations in the text. Circuit simulation software – The PSpice® and Multisim® manuals have been revised to include screenshots from the most recent versions of these software simulation applications. Each manual presents the simulation material in the same order as the material is encountered in the text. These manuals include example simulations of circuits from the text. Icons identify endofchapter problems that are good candidates for simulation using either PSpice or Multisim. Solving simultaneous equations – Most circuit analysis techniques in this text eventually require you to solve two or more simultaneous linear algebraic equations. Appendix A has been extensively revised and includes examples of paperandpencil techniques, calculator techniques, and computer software techniques. Student workbook – Students who could benefit from additional examples and practice problems can use the Student Workbook, which has been revised for the Eleventh Edition of the text. This workbook has examples and problems covering the following material: balancing power, simple resistive circuits, node voltage method, mesh current method, Thévenin and Norton equivalents, op amp circuits, firstorder circuits, secondorder circuits, AC steadystate analysis, and Laplace transform circuit analysis. The Student Workbook now includes access to Video Solutions, complete, stepbystep solution walkthroughs to representative homework problems. Learning Catalytics, a “bring your own device” student engagement, assessment, and classroom intelligence system is available with the Eleventh Edition. With Learning Catalytics you can: Use openended questions to get into the minds of students to understand what they do or don’t know and adjust lectures accordingly. Use a wide variety of question types to sketch a graph, annotate a circuit diagram, compose numeric or algebraic answers, and more. Access rich analytics to understand student performance. Use prebuilt questions or add your own to make Learning Catalytics fit your course exactly. Pearson Mastering Engineering is an online tutorial and assessment program that provides students with personalized feedback and hints and instructors with diagnostics to track students’ progress. With the Eleventh Edition, Mastering Engineering will offer new enhanced end ofchapter problems with hints and feedback, Coaching Activities, and Adaptive FollowUp assignments. Visit www.masteringengineering.com for more information. Hallmark Features Analysis Methods Students encountering circuit analysis for the first time can benefit from step http://www.masteringengineering.com bystep directions that lead them to a problem’s solution. We have compiled these directions in a collection of analysis methods, and revised many of the examples in the text to employ these analysis methods. Chapter Problems Users of Electric Circuits have consistently rated the Chapter Problems as one of the book’s most attractive features. In the Eleventh Edition, there are 1185 endofchapter problems with approximately 30% that have been revised from the previous edition. Problems are organized at the end of each chapter by section. Practical Perspectives The Eleventh Edition continues using Practical Perspectives to introduce the chapter. They provide realworld circuit examples, taken from realworld devices. Every chapter begins by describing a practical application of the material that follows. After presenting that material, the chapter revisits the Practical Perspective, performing a quantitative circuit analysis using the newly introduced chapter material. A special icon identifies endofchapter problems directly related to the Practical Perspective application. These problems provide additional opportunities for solving realworld problems using the chapter material. Assessment Problems Each chapter begins with a set of chapter objectives. At key points in the chapter, you are asked to stop and assess your mastery of a particular objective by solving one or more assessment problems. The answers to all of the assessment problems are given at the conclusion of each problem, so you can check your work. If you are able to solve the assessment problems for a given objective, you have mastered that objective. If you need more practice, several endofchapter problems that relate to the objective are suggested at the conclusion of the assessment problems. Examples Every chapter includes many examples that illustrate the concepts presented in the text in the form of a numeric example. There are now nearly 200 examples in this text, an increase of about 35% when compared to the previous edition. The examples illustrate the application of a particular concept, often employ an Analysis Method, and exemplify good problem solving skills. Fundamental Equations and Concepts Throughout the text, you will see fundamental equations and concepts set apart from the main text. This is done to help you focus on some of the key principles in electric circuits and to help you navigate through the important topics. Integration of Computer Tools Computer tools can assist students in the learning process by providing a visual representation of a circuit’s behavior, validating a calculated solution, reducing the computational burden of more complex circuits, and iterating toward a desired solution using parameter variation. This computational support is often invaluable in the design process. The Eleventh Edition supports PSpice and Multisim, both popular computer tools for circuit simulation and analysis. Chapter problems suited for exploration with PSpice and Multisim are marked accordingly. Design Emphasis The Eleventh Edition continues to support the emphasis on the design of circuits in many ways. First, many of the Practical Perspective discussions focus on the design aspects of the circuits. The accompanying Chapter Problems continue the discussion of the design issues in these practical examples. Second, designoriented Chapter Problems have been labeled explicitly, enabling students and instructors to identify those problems with a design focus. Third, the identification of problems suited to exploration with PSpice or Multisim suggests design opportunities using these software tools. Fourth, some problems in nearly every chapter focus on the use of realistic component values in achieving a desired circuit design. Once such a problem has been analyzed, the student can proceed to a laboratory to build and test the circuit, comparing the analysis with the measured performance of the actual circuit. Accuracy All text and problems in the Eleventh Edition have undergone our strict hallmark accuracy checking process, to ensure the most errorfree book possible. Resources For Students Mastering Engineering. Mastering Engineering provides tutorial homework problems designed to emulate the instructor’s office hour environment, guiding students through engineering concepts with selfpaced individualized coaching. These indepth tutorial homework problems provide students with feedback specific to their errors and optional hints that break problems down into simpler steps. Visit www.masteringengineering.com for more information. Learning Catalytics. Learning Catalytics is an interactive student response tool that encourages teambased learning by using student’s smartphones, tablets, or laptops to engage them in interactive tasks and thinking. Visit www.learningcatalytics.com for more information. http://www.masteringengineering.com http://www.learningcatalytics.com Student Workbook. This resource teaches students techniques for solving problems presented in the text. Organized by concepts, this is a valuable problemsolving resource for all levels of students. The Student Workbook now includes access to Video Solutions, complete, stepbystep solution walkthroughs