James_W._Nilsson_Susan_Riedel_Electric.pdf

 A List of Tables Table No. Title Page No. 1.1 The International System of Units (SI)...

 A List of Tables Table No. Title Page No. 1.1 The International System of Units (SI) 9 1.2 Derived Units in SI 9 1.3 Standardized Prefixes to Signify Powers of 10 9 1.4 Interpretation of Reference Directions in Fig. 1.5 13 4.1 Terms for Describing Circuits 91 4.2 PSpice Sensitivity Analysis Results 128 6.1 Terminal Equations for Ideal Inductors and Capacitors 203 6.2 Equations for Series- and Parallel-Connected Inductors and Capacitors 203 7.1 Value of e - t>t for t Equal to Integral Multiples of t 217 8.1 Natural Response Parameters of the Parallel RLC Circuit 269 8.2 The Response of a Second-Order Circuit is Overdamped, Underdamped, or Critically Damped 295 8.3 In Determining the Natural Response of a Second-Order Circuit, We First Determine Whether it is Over-, Under-, or Critically Damped, and Then We Solve the Appropriate Equations 295 8.4 In Determining the Step Response of a Second-Order Circuit, We Apply the Appropriate Equations Depending on the Damping 296 9.1 Impedance and Reactance Values 318 9.2 Admittance and Susceptance Values 322 9.3 Impedance and Related Values 345 10.1 Annual Energy Requirements of Electric Household Appliances 365 10.2 Three Power Quantities and Their Units 368 12.1 An Abbreviated List of Laplace Transform Pairs 435 12.2 An Abbreviated List of Operational Transforms 440 12.3 Four Useful Transform Pairs 451 13.1 Summary of the s-Domain Equivalent Circuits 468 13.2 Numerical Values of vo(t) 492 14.1 Input and Output Voltage Magnitudes for Several Frequencies 527 15.1 Normalized (so that vc = 1 rad>s) Butterworth Polynomials up to the Eighth Order 577 17.1 Fourier Transforms of Elementary Functions 653 17.2 Operational Transforms 658 18.1 Parameter Conversion Table 682 18.2 Terminated Two-Port Equations 688 Greek Alphabet A a Alpha I i Iota P r Rho B b Beta K k Kappa © s Sigma ≠ g Gamma ¶ l Lambda T t Tau ¢ d Delta M m Mu ⌼ y Upsilon E P Epsilon N n Nu £ f Phi Z z Zeta ⌶ j Xi X x Chi H h Eta O o Omicron ° c Psi ™ u Theta ß p Pi Æ v Omega ELECTRIC CIRCUITS TENTH EDITION This page intentionally left blank  ELECTRIC CIRCUITS TENTH EDITION James W. Nilsson Professor Emeritus Iowa State University Susan A. Riedel Marquette University Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Vice President and Editorial Director: Cover Design: Black Horse Designs Marcia J. Horton Cover Art: Inverter 04 Oil painting by Ben Leone Executive Editor: Andrew Gilfillan “TechScape” Collection. www.benleone.com Editorial Assistant: Sandra Rodriguez Manager, Cover Visual Research & Permissions: Marketing Manager: Tim Galligan Karen Sanatar Senior Managing Editor: Scott Disanno Photo Researcher: Marta Samsel Production Editor: Rose Kernan Composition: Integra Publishing Services Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Copyright © 2015, 2008, 2005 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, New Jersey, 07458. 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 likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey, 07458. Library of Congress Cataloging-in-Publication Data Nilsson, James William. Electric circuits / James W. Nilsson, Professor Emeritus, Iowa State University, Susan A. Riedel, Marquette University.—Tenth edition. pages cm ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0 1. Electric circuits. I. Riedel, Susan A. II. Title. TK545.N54 2015 621.319'2—dc23 2013037725 10 9 8 7 6 5 4 3 2 ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0 To Anna This page intentionally left blank Brief Contents List of Examples xiii Preface xvii Chapter 1 Circuit Variables 2 Chapter 2 Circuit Elements 24 Chapter 3 Simple Resistive Circuits 56 Chapter 4 Techniques of Circuit Analysis 88 Chapter 5 The Operational Amplifier 144 Chapter 6 Inductance, Capacitance, and Mutual Inductance 174 Chapter 7 Response of First-Order RL and RC Circuits 212 Chapter 8 Natural and Step Responses of RLC Circuits 264 Chapter 9 Sinusoidal Steady-State Analysis 304 Chapter 10 Sinusoidal Steady-State Power Calculations 358 Chapter 11 Balanced Three-Phase Circuits 396 Chapter 12 Introduction to the Laplace Transform 426 Chapter 13 The Laplace Transform in Circuit Analysis 464 Chapter 14 Introduction to Frequency Selective Circuits 520 Chapter 15 Active Filter Circuits 556 Chapter 16 Fourier Series 602 Chapter 17 The Fourier Transform 642 Chapter 18 Two-Port Circuits 676 Appendix A The Solution of Linear Simultaneous Equations 703 Appendix B Complex Numbers 723 Appendix C More on Magnetically Coupled Coils and Ideal Transformers 729 Appendix D The Decibel 737 Appendix E Bode Diagrams 739 Appendix F An Abbreviated Table of Trigonometric Identities 757 Appendix G An Abbreviated Table of Integrals 759 Appendix H Common Standard Component Values 761 Answers to Selected Problems 763 Index 775 vii This page intentionally left blank Contents List of Examples xiii Chapter 4 Techniques of Circuit Preface xvii Analysis 88 Practical Perspective: Circuits with Realistic Chapter 1 Circuit Variables 2 Resistors 89 4.1 Terminology 90 Practical Perspective: Balancing Power 3 4.2 Introduction to the Node-Voltage 1.1 Electrical Engineering: An Overview 4 Method 93 1.2 The International System of Units 8 4.3 The Node-Voltage Method and Dependent 1.3 Circuit Analysis: An Overview 10 1.4 Voltage and Current 11 Sources 95 1.5 The Ideal Basic Circuit Element 12 4.4 The Node-Voltage Method: Some Special 1.6 Power and Energy 14 Cases 96 Practical Perspective: Balancing Power 17 4.5 Introduction to the Mesh-Current Summary 18 Method 99 Problems 19 4.6 The Mesh-Current Method and Dependent Sources 102 Chapter 2 Circuit Elements 24 4.7 The Mesh-Current Method: Some Special Cases 103 Practical Perspective: Heating with Electric 4.8 The Node-Voltage Method Versus the Radiators 25 Mesh-Current Method 106 2.1 Voltage and Current Sources 26 4.9 Source Transformations 109 2.2 Electrical Resistance (Ohm’s Law) 30 4.10 Thévenin and Norton Equivalents 113 2.3 Construction of a Circuit Model 34 4.11 More on Deriving a Thévenin 2.4 Kirchhoff’s Laws 37 Equivalent 117 2.5 Analysis of a Circuit Containing Dependent 4.12 Maximum Power Transfer 120 Sources 42 4.13 Superposition 122 Practical Perspective: Heating with Electric Practical Perspective: Circuits with Realistic Radiators 46 Resistors 125 Summary 48 Summary 129 Problems 48 Problems 130 Chapter 3 Simple Resistive Circuits 56 Chapter 5 The Operational Practical Perspective: Resistive Touch Screens 57 Amplifier 144 3.1 Resistors in Series 58 Practical Perspective: Strain Gages 145 3.2 Resistors in Parallel 59 5.1 Operational Amplifier Terminals 146 