to representative homework problems. Introduction to Multisim and Introduction to PSpice Manuals—Updated for the Eleventh Edition, these manuals are excellent resources for those wishing to integrate PSpice or Multisim into their classes. Resources for Instructors All instructor resources are available for download at www.pearsonhighered.com. If you are in need of a login and password for this site, please contact your local Pearson representative. Instructor Solutions Manual—Fully workedout solutions to Assessment Problems and endofchapter problems. PowerPoint lecture images—All figures from the text are available in PowerPoint for your lecture needs. An additional set of full lecture slides with embedded assessment questions are available upon request. MasteringEngineering. This online tutorial and assessment program allows you to integrate dynamic homework with automated grading and personalized feedback. MasteringEngineering allows you to easily track the performance of your entire class on an assignmentbyassignment basis, or the detailed work of an individual student. For more information visit www.masteringengineering.com. Learning Catalytics—This “bring your own device” student engagement, assessment and classroom intelligence system enables you to measure student learning during class, and adjust your lectures accordingly. A wide variety of question and answer types allows you to author your own questions, or you can use questions already authored into the system. For more information visit www.learningcatalytics.com or click on the Learning Catalytics link http://www.pearsonhighered.com http://www.learningcatalytics.com inside Mastering Engineering. Prerequisites In writing the first 12 chapters of the text, we have assumed that the reader has taken a course in elementary differential and integral calculus. We have also assumed that the reader has had an introductory physics course, at either the high school or university level, that introduces the concepts of energy, power, electric charge, electric current, electric potential, and electromagnetic fields. In writing the final six chapters, we have assumed the student has had, or is enrolled in, an introductory course in differential equations. Course Options The text has been designed for use in a onesemester, twosemester, or a threequarter sequence. Singlesemester course: After covering Chapters 1–4 and Chapters 6–10 (omitting Sections 7.7 and 8.5) the instructor can develop the desired emphasis by covering Chapter 5 (operational amplifiers), Chapter 11 (threephase circuits), Chapters 13 and 14 (Laplace methods), or Chapter 18 (TwoPort Circuits). Twosemester sequence: Assuming three lectures per week, cover the first nine chapters during the first semester, leaving Chapters 10–18 for the second semester. Academic quarter schedule: Cover Chapters 1–6 in the first quarter, Chapters 7–12 in the second quarter, and Chapters 13–18 in the third quarter. Note that the introduction to operational amplifier circuits in Chapter 5 can be omitted with minimal effect on the remaining material. If Chapter 5 is omitted, you should also omit Section 7.7, Section 8.5, Chapter 15, and those assessment problems and endofchapter problems that pertain to operational amplifiers. There are several appendixes at the end of the book to help readers make effective use of their mathematical background. Appendix A presents several different methods for solving simultaneous linear equations; complex numbers are reviewed in Appendix B; Appendix C contains additional material on magnetically coupled coils and ideal transformers; Appendix D contains a brief discussion of the decibel; Appendix E is dedicated to Bode diagrams; Appendix F is devoted to an abbreviated table of trigonometric identities that are useful in circuit analysis; and an abbreviated table of useful integrals is given in Appendix G. Appendix H provides tables of common standard component values for resistors, inductors, and capacitors, to be used in solving many endofchapter problems. Selected Answers provides answers to selected endofchapter problems. Acknowledgments I will be forever grateful to Jim Nilsson for giving me the opportunity to collaborate with him on this textbook. I started by revising the PSpice supplement for the Third Edition, and became a coauthor of the Fifth Edition. Jim was a patient and gracious mentor, and I learned so much from him about teaching and writing and hard work. It is a great honor to be associated with him through this textbook, and to impact the education of the thousands of students who use this text. There were many hardworking people behind the scenes at our publisher who deserve my thanks and gratitude for their efforts on behalf of the Eleventh Edition. At Pearson, I would like to thank Norrin Dias, Erin Ault, Rose Kernan, and Scott Disanno for their continued support and encouragement, their professional demeanor, their willingness to lend an ear, and their months of long hours and no weekends. The author would also like to acknowledge the staff at Integra Software Solutions for their dedication and hard work in typesetting this text. I am very grateful for the many instructors and students who have done formal reviews of the text or offered positive feedback and suggestions for improvement more informally. I am pleased to receive email from instructors and students who use the book, even when they are pointing out an error I failed to catch in the review process. I have been contacted by people who use our text from all over the world, and I thank all of you for taking the time to do so. I use as many of your suggestions as possible to continue to improve the content, the pedagogy, and the presentation in this text. I am privileged to have the opportunity to impact the educational experience of the many thousands of future engineers who will use this text. Susan A. Riedel Electric Circuits Eleventh Edition Chapter 1 Circuit Variables Chapter Contents 1. 1.1 Electrical Engineering: An Overview 2. 1.2 The International System of Units 3. 1.3 Circuit Analysis: An Overview 4. 1.4 Voltage and Current 5. 1.5 The Ideal Basic Circuit Element 6. 1.6 Power and Energy Chapter Objectives 1. Understand and be able to use SI units and the standard prefixes for powers of 10. 2. Know and be able to use the definitions of voltage and current. 3. Know and be able to use the definitions of power and energy. 4. Be able to use the passive sign convention to calculate the power for an ideal basic circuit element given its voltage and current. Electrical engineering is an exciting and challenging profession for anyone who has a genuine interest in, and aptitude for, applied science and mathematics. Electrical engineers play a dominant role in developing systems that change the way people live and work. Satellite communication links, cell phones, computers, televisions, diagnostic and surgical medical equipment, robots, and aircraft represent systems that define a modern technological society. As an electrical engineer, you can participate in this ongoing technological revolution by improving and refining existing systems and by discovering and developing new systems to meet the needs of our ever changing society. This text introduces you to electrical engineering using the analysis and design of linear circuits. We begin by presenting an overview of electrical engineering, some ideas about an engineering point of view as it relates to circuit analysis, and a review of the International System of Units. We then describe generally what circuit analysis entails. Next, we introduce the concepts of voltage and current. We continue by discussing the ideal basic element and the need for a polarity reference system. We conclude the chapter by describing how current and voltage relate to power and energy. Practical Perspective Balancing Power One of the most important skills you will develop is the ability to check your answers for the circuits you design and analyze using the tools developed in this text. A common method used to check for valid answers is to calculate the power in the circuit. The linear circuits we study have no net power, so the sum of the power associated with all circuit components must be zero. If the total power for the circuit is zero, we say that the power balances, but if the total power is not zero, we need to find the errors in our calculation. As an example, we will consider a simple model for distributing electricity to a typical home. (Note that a more realistic model will be investigated in the Practical Perspective for Chapter 9.) The components labeled a and b represent the source of electrical power for the home. The components labeled c, d, and e represent the wires that carry the electrical current from the source to the devices in the home requiring electrical power. The components labeled f, g, and h represent lamps, televisions, hair dryers, refrigerators, and other devices that require power. romakoma/Shutterstock PhotoSerg/Shutterstock Once we have introduced the concepts of voltage, current, power, and energy, we will examine this circuit model in detail, and use a power balance to determine whether the results of analyzing this circuit are correct. 1.13 Full Alternative Text AfricaStudio/Shutterstock 1.1 Electrical Engineering: An Overview The electrical engineering profession focuses on systems that produce, transmit, and measure electric signals. Electrical engineering combines the physicist’s models of natural phenomena with the mathematician’s tools for manipulating those models to produce systems that meet practical needs. Electrical systems pervade our lives; they are found in homes, schools, workplaces, and transportation vehicles everywhere. We begin by presenting a few examples from each of the five major classifications of electrical systems: communication systems computer systems control systems power systems signalprocessing systems Then we describe how electrical engineers analyze and design such systems. Communication systems are electrical systems that generate, transmit, and distribute information. Wellknown examples include television equipment, such as cameras, transmitters, receivers, and monitors; radio telescopes, used to explore the universe; satellite systems, which return images of other planets and our own; radar systems, used to coordinate plane flights; and telephone systems. Figure 1.1 depicts the major components of a modern telephone system that supports mobile phones, landlines, and international calling. Inside a telephone, a microphone turns sound waves into electric signals. These signals are carried to local or mobile exchanges, where they are combined with the signals from tens, hundreds, or thousands of other telephones. The form of the signals can be radio waves traveling through air, electrical signals traveling in underground coaxial cable, light pulses traveling in fiberoptic cable, or microwave signals that travel through space. The combined signals are broadcast from a transmission antenna to a receiving antenna. There the combined signals are separated at an exchange, and each is routed to the appropriate telephone, where an earphone acts as a speaker to convert the received electric signals back into sound waves. At each stage of the process, electric circuits operate on the signals. Imagine the challenge involved in designing, building, and operating each circuit in a way that guarantees that all of the hundreds of thousands of simultaneous calls have highquality connections. Figure 1.1 A telephone system. Figure 1.1 Full Alternative Text Computer systems use electric signals to process information ranging from word processing to mathematical computations. Systems range in size and power from simple calculators to personal computers to supercomputers that perform such complex tasks as processing weather data and modeling chemical interactions of complex organic molecules. These systems include networks of integrated circuits—miniature assemblies of hundreds, thousands, or millions of electrical components that often operate at speeds and power levels close to fundamental physical limits, including the speed of light and the thermodynamic laws. Control systems use electric signals to regulate processes. Examples include the control of temperatures, pressures, and flow rates in an oil refinery; the fuel–air mixture in a fuelinjected automobile engine; mechanisms such as the motors, doors, and lights in elevators; and the locks in the Panama Canal. The autopilot and autolanding systems that help to fly and land airplanes are also familiar control systems. Power systems generate and distribute electric power. Electric power, which is the foundation of our technologybased society, usually is generated in large quantities by nuclear, hydroelectric, solar, and thermal (coal, oil, or gasfired) generators. Power is distributed by a grid of conductors that crisscross the country. A major challenge in designing and operating such a system is to provide sufficient redundancy and control so that failure of any piece of equipment does not leave a city, state, or region completely without power. Signalprocessing systems act on electric signals that represent information. They transform the signals and the information contained in them into a more suitable form. There are many different ways to process the signals and their information. For example, imageprocessing systems gather massive quantities of data from orbiting weather satellites, reduce the amount of data to a manageable level, and transform the remaining data into a video image for the evening news broadcast. A magnetic resonance imaging (MRI) scan is another example of an imageprocessing system. It takes signals generated by powerful magnetic fields and radio waves and transforms them into a detailed, threedimensional image such as the one shown in Fig. 1.2, which can be used to diagnose disease and injury. Figure 1.2 An MRI scan of an adult knee joint. Neil Borden/Science Source/Getty Images Figure 1.2 Full Alternative Text Considerable interaction takes place among the engineering disciplines involved in designing and operating these five classes of systems. Thus, communications engineers use digital computers to control the flow of information. Computers contain control systems, and control systems contain computers. Power systems require extensive communications systems to coordinate safely and reliably the operation of components, which may be spread across a continent. A signalprocessing system may involve a communications link, a computer, and a control system. A good example of the interaction among systems is a commercial airplane, such as the one shown in Fig. 1.3. A sophisticated communications system enables the pilot and the air traffic controller to monitor the plane’s location, permitting the air traffic controller to design a safe flight path for all of the nearby aircraft and enabling the pilot to keep the plane on its designated path. An onboard computer system manages engine functions, implements the navigation and flight control systems, and generates video information screens in the cockpit. A complex control system uses cockpit commands to adjust the position and speed of the airplane, producing the appropriate signals to the engines and the control surfaces (such as the wing flaps, ailerons, and rudder) to ensure the plane remains safely airborne and on the desired flight path. The plane must have its own power system to stay aloft and to provide and distribute the electric power needed to keep the cabin lights on, make the coffee, and