3.3 The Voltage-Divider and Current-Divider 5.2 Terminal Voltages and Currents 146 Circuits 61 5.3 The Inverting-Amplifier Circuit 150 3.4 Voltage Division and Current Division 64 5.4 The Summing-Amplifier Circuit 152 3.5 Measuring Voltage and Current 66 5.5 The Noninverting-Amplifier 3.6 Measuring Resistance—The Wheatstone Circuit 153 Bridge 69 5.6 The Difference-Amplifier Circuit 155 3.7 Delta-to-Wye (Pi-to-Tee) Equivalent 5.7 A More Realistic Model for the Operational Circuits 71 Amplifier 159 Practical Perspective: Resistive Touch Practical Perspective: Strain Screens 73 Gages 162 Summary 75 Summary 164 Problems 76 Problems 165 ix x Contents Chapter 6 Inductance, Capacitance, and 9.1 The Sinusoidal Source 306 Mutual Inductance 174 9.2 The Sinusoidal Response 309 9.3 The Phasor 310 Practical Perspective: Capacitive Touch 9.4 The Passive Circuit Elements in the Frequency Screens 175 Domain 315 6.1 The Inductor 176 9.5 Kirchhoff’s Laws in the Frequency 6.2 The Capacitor 182 Domain 319 6.3 Series-Parallel Combinations of Inductance 9.6 Series, Parallel, and Delta-to-Wye and Capacitance 187 Simplifications 320 6.4 Mutual Inductance 189 9.7 Source Transformations and Thévenin-Norton 6.5 A Closer Look at Mutual Inductance 193 Equivalent Circuits 327 Practical Perspective: Capacitive Touch 9.8 The Node-Voltage Method 330 Screens 200 9.9 The Mesh-Current Method 331 Summary 202 9.10 The Transformer 332 Problems 204 9.11 The Ideal Transformer 336 9.12 Phasor Diagrams 342 Chapter 7 Response of First-Order RL and Practical Perspective: A Household Distribution RC Circuits 212 Circuit 344 Practical Perspective: Artificial Pacemaker 213 Summary 345 7.1 The Natural Response of an RL Circuit 214 Problems 346 7.2 The Natural Response of an RC Circuit 220 7.3 The Step Response of RL and RC Circuits 224 Chapter 10 Sinusoidal Steady-State 7.4 A General Solution for Step and Natural Power Calculations 358 Responses 231 Practical Perspective: Vampire 7.5 Sequential Switching 236 Power 359 7.6 Unbounded Response 240 10.1 Instantaneous Power 360 7.7 The Integrating Amplifier 241 10.2 Average and Reactive Power 361 Practical Perspective: Artificial Pacemaker 245 10.3 The rms Value and Power Calculations 366 Summary 246 10.4 Complex Power 368 Problems 247 10.5 Power Calculations 369 10.6 Maximum Power Transfer 376 Chapter 8 Natural and Step Responses Practical Perspective: Vampire of RLC Circuits 264 Power 382 Practical Perspective: Clock for Computer Summary 384 Timing 265 Problems 385 8.1 Introduction to the Natural Response of a Parallel RLC Circuit 266 Chapter 11 Balanced Three-Phase 8.2 The Forms of the Natural Response of a Circuits 396 Parallel RLC Circuit 270 Practical Perspective: Transmission and 8.3 The Step Response of a Parallel RLC Circuit 280 Distribution of Electric Power 397 8.4 The Natural and Step Response of a Series RLC 11.1 Balanced Three-Phase Voltages 398 Circuit 285 11.2 Three-Phase Voltage Sources 399 8.5 A Circuit with Two Integrating Amplifiers 289 11.3 Analysis of the Wye-Wye Circuit 400 Practical Perspective: Clock for Computer 11.4 Analysis of the Wye-Delta Circuit 405 Timing 293 11.5 Power Calculations in Balanced Three-Phase Summary 295 Circuits 408 Problems 296 11.6 Measuring Average Power in Three-Phase Circuits 413 Chapter 9 Sinusoidal Steady-State Practical Perspective: Transmission and Analysis 304 Distribution of Electric Power 416 Practical Perspective: A Household Distribution Summary 417 Circuit 305 Problems 418  Contents xi Chapter 12 Introduction to the Laplace Chapter 15 Active Filter Circuits 556 Transform 426 Practical Perspective: Bass Volume Practical Perspective: Transient Effects 427 Control 557 12.1 Definition of the Laplace Transform 428 15.1 First-Order Low-Pass and High-Pass 12.2 The Step Function 429 Filters 558 12.3 The Impulse Function 431 15.2 Scaling 562 12.4 Functional Transforms 434 15.3 Op Amp Bandpass and Bandreject Filters 564 12.5 Operational Transforms 435 15.4 Higher Order Op Amp Filters 571 12.6 Applying the Laplace Transform 440 15.5 Narrowband Bandpass and Bandreject 12.7 Inverse Transforms 442 Filters 584 12.8 Poles and Zeros of F(s) 452 Practical Perspective: Bass Volume 12.9 Initial- and Final-Value Theorems 453 Control 589 Practical Perspective: Transient Summary 592 Effects 456 Problems 593 Summary 457 Problems 458 Chapter 16 Fourier Series 602 Practical Perspective: Active High-Q Filters 603 Chapter 13 The Laplace Transform in 16.1 Fourier Series Analysis: An Overview 605 Circuit Analysis 464 16.2 The Fourier Coefficients 606 16.3 The Effect of Symmetry on the Fourier Practical Perspective: Surge Suppressors 465 Coefficients 609 13.1 Circuit Elements in the s Domain 466 16.4 An Alternative Trigonometric Form of the 13.2 Circuit Analysis in the s Domain 468 Fourier Series 615 13.3 Applications 470 16.5 An Application 617 13.4 The Transfer Function 482 16.6 Average-Power Calculations with Periodic 13.5 The Transfer Function in Partial Fraction Functions 621 Expansions 484 16.7 The rms Value of a Periodic Function 624 13.6 The Transfer Function and the Convolution 16.8 The Exponential Form of the Fourier Integral 487 Series 625 13.7 The Transfer Function and the Steady-State 16.9 Amplitude and Phase Spectra 628 Sinusoidal Response 493 Practical Perspective: Active High-Q Filters 630 13.8 The Impulse Function in Circuit Summary 632 Analysis 496 Problems 633 Practical Perspective: Surge Suppressors 503 Summary 504 Problems 505 Chapter 17 The Fourier Transform 642 Practical Perspective: Filtering Digital Signals 643 Chapter 14 Introduction to Frequency 17.1 The Derivation of the Fourier Transform 644 Selective Circuits 520 17.2 The Convergence of the Fourier Integral 646 Practical Perspective: Pushbutton Telephone 17.3 Using Laplace Transforms to Find Fourier Circuits 521 Transforms 648 14.1 Some Preliminaries 522 17.4 Fourier Transforms in the Limit 651 14.2 Low-Pass Filters 524 17.5 Some Mathematical Properties 653 14.3 High-Pass Filters 530 17.6 Operational Transforms 655 14.4 Bandpass Filters 534 17.7 Circuit Applications 659 14.5 Bandreject Filters 543 17.8 Parseval’s Theorem 662 Practical Perspective: Pushbutton Telephone Practical Perspective: Filtering Digital Circuits 548 Signals 669 Summary 548 Summary 670 Problems 549 Problems 670 xii Contents Chapter 18 Two-Port Circuits 676 Appendix C More on Magnetically Practical Perspective: Characterizing an Coupled Coils and Ideal Unknown Circuit 677 Transformers 729 18.1 The Terminal Equations 678 C.1 Equivalent Circuits for Magnetically Coupled 18.2 The Two-Port Parameters 679 Coils 729 18.3 Analysis of the Terminated Two-Port C.2 The Need for Ideal Transformers in the Circuit 687 Equivalent Circuits 733 18.4 