activate the entertainment system. Signal processing systems reduce the noise in air traffic communications and transform information about the plane’s location into the more meaningful form of a video display in the cockpit. Engineering challenges abound in the design of each of these systems and their integration into a coherent whole. For example, these systems must operate in widely varying and unpredictable environmental conditions. Perhaps the most important engineering challenge is to guarantee that sufficient redundancy is incorporated in the designs, ensuring that passengers arrive safely and on time at their desired destinations. Figure 1.3 Interacting systems on a commercial aircraft. Figure 1.3 Full Alternative Text Although electrical engineers may be interested primarily in one area, they must also be knowledgeable in other areas that interact with this area of interest. This interaction is part of what makes electrical engineering a challenging and exciting profession. The emphasis in engineering is on making things work, so an engineer is free to acquire and use any technique from any field that helps to get the job done. Circuit Theory An electric circuit is a mathematical model that approximates the behavior of an actual electrical system. Since electric circuits are found in every branch of electrical engineering, they provide an important foundation for learning how to design and operate systems such as those just described. The models, the mathematical techniques, and the language of circuit theory will form the intellectual framework for your future engineering endeavors. Note that the term electric circuit is commonly used to refer to an actual electrical system as well as to the model that represents it. In this text, when we talk about an electric circuit, we always mean a model, unless otherwise stated. It is the modeling aspect of circuit theory that has broad applications across engineering disciplines. Circuit theory is a special case of electromagnetic field theory: the study of static and moving electric charges. But applying generalized field theory to the study of electric signals is cumbersome and requires advanced mathematics. Consequently, a course in electromagnetic field theory is not a prerequisite to understanding the material in this book. We do, however, assume that you have had an introductory physics course in which electrical and magnetic phenomena were discussed. Three basic assumptions permit us to use circuit theory, rather than electromagnetic field theory, to study a physical system represented by an electric circuit. 1. Electrical effects happen instantaneously throughout a system. We can make this assumption because we know that electric signals travel at or near the speed of light. Thus, if the system is physically small, electric signals move through it so quickly that we can consider them to affect every point in the system simultaneously. A system that is small enough so that we can make this assumption is called a lumpedparameter system. 2. The net charge on every component in the system is always zero. Thus, no component can collect a net excess of charge, although some components, as you will learn later, can hold equal but opposite separated charges. 3. There is no magnetic coupling between the components in a system. As we demonstrate later, magnetic coupling can occur within a component. That’s it; there are no other assumptions. Using circuit theory provides simple solutions (of sufficient accuracy) to problems that would become hopelessly complicated if we were to use electromagnetic field theory. These benefits are so great that engineers sometimes specifically design electrical systems to ensure that these assumptions are met. The importance of assumptions 2 and 3 becomes apparent after we introduce the basic circuit elements and the rules for analyzing interconnected elements. Let’s take a closer look at assumption 1. The question is, “How small does a physical system have to be to qualify as a lumpedparameter system?” To get a quantitative answer to this question, remember that electric signals propagate as waves. If the wavelength of the signal is large compared to the physical dimensions of the system, we have a lumpedparameter system. The wavelength λ is the velocity divided by the repetition rate, or frequency, of the signal; that is, λ=c/f . The frequency f is measured in hertz (Hz). For example, power systems in the United States operate at 60 Hz. If we use the speed of light (c=3×108 m/s) as the velocity of propagation, the wavelength is 5×106 m. If the power system of interest is physically smaller than this wavelength, we can represent it as a lumpedparameter system and use circuit theory to analyze its behavior. How do we define smaller? A good rule is the rule of 1/10th: If the dimension of the system is less than 1/10th the dimension of the wavelength, you have a lumpedparameter system. Thus, as long as the physical dimension of the power system is less than 5×105 m (which is about 310 miles), we can treat it as a lumpedparameter system. Now consider a communication system that sends and receives radio signals. The propagation frequency of radio signals is on the order of 109 Hz, so the wavelength is 0.3 m. Using the rule of 1N10th, a communication system qualifies as a lumpedparameter system if its dimension is less than 3 cm. Whenever any of the pertinent physical dimensions of a system under study approaches the wavelength of its signals, we must use electromagnetic field theory to analyze that system. Throughout this book we study circuits derived from lumpedparameter systems. Problem Solving As a practicing engineer, you will not be asked to solve problems that have already been solved. Whether you are improving the performance of an existing system or designing a new system, you will be working on unsolved problems. As a student, however, you will read and discuss problems with known solutions. Then, by solving related homework and exam problems on your own, you will begin to develop the skills needed to attack the unsolved problems you’ll face as a practicing engineer. Let’s review several general problemsolving strategies. Many of these pertain to thinking about and organizing your solution strategy before proceeding with calculations. 1. Identify what’s given and what’s to be found. In problem solving, you need to know your destination before you can select a route for getting there. What is the problem asking you to solve or find? Sometimes the goal of the problem is obvious; other times you may need to paraphrase or make lists or tables of known and unknown information to see your objective. On one hand, the problem statement may contain extraneous information that you need to weed out before proceeding. On the other hand, it may offer incomplete information or more complexities than can be handled by the solution methods you know. In that case, you’ll need to make assumptions to fill in the missing information or simplify the problem context. Be prepared to circle back and reconsider supposedly extraneous information and/or your assumptions if your calculations get bogged down or produce an answer that doesn’t seem to make sense. 2. Sketch a circuit diagram or other visual model. Translating a verbal problem description into a visual model is often a useful step in the solution process. If a circuit diagram is already provided, you may need to add information to it, such as labels, values, or reference directions. You may also want to redraw the circuit in a simpler, but equivalent, form. Later in this text you will learn the methods for developing such simplified equivalent circuits. 3. Think of several solution methods and decide on a way of choosing among them. This course will help you build a collection of analytical tools, several of which may work on a given problem. But one method may produce fewer equations to be solved than another, or it may require only algebra instead of calculus to reach a solution. Such efficiencies, if you can anticipate them, can streamline your calculations considerably. Having an alternative method in mind also gives you a path to pursue if your first solution attempt bogs down. 4. Calculate a solution. Your planning up to this point should have helped you identify a good analytical method and the correct equations for the problem. Now comes the solution of those equations. Paperandpencil, calculator, and computer methods are all available for performing the actual calculations of circuit analysis. Efficiency and your instructor’s preferences will dictate which tools you should use. 5. Use your creativity. If you suspect that your answer is off base or if the calculations seem to go on and on without moving you toward a solution, you should pause and consider alternatives. You may need to revisit your assumptions or select a different solution method. Or you may need to take a less conventional problemsolving approach, such as working backward from a solution. This text provides answers to all of the Assessment Problems and many of the Chapter Problems so that you may work backward when you get stuck. In the real world, you won’t be given answers in advance, but you may have a desired problem outcome in mind from which you can work backward. Other creative approaches include allowing yourself to see parallels with other types of problems you’ve successfully solved, following your intuition or hunches about how to proceed, and simply setting the problem aside temporarily and coming back to it later. 6. Test your solution. Ask yourself whether the solution you’ve obtained makes sense. Does the magnitude of the answer seem reasonable? Is the solution physically realizable? Are the units correct? You may want to rework the problem using an alternative method to validate your original answer and help you develop your intuition about the most efficient solution methods for various kinds of problems. In the real world, safetycritical designs are always checked by several independent means. Getting into the habit of checking your answers will benefit you both as a student and as a practicing engineer. These problemsolving steps cannot be used as a recipe to solve every problem in this or any other course. You may need to skip, change the order of, or elaborate on certain steps to solve a particular problem. Use these steps as a guideline to develop a problemsolving style that works for you. 1.2 The International System of Units Engineers use quantitative measures to compare theoretical results to experimental results and compare competing engineering designs. Modern engineering is a multidisciplinary profession in which teams of engineers work together on projects, and they can communicate their results in a meaningful way only if they all use the same units of measure. The International System of Units (abbreviated SI) is used by all the major engineering societies and most engineers throughout the world; hence we use it in this book. The SI units are based on seven defined quantities: length mass time electric current thermodynamic temperature amount of substance luminous intensity These quantities, along with the basic unit and symbol for each, are listed in Table 1.1. Although not strictly SI units, the familiar time units of minute (60 s), hour (3600 s), and so on are often used in engineering calculations. In addition, defined quantities are combined to form derived units. Some quantities, such as force, energy, power, and electric charge, you already know through previous physics courses. Table 1.2 lists the derived units used in this book. Table 1.1 The International System of Units (SI) National Institute of Standards and Technology Special Publication 330, 2008 Edition, Natl. Inst. Stand. Technol. Spec. Pub. 330, 2008 Ed., 96 pages (March 2008) Table 1.1 Full Alternative Text Table 1.2 Derived Units in SI National Institute of Standards and Technology Special Publication 330, 2008 Edition, Natl. Inst. Stand. Technol. Spec. Pub. 330, 2008 Ed., 96 pages (March 2008) Table 1.2 Full Alternative Text In many cases, the SI unit is either too small or too large to use conveniently. Standard prefixes corresponding to powers of 10, as listed in Table 1.3, are then applied to the basic unit. Engineers often use only the prefixes for powers divisible by 3; thus centi, deci, deka, and hecto are used rarely. Also, engineers often select the prefix that places the base number in the range between 1 and 1000. Suppose that a time calculation yields a result of 10−5 s, that is, 0.00001 s. Most engineers would describe this quantity as 10 μs, that is, 10−5=10×10−6 s, rather than as 0.01 ms or 10,000 ns. Table 1.3 Standardized Prefixes to Signify Powers of 10 National Institute of Standards and Technology Special Publication 330, 2008 Edition, Natl. Inst. Stand. Technol. Spec. Pub. 330, 2008 Ed., 96 pages (March 2008) Table 1.3 Full Alternative Text Example 1.1 illustrates a method for converting from one set of units to another and also uses powerof10 prefixes. Example 1.1 Using SI Units and Prefixes for Powers of 10 If a signal can travel in a cable at 80% of the speed of light, what length of cable, in inches, represents 1 ns? Solution First, note that 1 ns=10−9 s. Also, recall that the speed of light c=3×108 m/s. Then, 80% of the speed of light is 0.8c=(0.8)(3×108)=2.4×108 m/s. Using a product of ratios, we can convert 80% of the speed of light from meters per second to inches per nanosecond. The result is the distance in inches traveled in 1 nanosecond: 2.4× 10 8 meters 1 second ⋅ 1 second 10 9 nanoseconds ⋅ 100 centimeters 1 meter ⋅ 1 inch 2.54 centimeters =9.45 inches/nanosecond. Therefore, a signal traveling at 80% of the speed of light will cover 9.45 inches of cable in 1 nanosecond. Assessment Problems Objective 1—Understand and be able to use SI units and the standard prefixes for powers of 10 1. 1.1 Assume a telephone signal travels through a cable at twothirds the speed of light. How long does it take the signal to get from New York City to Miami if the distance is approximately 1100 miles? Answer: 8.85 ms. 2. 1.2 How many dollars per millisecond would the federal government have to collect to retire a deficit of $100 billion in one year? Answer: $3.17/ms. SELFCHECK: Also try Chapter Problems 1.2, 1.3, and 1.6. 1.3 Circuit Analysis: An Overview We look broadly at engineering design, specifically the design of electric circuits, before becoming involved in the details of circuit analysis. This overview provides you with a perspective on where circuit analysis fits within the whole of circuit design. Even though this book focuses on circuit analysis, we try to provide opportunities for circuit design where appropriate. All engineering designs begin with a need 1, as shown in Fig. 1.4. This need may come from the desire to improve on an existing design, or it may be something brand new. A careful assessment of the need results in design specifications, which are measurable characteristics of a proposed design. Once a design is proposed, the design specifications 2 allow us to assess whether or not the design actually meets the need. Figure 1.4 A conceptual model for electrical engineering design. Figure 1.4 Full Alternative Text A concept 3 for the design comes next. The concept derives from a complete understanding of the design specifications coupled with an insight into the need, which comes from education and experience. The concept may be realized as a sketch, as a written description, or as some other form. Often the next step is to translate the concept into a mathematical