Interconnected Two-Port Circuits 692 Practical Perspective: Characterizing an Unknown Circuit 695 Appendix D The Decibel 737 Summary 696 Problems 696 Appendix E Bode Diagrams 739 E.1 Real, First-Order Poles and Zeros 739 Appendix A The Solution of Linear E.2 Straight-Line Amplitude Plots 740 Simultaneous Equations 703 E.3 More Accurate Amplitude Plots 744 A.1 Preliminary Steps 703 E.4 Straight-Line Phase Angle Plots 745 A.2 Cramer’s Method 704 E.5 Bode Diagrams: Complex Poles and Zeros 747 A.3 The Characteristic Determinant 704 E.6 Amplitude Plots 749 A.4 The Numerator Determinant 704 E.7 Correcting Straight-Line Amplitude Plots 750 A.5 The Evaluation of a Determinant 705 E.8 Phase Angle Plots 753 A.6 Matrices 707 A.7 Matrix Algebra 708 Appendix F An Abbreviated Table of A.8 Identity, Adjoint, and Inverse Matrices 712 A.9 Partitioned Matrices 715 Trigonometric Identities 757 A.10 Applications 718 Appendix G An Abbreviated Table of Appendix B Complex Numbers 723 Integrals 759 B.1 Notation 723 B.2 The Graphical Representation of a Complex Number 724 Appendix H Common Standard B.3 Arithmetic Operations 725 Component Values 761 B.4 Useful Identities 726 B.5 The Integer Power of a Complex Answers to Selected Problems 763 Number 727 B.6 The Roots of a Complex Number 727 Index 775 List of Examples Chapter 1 4.6 Understanding the Node-Voltage Method Versus Mesh-Current Method 107 1.1 Using SI Units and Prefixes for Powers of 10 10 4.7 Comparing the Node-Voltage and Mesh-Current 1.2 Relating Current and Charge 14 Methods 108 1.3 Relating Voltage, Current, Power, and Energy 16 4.8 Using Source Transformations to Solve a Circuit 110 Chapter 2 4.9 Using Special Source Transformation 2.1 Testing Interconnections of Ideal Sources 28 Techniques 112 2.2 Testing Interconnections of Ideal Independent 4.10 Finding the Thévenin Equivalent of a Circuit and Dependent Sources 29 with a Dependent Source 116 2.3 Calculating Voltage, Current, and Power for a 4.11 Finding the Thévenin Equivalent Using a Test Simple Resistive Circuit 33 Source 118 2.4 Constructing a Circuit Model of a Flashlight 34 4.12 Calculating the Condition for Maximum Power 2.5 Constructing a Circuit Model Based on Terminal Transfer 121 Measurements 36 4.13 Using Superposition to Solve a Circuit 124 2.6 Using Kirchhoff’s Current Law 39 2.7 Using Kirchhoff’s Voltage Law 40 Chapter 5 2.8 Applying Ohm’s Law and Kirchhoff’s Laws to 5.1 Analyzing an Op Amp Circuit 149 Find an Unknown Current 40 5.2 Designing an Inverting Amplifier 151 2.9 Constructing a Circuit Model Based on Terminal 5.3 Designing a Noninverting Amplifier 154 Measurements 41 5.4 Designing a Difference Amplifier 155 2.10 Applying Ohm’s Law and Kirchhoff’s Laws to Find an Unknown Voltage 44 2.11 Applying Ohm’s Law and Kirchhoff’s Law in an Chapter 6 Amplifier Circuit 45 6.1 Determining the Voltage, Given the Current, at the Terminals of an Inductor 177 Chapter 3 6.2 Determining the Current, Given the Voltage, at the Terminals of an Inductor 178 3.1 Applying Series-Parallel Simplification 60 6.3 Determining the Current, Voltage, Power, 3.2 Analyzing the Voltage-Divider Circuit 62 and Energy for an Inductor 180 3.3 Analyzing a Current-Divider Circuit 63 6.4 Determining Current, Voltage, Power, and 3.4 Using Voltage Division and Current Division to Energy for a Capacitor 184 Solve a Circuit 66 6.5 Finding v, p, and w Induced by a Triangular 3.5 Using a d’Arsonval Ammeter 68 Current Pulse for a Capacitor 185 3.6 Using a d’Arsonval Voltmeter 68 6.6 Finding Mesh-Current Equations for a Circuit 3.7 Applying a Delta-to-Wye Transform 72 with Magnetically Coupled Coils 192 Chapter 4 Chapter 7 4.1 Identifying Node, Branch, Mesh and Loop in a 7.1 Determining the Natural Response of an Circuit 90 RL Circuit 218 4.2 Using the Node-Voltage Method 94 7.2 Determining the Natural Response of an 4.3 Using the Node-Voltage Method with RL Circuit with Parallel Inductors 219 Dependent Sources 95 7.3 Determining the Natural Response of an 4.4 Using the Mesh-Current Method 101 RC Circuit 222 4.5 Using the Mesh-Current Method with 7.4 Determining the Natural Response of an Dependent Sources 102 RC Circuit with Series Capacitors 223 xiii xiv List of Examples 7.5 Determining the Step Response of an Chapter 9 RL Circuit 227 9.1 Finding the Characteristics of a Sinusoidal 7.6 Determining the Step Response of an Current 307 RC Circuit 230 9.2 Finding the Characteristics of a Sinusoidal 7.7 Using the General Solution Method to Find an Voltage 308 RC Circuit’s Step Response 233 9.3 Translating a Sine Expression to a Cosine 7.8 Using the General Solution Method with Zero Expression 308 Initial Conditions 234 9.4 Calculating the rms Value of a Triangular 7.9 Using the General Solution Method to Find an Waveform 308 RL Circuit’s Step Response 234 9.5 Adding Cosines Using Phasors 314 7.10 Determining the Step Response of a Circuit 9.6 Combining Impedances in Series 321 with Magnetically Coupled Coils 235 9.7 Combining Impedances in Series and in 7.11 Analyzing an RL Circuit that has Sequential Parallel 323 Switching 237 9.8 Using a Delta-to-Wye Transform in the 7.12 Analyzing an RC Circuit that has Sequential Frequency Domain 325 Switching 239 9.9 Performing Source Transformations in the 7.13 Finding the Unbounded Response in an Frequency Domain 327 RC Circuit 241 9.10 Finding a Thévenin Equivalent in the 7.14 Analyzing an Integrating Amplifier 243 Frequency Domain 328 7.15 Analyzing an Integrating Amplifier that has 9.11 Using the Node-Voltage Method in the Sequential Switching 243 Frequency Domain 330 9.12 Using the Mesh-Current Method in the Chapter 8 Frequency Domain 331 8.1 Finding the Roots of the Characteristic 9.13 Analyzing a Linear Transformer in the Equation of a Parallel RLC Circuit 269 Frequency Domain 335 8.2 Finding the Overdamped Natural Response of a 9.14 Analyzing an Ideal Transformer Circuit in the Parallel RLC Circuit 272 Frequency Domain 340 8.3 Calculating Branch Currents in the Natural 9.15 Using Phasor Diagrams to Analyze a Response of a Parallel RLC Circuit 273 Circuit 342 8.4 Finding the Underdamped Natural Response of 9.16 Using Phasor Diagrams to Analyze Capacitive a Parallel RLC Circuit 275 Loading Effects 343 8.5 Finding the Critically Damped Natural Response of a Parallel RLC Circuit 278 Chapter 10 8.6 Finding the Overdamped Step Response of a Parallel RLC Circuit 282 10.1 Calculating Average and Reactive Power 364 8.7 Finding the Underdamped Step Response of a 10.2 Making Power Calculations Involving Parallel RLC Circuit 283 Household Appliances 365 8.8 Finding the Critically Damped Step Response 10.3 Determining Average Power Delivered to a of a Parallel RLC Circuit 283 Resistor by Sinusoidal Voltage 367 8.9 Comparing the Three-Step Response Forms 284 10.4 Calculating Complex Power 369 8.10 Finding Step Response of a Parallel RLC Circuit 10.5 Calculating Average and Reactive Power 372 with Initial Stored Energy 284 10.6 Calculating Power in Parallel Loads 373 8.11 Finding the Underdamped Natural Response of 10.7 Balancing Power Delivered with Power a Series RLC Circuit 287 Absorbed in an ac Circuit 374 8.12 Finding the Underdamped Step Response of a 10.8 Determining Maximum Power Transfer without Series RLC Circuit 288 Load Restrictions 378 8.13 Analyzing Two Cascaded Integrating 10.9 Determining Maximum Power Transfer with Amplifiers 290 Load Impedance Restriction 379 8.14 Analyzing Two Cascaded Integrating Amplifiers 10.10 Finding Maximum Power Transfer with with Feedback Resistors 293 Impedance Angle Restrictions 380 10.11 Finding Maximum Power Transfer in a Circuit with an Ideal Transformer 381  List of Examples xv Chapter 11 15.9 Designing a Fourth-Order Low-Pass Butterworth Filter 579 11.1 Analyzing a Wye-Wye Circuit 403 15.10 Determining the Order of a Butterworth 11.2 Analyzing a Wye-Delta Circuit 406 Filter 582 11.3 Calculating Power in a Three-Phase Wye-Wye 15.11 An Alternate Approach to Determining Circuit 411 the Order of a Butterworth Filter 582 11.4 Calculating Power in a Three-Phase Wye-Delta 15.12 Designing a High-Q Bandpass Filter 586 Circuit 411 15.13 Designing a High-Q Bandreject Filter 588 11.5 Calculating Three-Phase Power with an Unspecified Load 412 11.6 Computing Wattmeter Readings in Three-Phase Chapter 16 Circuits 415 16.1 Finding the Fourier Series of a Triangular Waveform with No Symmetry 607 Chapter 12 16.2 Finding the Fourier Series of an Odd Function 12.1 Using Step Functions to Represent a Function with Symmetry 614 of Finite Duration 430 16.3 Calculating Forms of the Trigonometric Fourier Series for Periodic Voltage 616 Chapter 13 16.4 Calculating Average Power for a Circuit with a Periodic Voltage Source 623 13.1 Deriving the Transfer Function of a Circuit 483 16.5 Estimating the rms Value of a Periodic 13.2 Analyzing the Transfer Function Function 625 of a Circuit 485 16.6 Finding the Exponential Form of the Fourier 13.3 Using the Convolution Integral to Find Series 627 an Output Signal 491 13.4 Using the Transfer Function to Find the Steady-State Sinusoidal Response 495 Chapter 17 17.1 Using the Fourier Transform to Find Chapter 14 the Transient Response 660 17.2 Using the Fourier Transform to Find the 14.1 Designing a Low-Pass Filter 527 Sinusoidal Steady-State Response 661 14.2 Designing a Series RC Low-Pass Filter 528 17.3 Applying Parseval’s Theorem 664 14.3 Designing a Series RL High-Pass Filter 532 17.4 Applying Parseval’s Theorem to an Ideal 14.4 Loading the Series RL High-Pass Filter 532 Bandpass Filter 665 14.5 Designing a Bandpass Filter 538 17.5 Applying Parseval’s Theorem to a Low-Pass 14.6 Designing a Parallel RLC Bandpass Filter 539 Filter 666 14.7 Determining Effect of a Nonideal Voltage Source on a RLC Bandpass Filter 540 14.8 Designing a Series RLC Bandreject Filter 546 Chapter 18 18.1 Finding the z Parameters of a Two-Port Circuit 679 Chapter 15 18.2 Finding the a Parameters from 15.1 Designing a Low-Pass Op Amp Filter 559 Measurements 681 15.2 Designing a High-Pass Op Amp Filter 561 18.3 Finding h Parameters from Measurements 15.3 Scaling a Series RLC Circuit 563 and Table 18.1 684 15.4 Scaling a Prototype Low-Pass Op Amp 18.4 Analyzing a Terminated Two-Port Circuit 690 Filter 563 18.5 Analyzing Cascaded Two-Port Circuits 694 15.5 Designing a Broadband Bandpass Op Amp Filter 567 15.6 Designing a Broadband Bandreject Op Amp Filter 570 15.7 Designing a Fourth-Order Low-Pass Op Amp Filter 574 15.8 Calculating Butterworth Transfer Functions 577 This page intentionally left blank Preface The first edition of Electric Circuits, an introductory circuits text, was pub- lished in 1983. It included 100 worked examples and about 600 problems. It did not include a student workbook, supplements for PSpice or MultiSim, or any web support. Support for instructors was limited to a solution man- ual for the problems and enlarged copies of many text figures, suitable for making transparencies. Much has changed in the 31 years since Electric Circuits first appeared, and during that time this text has evolved to better meet the needs of both students and their instructors. As an example, the text now includes about 150 worked examples, about 1850 problems, and extensive supplements and web content. The tenth edition is designed to revise and improve the material presented in the text, in its supplements, and on the web. Yet the fundamental goals of the text are unchanged. These goals are: To build an understanding of concepts and ideas explicitly in terms of previous learning. Students are constantly challenged by the need to layer new concepts on top of previous concepts they may still be struggling to master. This text provides an important focus on helping students understand how new concepts are related to and rely upon concepts previously presented. To emphasize the relationship between conceptual understanding and problem-solving approaches. Developing problem-solving skills continues to be the central challenge in a first-year circuits course. In this text we include numerous Examples that present problem- solving techniques followed by Assessment Problems that enable students to test their mastery of the material and techniques intro- duced. The problem-solving process we illustrate is based on con- cepts rather than the use of rote procedures. This encourages students to think about a problem before attempting to solve it. To provide students with a strong foundation of engineering prac- tices. There are limited opportunities in a first-year circuit analysis course to introduce students to realistic engineering experiences. We continue to take advantage of the opportunities that do exist by including problems and examples that use realistic component values and represent realizable circuits. We include many problems related to the Practical Perspective problems that begin each chapter. We also include problems intended to stimulate the students’ interest in engineering, where the problems require the type of insight typical of a practicing engineer. WHY THIS EDITION? The tenth edition revision of Electric Circuits began with a thorough review of the text. This review provided a clear picture of what matters most to instructors and their students and led to the following changes: Problem solving is fundamental to the study of circuit analysis. Having a wealth of new problems to assign and work is a key to suc- cess in any circuits course. Therefore, existing