model. A commonly used mathematical model for electrical systems is a circuit model 4. The elements that make up the circuit model are called ideal circuit components. An ideal circuit component is a mathematical model of an actual electrical component, like a battery or a light bulb. The ideal circuit components used in a circuit model should represent the behavior of the actual electrical components to an acceptable degree of accuracy. The tools of circuit analysis 5, the focus of this book, are then applied to the circuit. Circuit analysis uses mathematical techniques to predict the behavior of the circuit model and its ideal circuit components. A comparison between the desired behavior, from the design specifications, and the predicted behavior, from circuit analysis, may lead to refinements in the circuit model and its ideal circuit elements. Once the desired and predicted behaviors are in agreement, a physical prototype 6 can be constructed. The physical prototype is an actual electrical system, constructed from actual electrical components. Measurements determine the quantitative behavior of the physical system. This actual behavior is compared with the desired behavior from the design specifications and the predicted behavior from circuit analysis. The comparisons may result in refinements to the physical prototype, the circuit model, or both. This iterative process, in which models, components, and systems are continually refined, usually produces a design that accurately satisfies the design specifications and thus meets the need. Circuit analysis clearly plays a very important role in the design process. Because circuit analysis is applied to circuit models, practicing engineers try to use mature circuit models so that the resulting designs will meet the design specifications in the first iteration. In this book, we use models that have been tested for at least 40 years; you can assume that they are mature. The ability to model actual electrical systems with ideal circuit elements makes circuit theory extremely useful to engineers. Saying that the interconnection of ideal circuit elements can be used to quantitatively predict the behavior of a system implies that we can describe the interconnection with mathematical equations. For the mathematical equations to be useful, we must write them in terms of measurable quantities. In the case of circuits, these quantities are voltage and current, which we discuss in Section 1.4. The study of circuit analysis involves understanding the behavior of each ideal circuit element in terms of its voltage and current and understanding the constraints imposed on the voltage and current as a result of interconnecting the ideal elements. 1.4 Voltage and Current The concept of electric charge is the basis for describing all electrical phenomena. Let’s review some important characteristics of electric charge. Electric charge is bipolar, meaning that electrical effects are described in terms of positive and negative charges. Electric charge exists in discrete quantities, which are integer multiples of the electronic charge, 1.6022×10−19 C. Electrical effects are attributed to both the separation of charge and charges in motion. In circuit theory, the separation of charge creates an electric force (voltage), and the motion of charge creates an electric fluid (current). The concepts of voltage and current are useful from an engineering point of view because they can be expressed quantitatively. Whenever positive and negative charges are separated, energy is expended. Voltage is the energy per unit charge created by the separation. We express this ratio in differential form as Definition of Voltage v=dwdq, (1.1) where v=the voltage in volts,w=the energy in joules,q=the charge in coulombs. The electrical effects caused by charges in motion depend on the rate of charge flow. The rate of charge flow is known as the electric current, which is expressed as Definition of Current i=dqdt, (1.2) where i=the current in amperes,q=the charge in coulombs,t=the time in seconds. Equations 1.1 and 1.2 define the magnitude of voltage and current, respectively. The bipolar nature of electric charge requires that we assign polarity references to these variables. We will do so in Section 1.5. Although current is made up of discrete moving electrons, we do not need to consider them individually because of the enormous number of them. Rather, we can think of electrons and their corresponding charge as one smoothly flowing entity. Thus, i is treated as a continuous variable. One advantage of using circuit models is that we can model a component strictly in terms of the voltage and current at its terminals. Thus, two physically different components could have the same relationship between the terminal voltage and terminal current. If they do, for purposes of circuit analysis, they are identical. Once we know how a component behaves at its terminals, we can analyze its behavior in a circuit. However, when developing component models, we are interested in a component’s internal behavior. We might want to know, for example, whether charge conduction is taking place because of free electrons moving through the crystal lattice structure of a metal or whether it is because of electrons moving within the covalent bonds of a semiconductor material. These concerns are beyond the realm of circuit theory, so in this book we use component models that have already been developed. 1.5 The Ideal Basic Circuit Element An ideal basic circuit element has three attributes. 1. It has only two terminals, which are points of connection to other circuit components. 2. It is described mathematically in terms of current and/or voltage. 3. It cannot be subdivided into other elements. Using the word ideal implies that a basic circuit element does not exist as a realizable physical component. Ideal elements can be connected in order to model actual devices and systems, as we discussed in Section 1.3. Using the word basic implies that the circuit element cannot be further reduced or subdivided into other elements. Thus, the basic circuit elements form the building blocks for constructing circuit models, but they themselves cannot be modeled with any other type of element. Figure 1.5 represents an ideal basic circuit element. The box is blank because we are making no commitment at this time as to the type of circuit element it is. In Fig. 1.5, the voltage across the terminals of the box is denoted by v, and the current in the circuit element is denoted by i. The plus and minus signs indicate the polarity reference for the voltage, and the arrow placed alongside the current indicates its reference direction. Table 1.4 interprets the voltage polarity and current direction, given positive or negative numerical values of v and i. Note that algebraically the notion of positive charge flowing in one direction is equivalent to the notion of negative charge flowing in the opposite direction. Figure 1.5 An ideal basic circuit element. Figure 1.5 Full Alternative Text Table 1.4 Interpretation of Reference Directions in Fig. 1.5 Table 1.4 Full Alternative Text Assigning the reference polarity for voltage and the reference direction for current is entirely arbitrary. However, once you have assigned the references, you must write all subsequent equations to agree with the chosen references. The most widely used sign convention applied to these references is called the passive sign convention, which we use throughout this book. Passive Sign Convention Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element (as in Fig. 1.5), use a positive sign in any expression that relates the voltage to the current. Otherwise, use a negative sign. We apply this sign convention in all the analyses that follow. Our purpose for introducing it even before we have introduced the different types of basic circuit elements is to emphasize that selecting polarity references is not a function either of the basic elements or the type of interconnections made with the basic elements. We apply and interpret the passive sign convention for power calculations in Section 1.6. Example 1.2 illustrates one use of the equation defining current. Example 1.2 Relating Current and Charge No charge exists at the upper terminal of the element in Fig. 1.5 for t<0. At t=0, a 5 A current begins to flow into the upper terminal. 