end-of-chapter prob- lems were revised, and new end-of-chapter problems were added. As a result, more than 40% of the problems in the tenth edition have never appeared in any previous edition of the text. xvii xviii Preface Both students and instructors want to know how the generalized techniques presented in a first-year circuit analysis course relate to problems faced by practicing engineers. The Practical Perspective problems provide this connection between circuit analysis and the real world. We have created new Practical Perspective problems for Chapters 2, 3, 6, 7, 8, and 10. Many of the new problems represent the world of the 21st century. Each Practical Perspective problem is solved, at least in part, at the end of the chapter, and additional end- of-chapter problems can be assigned to allow students to explore the Practical Perspective topic further. The PSpice and Multisim manuals have been revised to include screenshots from the most recent versions of these software simula- tion applications. Each manual presents the simulation material in the same order as the material is presented in the text. These manu- als continue to include examples of circuits to be simulated that are drawn directly from the text. The text continues to indicate end-of- chapter problems that are good candidates for simulation using either PSpice or Multisim. Students who could benefit from additional examples and practice problems can use the Student Workbook, which has been revised to reflect changes to the tenth 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, first- order circuits, second-order circuits, AC steady-state analysis, and Laplace transform circuit analysis. The Student Workbook now includes access to Video Solutions, complete, step-by-step solution walkthroughs to representative homework problems. Learning Catalytics, a “bring your own device” student engagement, assessment, and classroom intelligence system is now available with the tenth edition. With Learning Catalytics you can: Use open-ended 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 pre-built questions or add your own to make Learning Catalytics fit your course exactly. MasteringEngineering 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 tenth edition, MasteringEngineering will offer new tutorial homework prob- lems, Coaching Activities, and Adaptive Follow-Up assignments. Visit www.masteringengineering.com for more information. HALLMARK FEATURES Chapter Problems Users of Electric Circuits have consistently rated the Chapter Problems as one of the book’s most attractive features. In the tenth edition, there are over 1650 end-of-chapter problems with approximately 40% that have never appeared in a previous edition. Problems are organized at the end of each chapter by section.  Preface xix Practical Perspectives The tenth edition continues the use of Practical Perspectives introduced with the chapter openers. They offer examples of real-world circuits, taken from real-world devices. The Practical Perspectives for six of the chapters are brand new to this edition. Every chapter begins with a brief descrip- tion of a practical application of the material that follows. Once the chap- ter material is presented, the chapter concludes with a quantitative analysis of the Practical Perspective application. A group of end-of-chap- ter problems directly relates to the Practical Perspective application. Solving some of these problems enables you to understand how to apply the chapter contents to the solution of a real-world problem. 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 end-of-chapter 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 nearly 150 examples in this text. The examples are intended to illus- trate the application of a particular concept, and also to encourage 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 solu- tion, reducing the computational burden of more complex circuits, and iterating toward a desired solution using parameter variation. This compu- tational support is often invaluable in the design process. The tenth edition includes the support of 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 tenth edition continues to support the emphasis on the design of cir- cuits 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, design-oriented 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 explo- ration with PSpice or Multisim suggests design opportunities using these xx Preface 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 lab- oratory to build and test the circuit, comparing the analysis with the meas- ured performance of the actual circuit. Accuracy All text and problems in the tenth edition have undergone our strict hallmark accuracy checking process, to ensure the most error-free book possible. RESOURCES FOR STUDENTS MasteringEngineering. MasteringEngineering provides tutorial home- work problems designed to emulate the instructor’s office hour environ- ment, guiding students through engineering concepts with self-paced individualized coaching. These in-depth tutorial homework problems pro- vide students with feedback specific to their errors and optional hints that break problems down into simpler steps. Visit www.masteringengineering.com for more information. Student Workbook. This resource teaches students techniques for solving problems presented in the text. Organized by concepts, this is a valuable problem-solving resource for all levels of students. The Student Workbook now includes access to Video Solutions, com- plete, step-by-step solution walkthroughs to representative homework problems. Introduction to Multisim and Introduction to PSpice Manuals—Updated for the tenth edition, these manuals are excellent resources for those wish- ing to integrate PSpice or Multisim into their classes. RESOURCES FOR INSTRUCTORS All instructor resources are available for download at www.pearson highered.com. If you are in need of a login and password for this site, please contact your local Pearson representative. Instructor Solutions Manual—Fully worked-out solutions to Assessment Problems and end-of-chapter 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 assignment-by-assignment basis, or the detailed work of an individual student. For more information visit www.masteringengineeing.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.  Preface xxi 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 poten- tial, 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 one-semester, two-semester, or a three-quarter sequence. Single-semester course: After covering Chapters 1–4 and Chapters 6–10 (omitting Sections 7.7 and 8.5) the instructor can choose from Chapter 5 (operational amplifiers), Chapter 11 (three-phase circuits), Chapters 13 and 14 (Laplace methods), and Chapter 18 (Two-Port Circuits) to develop the desired emphasis. Two-semester sequence: Assuming three lectures per week, the first nine chapters can be covered during the first semester, leaving Chapters 10–18 for the second semester. Academic quarter schedule: The book can be subdivided into three parts: Chapters 1–6, Chapters 7–12, and Chapters 13–18. The introduction to operational amplifier circuits in Chapter 5 can be omitted without interfering with the reading of subsequent chapters. For example, if Chapter 5 is omitted, the instructor can simply skip Section 7.7, Section 8.5, Chapter 15, and those assessment problems and end-of- chapter problems in the chapters following Chapter 5 that pertain to oper- ational amplifiers. There are several appendixes at the end of the book to help readers make effective use of their mathematical background. Appendix A reviews Cramer’s method of solving simultaneous linear equations and simple matrix algebra; complex numbers are reviewed in Appendix B; Appendix C contains additional material on magnetically coupled coils and ideal trans- formers; 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, induc- tors, and capacitors, to be used in solving many end-of-chapter problems. Selected Answers provides answers to selected end-of-chapter problems. ACKNOWLEDGMENTS There were many hard-working people behind the scenes at our pub- lisher who deserve our thanks and gratitude for their efforts on behalf of the tenth edition. At Pearson, we would like to thank Andrew Gilfillan, Rose Kernan, Gregory Dulles, Tim Galligan, 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 authors would also like to acknowledge the staff at Integra Software Solutions for their dedication and hard work in typeset- ting this text. The authors would also like to thank Kurt Norlin for his help in accuracy checking the text and problems. xxii Preface We are 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. We are pleased to receive email from instructors and students who use the book, even when they are pointing out an error we failed to catch in the review process. We have been contacted by people who use our text from all over the world, and we thank all of you for taking the time to do so. We use as many of your suggestions as possible to continue to improve the content, the pedagogy, and the presentation in this text. We are privi- leged to have the opportunity to impact the educational experience of the many thousands of future engineers who will use this text. JAMES W. NILSSON SUSAN A. RIEDEL ELECTRIC CIRCUITS TENTH EDITION  CHAPTER CHAPTER CONTENTS 1 Circuit Variables Electrical engineering is an exciting and challenging profession for anyone who has a genuine interest in, and aptitude for, 1.1 Electrical Engineering: An Overview p. 4 1.2 The International System of Units p. 8 applied science and mathematics. Over the past century and a 1.3 Circuit Analysis: An Overview p. 10 half, electrical engineers have played a dominant role in the 1.4 Voltage and Current p. 11 development of systems that have changed the way people live 1.5 The Ideal Basic Circuit Element p. 12 and work. Satellite communication links, telephones, digital com- 1.6 Power and Energy p. 14 puters, televisions, diagnostic and surgical medical equipment, assembly-line robots, and electrical power tools are representa- CHAPTER OBJECTIVES tive components of systems that define a modern technological society. As an electrical engineer, you can participate in this ongo- 1 Understand and be able to use SI units and the standard prefixes for powers of 10. ing technological revolution by improving and refining these 2 Know and be able to use the definitions of existing systems and by discovering and developing new systems voltage and current. to meet the needs of our ever-changing society. 3 Know and be able to use the definitions of As you embark on the study of circuit analysis, you need to power and energy. 4 Be able to use the passive sign convention to gain a feel for where this study fits into the hierarchy of topics calculate the power for an ideal basic circuit that comprise an introduction to electrical engineering. Hence we element given its voltage and current. 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 follow these concepts with discussion of an 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. 2 Practical Perspective Balancing Power One of the most important skills you will develop is the below. (Note that a more realistic model will be investigated ability to check your answers for the circuits you design in the Practical Perspective for Chapter 9.) The components and analyze using the tools developed in this text. A com- labeled a and b represent the electrical source to the home. mon method used to check for valid answers is to balance The components labeled c, d, and e represent the wires that the power in the circuit. The linear circuits we study have carry the electrical current from the source to the devices in no net power, so the sum of the power associated with each the home requiring electrical power. The components labeled circuit component must be zero. If the total power for f, g, and h represent lamps, televisions, hair dryers, refriger- the circuit is zero, we say that the power balances, but if ators, and other devices that require power. the total power is not zero, we need to find the errors in Once we have introduced the concepts of voltage, current, our calculation. power, and energy, we will examine this circuit model in detail, As an example, we will consider a very simple model for and use a power balance to determine whether the results of the distribution of electricity to a typical home, as shown analyzing this circuit are correct. c a f d h b g e romakoma / Shutterstock Elena Elisseeva /Alamy 3 4 Circuit Variables 1.1 Electrical Engineering: An Overview Electrical engineering is the profession concerned with systems that produce, transmit, and measure electric signals. Electrical engineering combines the physicist’s models of natural phenomena with the mathe- matician’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 class- ifications of electrical systems: communication systems computer systems control systems power systems signal-processing systems Then we describe how electrical engineers analyze and design such systems. Communication systems are electrical systems that generate, trans- mit, and distribute information. Well-known examples include television equipment, such as cameras, transmitters, receivers, and VCRs; radio tele- scopes, 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 