1. Derive the expression for the charge accumulating at the upper terminal of the element for t>0. 2. If the current is stopped after 10 seconds, how much charge has accumulated at the upper terminal? Solution 1. From the definition of current given in Eq. 1.2, the expression for charge accumulation due to current flow is q(t)=∫0ti(x)dx. Therefore, q(t)=∫0t5dx=5x0t=5t−5(0)=5t C for t>0. 2. The total charge that accumulates at the upper terminal in 10 seconds due to a 5 A current is q(10)=5(10)=50 C. Assessment Problems Objective 2—Know and be able to use the definitions of voltage and current 1. 1.3 The current at the terminals of the element in Fig. 1.5 is i=0,t<0;i=20e−5000t, A,t≥0; Calculate the total charge (in microcoulombs) entering the element at its upper terminal. Answer: 4000 μC. 2. 1.4 The expression for the charge entering the upper terminal of Fig. 1.5 is q=1α2−(tα+1α2)e−αt C. Find the maximum value of the current entering the terminal if α=0.03679 s−1. Answer: 10 A. SELFCHECK: Also try Chapter Problem 1.7. 1.6 Power and Energy Power and energy calculations are important in circuit analysis. Although voltage and current are useful variables in the analysis and design of electrically based systems, the useful output of the system often is nonelectrical (e.g., sound emitted from a speaker or light from a light bulb), and this output is conveniently expressed in terms of power or energy. Also, all practical devices have limitations on the amount of power that they can handle. In the design process, therefore, voltage and current calculations by themselves are not sufficient to determine whether or not a design meets its specifications. We now relate power and energy to voltage and current and at the same time use the power calculation to illustrate the passive sign convention. Recall from basic physics that power is the time rate of expending or absorbing energy. (A water pump rated 75 kW can deliver more liters per second than one rated 7.5 kW.) Mathematically, energy per unit time is expressed in the form of a derivative, or Definition of Power p=dwdt, (1.3) where p=the power in watts,w=the energy in joules,t=the time in seconds. Thus, 1 W is equivalent to 1 J/s. The power associated with the flow of charge follows directly from the definition of voltage and current in Eqs. 1.1 and 1.2, or p=dwdt=(dwdq)(dqdt), so Power Equation p=vi,(1.4) where p=the power in watts,v=the voltage in volts,i=the current in amperes. Equation 1.4 shows that the power associated with a basic circuit element is the product of the current in the element and the voltage across the element. Therefore, power is a quantity associated with a circuit element, and we have to determine from our calculation whether power is being delivered to the circuit element or extracted from it. This information comes from correctly applying and interpreting the passive sign convention (Section 1.5). If we use the passive sign convention, Eq. 1.4 is correct if the reference direction for the current is in the direction of the reference voltage drop across the terminals. Otherwise, Eq. 1.4 must be written with a minus sign. In other words, if the current reference is in the direction of a reference voltage rise across the terminals, the expression for the power is p=−vi. The algebraic sign of power is based on charge movement through voltage drops and rises. As positive charges move through a drop in voltage, they lose energy, and as they move through a rise in voltage, they gain energy. Figure 1.6 summarizes the relationship between the polarity references for voltage and current and the expression for power. Figure 1.6 Polarity references and the expression for power. Figure 1.6 Full Alternative Text 1.69 Full Alternative Text 1.69 Full Alternative Text 1.69 Full Alternative Text We can now state the rule for interpreting the algebraic sign of power: Interpreting Algebraic Sign of Power If the power is positive (that is, if p>0), power is being delivered to the circuit element represented by the box. If the power is negative (that is, if p<0), power is being extracted from the circuit element. Example 1.3 shows that the passive sign convention generates the correct sign for power regardless of the voltage polarity and current direction you choose. Example 1.3 Using the Passive Sign Convention 1. Suppose you have selected the polarity references shown in Fig. 1.6(b). Your calculations for the current and voltage yield the following numerical results: i=4 A and v=−10 V. Calculate the power associated with the circuit element and determine whether it is absorbing or supplying power. 2. Your classmate is solving the same problem but has chosen the reference polarities shown in Fig. 1.6(c). Her calculations for the current and voltage show that i=−4 A and v=10 V. What power does she calculate? Solution 1. The power associated with the circuit element in Fig. 1.6(b) is p=−(−10)(4)=40 W. Thus, the circuit element is absorbing 40 W. 2. Your classmate calculates that the power associated with the circuit element in Fig. 1.6(c) is p=−(10)(−4)=40 W. Using the reference system in Fig. 1.6(c) gives the same conclusion as using the reference system in Fig. 1.6(b)—namely, that the circuit element is absorbing 40 W. In fact, any of the reference systems in Fig. 1.6 yields this same result. Example 1.4 illustrates the relationship between voltage, current, power, and energy for an ideal basic circuit element and the use of the passive sign convention. Example 1.4 Relating Voltage, Current, Power, and Energy Assume that the voltage at the terminals of the element in Fig. 1.5, whose current was defined in Assessment Problem 1.3, is v=0t<0;v=10e−5000t kV, t≥0. 1. Calculate the power supplied to the element at 1 ms. 2. Calculate the total energy (in joules) delivered to the circuit element. Solution 1. Since the current is entering the + terminal of the voltage drop defined for the element in Fig. 1.5, we use a “+” sign in the power equation. p = vi = (10,000e−5000t)(20e−5000t) = 200,000e −10,000t W.p(0.001)= 200,000e − 10,000(0.0001) = 200,000e −10= 200,000(45.4×10−6) = 9.08 W. 2. From the definition of power given in Eq. 1.3, the expression for energy is w(t)=∫0tp(x)dx. To find the total energy delivered, integrate the expresssion for power from zero to infinity. Therefore, wtotal=∫0∞200,000e−10,000x dx=200,000e−10,000x−10,0000∞ =−20e−∞−(−20e−0 )=0+20=20 J. Thus, the total energy supplied to the circuit element is 20 J. Assessment Problems Objective 3—Know and use the definitions of power and energy; Objective 4—Be able to use the passive sign convention 1. 1.5 Assume that a 20 V voltage drop occurs across an element from terminal 2 to terminal 1 and that a current of 4 A enters terminal 2. 1. Specify the values of v and i for the polarity references shown in Fig. 1.6(a)–(d). 2. Calculate the power associated with the circuit element. 3. Is the circuit element absorbing or delivering power? Answer: 1. Circuit 1.6(a): v = −20 V,i=−4 A; circuit 1.6(b): v = −20 V,v= −20 V,i=4 A; circuit 1.6(c): v = 20 V,i=−4 A; circuit 1.6(d): v = 20 V,i=4 A; 2. 80 W; 3. absorbing. 2. 1.6 The voltage and current at the terminals of the circuit element in Fig. 1.5 are zero for t<0. For t≥0, they are v = 80,000t e −500t V, t≥0; i = 15t e −500t A, t≥0. 