sys- tem. Starting at the left of the figure, inside a telephone, a microphone turns sound waves into electric signals. These signals are carried to a switching center where they are combined with the signals from tens, hundreds, or thousands of other telephones. The combined signals leave the switching center; their form depends on the distance they must travel. In our example, they are sent through wires in underground coaxial cables to a microwave transmission station. Here, the signals are transformed into microwave fre- Transmission Communications Receiving quencies and broadcast from a transmission antenna through air and space, antenna satellite antenna via a communications satellite, to a receiving antenna. The microwave receiving station translates the microwave signals into a form suitable for further transmission, perhaps as pulses of light to be sent through fiber-optic cable. On arrival at the second switching center, the combined signals are separated, and each is routed to the appropriate telephone, where an ear- phone 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 Microwave station 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 high-quality connections. Coaxial Fiber-optic Computer systems use electric signals to process information rang- cable cable ing from word processing to mathematical computations. Systems range in size and power from pocket calculators to personal computers to supercomputers that perform such complex tasks as processing weather Switching center data and modeling chemical interactions of complex organic molecules. These systems include networks of microcircuits, or integrated circuits— postage-stampsized assemblies of hundreds, thousands, or millions of Microphone Wire Cable electrical components that often operate at speeds and power levels close to fundamental physical limits, including the speed of light and the thermo- dynamic laws. Control systems use electric signals to regulate processes. Examples include the control of temperatures, pressures, and flow rates in an oil Telephone Telephone refinery; the fuel-air mixture in a fuel-injected automobile engine; mecha- Figure 1.1  A telephone system. nisms such as the motors, doors, and lights in elevators; and the locks in the  1.1 Electrical Engineering: An Overview 5 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 technology-based society, usually is gener- ated in large quantities by nuclear, hydroelectric, and thermal (coal-, oil-, or gas-fired) 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. Signal-processing systems act on electric signals that represent infor- mation. 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, image-processing 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 computerized tomography (CT) scan is another example of an image-processing system. It takes signals generated by a special X-ray machine and transforms them into an image such as the one in Fig. 1.2. Although the original X-ray sig- nals are of little use to a physician, once they are processed into a recog- nizable image the information they contain can be used in the diagnosis of disease and injury. Considerable interaction takes place among the engineering disci- plines involved in designing and operating these five classes of systems. Thus communications engineers use digital computers to control the flow Pearson Education of information. Computers contain control systems, and control systems contain computers. Power systems require extensive communications sys- tems to coordinate safely and reliably the operation of components, which may be spread across a continent. A signal-processing 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 communica- Figure 1.2  A CT scan of an adult head. tions 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. On the newest commercial airplanes, an onboard computer system is used for managing engine functions, implementing the navigation and flight control systems, and generating video informa- tion screens in the cockpit. A complex control system uses cockpit com- mands 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 air- borne 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 show the movie. 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 vary- ing and unpredictable environmental conditions. Perhaps the most important engineering challenge is to guarantee that sufficient redun- dancy is incorporated in the designs to ensure that passengers arrive safely and on time at their desired destinations. 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 Figure 1.3  An airplane. 6 Circuit Variables engineering a challenging and exciting profession. The emphasis in engi- neering 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 In a field as diverse as electrical engineering, you might well ask whether all of its branches have anything in common. The answer is yes—electric circuits. An electric circuit is a mathematical model that approximates the behavior of an actual electrical system. As such, it provides an impor- tant foundation for learning—in your later courses and as a practicing engineer—the details of 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 engi- neering 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. Although generalized field theory might seem to be an appropriate starting point for investigating electric sig- nals, its application is not only cumbersome but also requires the use of 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. These assumptions are as follows: 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 con- sider them to affect every point in the system simultaneously. A sys- tem that is small enough so that we can make this assumption is called a lumped-parameter 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 oppo- site 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 impor- tance of assumptions 2 and 3 becomes apparent after we introduce the basic circuit elements and the rules for analyzing interconnected elements. However, we need to take a closer look at assumption 1. The question is, “How small does a physical system have to be to qualify as a lumped- parameter system?” We can get a quantitative handle on the question by noting that electric signals propagate by wave phenomena. If the wave- length of the signal is large compared to the physical dimensions of the  1.1 Electrical Engineering: An Overview 7 system, we have a lumped-parameter system. The wavelength l is the velocity divided by the repetition rate, or frequency, of the signal; that is, l = 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 lumped-parameter system and use cir- cuit 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 1>10th (or smaller) of the dimension of the wavelength, you have a lumped-parameter system. Thus, as long as the physical dimension of the power system is less than 5 * 105 m, we can treat it as a lumped-parameter system. On the other hand, the propagation frequency of radio signals is on the order of 109 Hz. Thus the wavelength is 0.3 m. Using the rule of 1>10th, the relevant dimensions of a communication system that sends or receives radio signals must be less than 3 cm to qualify as a lumped-parameter system. 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 lumped-parameter systems. Problem Solving As a practicing engineer, you will not be asked to solve problems that have already been solved. Whether you are trying to improve the per- formance of an existing system or creating a new system, you will be work- ing on unsolved problems. As a student, however, you will devote much of your attention to the discussion of problems already solved. By reading about and discussing how these problems were solved in the past, and by solving related homework and exam problems on your own, you will begin to develop the skills to successfully attack the unsolved problems you’ll face as a practicing engineer. Some general problem-solving procedures are presented here. Many of them 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 get- ting 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. 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 given the solution methods at your disposal. 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 recon- sider 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. 8 Circuit Variables 3. Think of several solution methods and decide on a way of choosing among them. This course will help you build a collection of analyt- ical 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 solu- tion. 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 equa- tions for the problem. Now comes the solution of those equations. Paper-and-pencil, calculator, and computer methods are all avail- able 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 solu- tion, 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 problem-solving 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 rea- sonable? Is the solution physically realizable? You may want to go further and rework the problem via an alternative method. Doing so will not only test the validity of your original answer, but will also help you develop your intuition about the most efficient solution methods for various kinds of problems. In the real world, safety- critical designs are always checked by several independent means. Getting into the habit of checking your answers will benefit you as a student and as a practicing engineer. These problem-solving steps cannot be used as a recipe to solve every prob- lem 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 problem-solving style that works for you. 1.2 The International System of Units Engineers compare theoretical results to experimental results and com- pare competing engineering designs using quantitative measures. 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.  1.2 The International System of Units 9 TABLE 1.1 The International System of Units (SI) Quantity Basic Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature degree kelvin K Amount of substance mole mol Luminous intensity candela cd National Institute of Standards and Technology Special Publication 330, 2008 Edition, Natl. Inst. Stand. Technol. Spec. Pub. 330, 2008 Ed., 96 pages (March 2008) 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, such as force, energy, power, and electric charge, you already know through previ- ous physics courses. Table 1.2 lists the derived units used in this book. In many cases, the SI unit is either too small or too large to use conve- niently. Standard prefixes corresponding to powers of 10, as listed in Table 1.3, are then applied to the basic unit. All of these prefixes are cor- rect, but engineers often use only the ones for powers divisible by 3; thus centi, deci, deka, and hecto are used rarely. Also, engineers often select the TABLE 1.3 Standardized Prefixes to Signify prefix that places the base number in the range between 1 and 1000. Powers of 10 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 ms, that is, Prefix Symbol Power 10-5 = 10 * 10-6 s, rather than as 0.01 ms or 10,000,000 ps. atto a 10 - 18 TABLE 1.2 Derived Units in SI femto f 10 - 15 pico p 10 - 12 Quantity Unit Name (Symbol) Formula nano n 10 - 9 Frequency hertz (Hz) s-1 micro m 10 - 6 Force newton (N) kg # m>s2 milli m 10 - 3 Energy or work joule (J) N#m centi c 10 - 2 Power watt (W) J>s deci d 10 - 1 Electric charge coulomb (C) A#s deka da 10 Electric potential volt (V) J>C hecto h 102 Electric resistance ohm ( Æ ) V>A kilo k 103 Electric conductance siemens (S) A>V mega M 106 Electric capacitance farad (F) C>V giga G 109 Magnetic flux weber (Wb) V#s tera T 1012 Inductance henry (H) Wb>A National Institute of Standards and Technology Special National Institute of Standards and Technology Special Publication 330, 2008 Edition, Natl. Inst. Stand. Publication 330, 2008 Edition, Natl. Inst. Stand. Technol. Spec. Technol. Spec. Pub. 330, 2008 Ed., 96 pages (March 2008) Pub. 330, 2008 Ed., 96 pages (March 2008) 10 Circuit Variables Example 1.1 illustrates a method for converting from one set of units to another and also uses power-of-ten 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 Therefore, a signal traveling at 80% of the speed of light, what length of cable, in inches, represents 1 ns? light will cover 9.45 inches of cable in 1 nanosecond. 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 ns: 2.4 * 108 meters # 1 second # 100 centimeters # 1 inch 1 second 9 1 meter 2.54 centimeters 10 nanoseconds (2.4 * 108)(100) = = 9.45 inches>nanosecond (109)(2.54) ASSESSMENT PROBLEMS Objective 1—Understand and be able to use SI units and the standard prefixes for powers of 10 1.1 Assume a telephone signal travels through a 1.2 How many dollars per millisecond would the cable at two-thirds the speed of light. How long federal government have to collect to retire a does it take the signal to get from New York deficit of $100 billion in one year? City to Miami if the distance is approximately 1100 miles? Answer: $3.17>ms. Answer: 8.85 ms. NOTE: Also try Chapter Problems 1.1, 1.3, and 1.5. 1.3 Circuit Analysis: An Overview Before becoming involved in the details of circuit analysis, we need to take a broad look at engineering design, specifically the design of electric circuits. The purpose of this overview is to provide you with a perspective