1. Find the time when the power delivered to the circuit element is maximum. 2. Find the maximum value of power. 3. Find the total energy delivered to the circuit element. Answer: 1. 2 ms; 2. 649.6 mW; 3. 2.4 mJ. 3. 1.7 A highvoltage directcurrent (dc) transmission line between Celilo, Oregon, and Sylmar, California, is operating at 800 kV and carrying 1800 A, as shown. Calculate the power (in megawatts) at the Oregon end of the line and state the direction of power flow. Answer: 1440 MW, Celilo to Sylmar SELFCHECK: Also try Chapter Problems 1.15, 1.18, and 1.25. Practical Perspective Balancing Power A circuit model for distributing power to a typical home is shown in Fig. 1.7, with voltage polarities and current directions defined for all of the circuit components. Circuit analysis gives values for all of these voltages and currents, as summarized in Table 1.5. To determine whether or not the values given are correct, calculate the power associated with each component. Use the passive sign convention in the power calculations, as shown in the following. Figure 1.7 Circuit model for power distribution in a home, with voltages and currents defined. Figure 1.7 Full Alternative Text Table 1.5 Voltage and Current Values for the Circuit in Fig. 1.7 Table 1.5 Full Alternative Text p a = v a i a =( 120 )( −10 )=−1200 W p b = − v b i b =−( 120 )( 9 )=−1080 W p c = v c i c =( 10 )( 10 )=100 W p d = − v d i d =−( 10 )( 1 )=−10 W p e = v e i e =( −10 )( −9 )=90 W p f = − v f i f =−( −100 )( 5 )=500 W p g = v g i g =( 120 )( 4 )=480 W p h = v h i h =( −220 )( −5 )=1100 W The power calculations show that components a, b, and d are supplying power, since the power values are negative, while components c, e, f, g, and h are absorbing power. Now check to see if the power balances by finding the total power supplied and the total power absorbed. psupplied=pa+pb+pd=−1200−1080−10= −2290 Wpabsorbed=pc+pe+pf+pg+ph=100+90+500+480+1100=2270 Wpsupplied −2290+2270=−20 W Something is wrong—if the values for voltage and current in this circuit are correct, the total power should be zero! There is an error in the data, and we can find it from the calculated powers if the error exists in the sign of a single component. Note that if we divide the total power by 2, we get −10 W, which is the power calculated for component d. If the power for component d is +10 W, the total power would be 0. Circuit analysis techniques from upcoming chapters can be used to show that the current through component d should be −1 A, not +1 A as given in Table 1.5. SELFCHECK: Assess your understanding of the Practical Perspective by trying Chapter Problems 1.34 and 1.35. Summary The International System of Units (SI) enables engineers to communicate in a meaningful way about quantitative results. Table 1.1 summarizes the SI units; Table 1.2 presents some useful derived SI units. (See page 10.) A circuit model is a mathematical representation of an electrical system. Circuit analysis, used to predict the behavior of a circuit model, is based on the variables of voltage and current. (See page 12.) Voltage is the energy per unit charge created by charge separation and has the SI unit of volt. (See page 13.) v=dw/dq Current is the rate of charge flow and has the SI unit of ampere. (See page 13.) i=dq/dt The ideal basic circuit element is a twoterminal component that cannot be subdivided; it can be described mathematically in terms of its terminal voltage and current. (See page 14.) The passive sign convention uses a positive sign in the expression that relates the voltage and current at the terminals of an element when the reference direction for the current through the element is in the direction of the reference voltage drop across the element. (See page 14.) Power is energy per unit of time and is equal to the product of the terminal voltage and current; it has the SI unit of watt. (See page 16.) p=dw/dt=vi The algebraic sign of power is interpreted as follows: If p>0, power is being delivered to the circuit or circuit component. If p<0, power is being extracted from the circuit or circuit component. (See page 16.) Problems Section 1.2 1. 1.1 The line described in Assessment Problem 1.7 is 845 mi in length. The line contains four conductors, each weighing 2526 lb per 1000 ft. How many kilograms of conductor are in the line? 2. 1.2 A 32inch monitor contains 3840×2160 picture elements, or pixels. Each pixel is represented in 24 bits of memory. A byte of memory is 8 bits. 1. a) How many megabytes (MB) of memory are required to store the information displayed on the monitor? 2. b) To display a video on the monitor, the image must be refreshed 30 times per second. How many terabytes (TB) of memory are required to store a 2 hr video? 3. c) For the video described in part (b), how fast must the image data in memory be moved to the monitor? Express your answer in gigabits per second (Gb/s). 3. 1.3 Some species of bamboo can grow (250 mm/day). Assume individual cells in the plant are 10 μm long. 1. a) How long, on average, does it take a bamboo stalk to grow 1 cell length? 2. b) How many cell lengths are added in one week, on average? 4. 1.4 A handheld video player displays 480×320 picture elements (pixels) in each frame of the video. Each pixel requires 2 bytes of memory. Videos are displayed at a rate of 30 frames per second. How many hours of video will fit in a 32 gigabyte memory? 5. 1.5 The 16 gigabyte (GB=230 bytes) flash memory chip for an MP3 player is 11 mm by 15 mm by 1 mm. This memory chip holds 20,000 photos. 1. a) How many photos fit into a cube whose sides are 1 mm? 2. b) How many bytes of memory are stored in a cube whose sides are 200 μm? 6. 1.6 There are approximately 260 million passenger vehicles registered in the United States. Assume that the battery in the average vehicle stores 540 watthours (Wh) of energy. Estimate (in gigawatthours) the total energy stored in US passenger vehicles. Section 1.4 1. 1.7 The current entering the upper terminal of Fig. 1.5 is i=24 cos 4000t A Assume the charge at the upper terminal is zero at the instant the current is passing through its maximum value. Find the expression for q(t). 2. 1.8 How much energy is imparted to an electron as it flows through a 6 V battery from the positive to the negative terminal? Express your answer in attojoules. 3. 1.9 In electronic circuits it is not unusual to encounter currents in the microampere range. Assume a 35 μA current, due to the flow of electrons. What is the average number of electrons per second that flow past a fixed reference cross section that is perpendicular to the direction of flow? 4. 1.10 There is no charge at the upper terminal of the element in Fig. 1.5 for t<0. At t=0 a current of 125e−2500t mA enters the upper terminal. 1. a) Derive the expression for the charge that accumulates at the upper terminal for t>0. 2. b) Find the total charge that accumulates at the upper terminal. 3. c) If the current is stopped at t=0.5 ms, how much charge has accumulated at the upper terminal? 5. 1.11 The current at the terminals of the element in Fig. 1.5 is i = 0,t<0;i = 40te−500tA,t≥0. 1. a) Find the expression for the charge accumulating at the upper terminal. 2. b) Find the charge that has accumulated at t=1 ms. Sections 1.5–1.6 1. 1.12 When a car has a dead battery, it can often be started by connecting the battery from another car across its terminals. The positive terminals are connected together as are the negative terminals. The connection is illustrated in Fig. P1.12. Assume the current i in Fig. P1.12 is measured and found to be 40 A. 1. a) Which car has the dead battery? 2. b) If this connection is maintained for 1.5 min, how much energy is transferred to the dead battery? Figure P1.12 Figure P1.12 Full Alternative Text 2. 1.13 Two