Electrical Engineering Principles and Applications PDF

Practical Applications of Electrical Engineering Principles 1.1 Using Resistance to Measure Strain 29 2.1 An Important Engineering Problem: Energy-Storage Systems for Electric Vehicles 100 3.1 Electronic Photo Flash 145 4.1 Electronics and the Art of Automotive Maintenance 190 6.1 Active Noise Cancellation 287 7.1 Biomedical Engineering Application of Electronics: Cardiac Pacemaker 385 8.1 Fresh Bread Anyone? 408 9.1 The Virtual First-Down Line 444 11.1 Electronic Stud Finder 549 12.1 Where Did Those Trout Go? 593 13.1 Soup Up Your Automobile by Changing Its Software? 618 14.1 Mechanical Application of Negative Feedback: Power Steering 666 16.1 Magnetic Flowmeters, Faraday, and The Hunt for Red October 768 vi Contents Practical Applications of 3.3 Physical Characteristics of Electrical Engineering Principles vi Capacitors 134 3.4 Inductance 138 Preface xi 3.5 Inductances in Series and Parallel 143 3.6 Practical Inductors 144 1 3.7 Mutual Inductance 147 Introduction 1 3.8 Symbolic Integration and 1.1 Overview of Electrical Engineering 2 Differentiation Using MATLAB 148 1.2 Circuits, Currents, and Voltages 6 Summary 152 1.3 Power and Energy 13 Problems 153 1.4 Kirchhoff’s Current Law 16 1.5 Kirchhoff’s Voltage Law 19 1.6 Introduction to Circuit Elements 22 1.7 Introduction to Circuits 30 4 Transients 162 Summary 34 Problems 35 4.1 First-Order RC Circuits 163 4.2 DC Steady State 167 4.3 RL Circuits 169 2 4.4 RC and RL Circuits with General Resistive Circuits 46 Sources 173 2.1 Resistances in Series and Parallel 47 4.5 Second-Order Circuits 179 2.2 Network Analysis by Using Series 4.6 Transient Analysis Using the MATLAB and Parallel Equivalents 51 Symbolic Toolbox 191 2.3 Voltage-Divider and Current-Divider Summary 197 Circuits 55 Problems 198 2.4 Node-Voltage Analysis 60 2.5 Mesh-Current Analysis 79 2.6 Thévenin and Norton Equivalent Circuits 88 5 2.7 Superposition Principle 101 Steady-State Sinusoidal Analysis 209 2.8 Wheatstone Bridge 104 5.1 Sinusoidal Currents and Voltages 210 Summary 107 5.2 Phasors 216 Problems 109 5.3 Complex Impedances 222 5.4 Circuit Analysis with Phasors and 3 Complex Impedances 225 5.5 Power in AC Circuits 231 Inductance and Capacitance 124 5.6 Thévenin and Norton Equivalent 3.1 Capacitance 125 Circuits 244 3.2 Capacitances in Series and Parallel 132 5.7 Balanced Three-Phase Circuits 249 vii viii Contents 5.8 AC Analysis Using MATLAB 261 Summary 265 9 Computer-Based Instrumentation Systems 433 Problems 266 9.1 Measurement Concepts and Sensors 434 6 9.2 Signal Conditioning 439 Frequency Response, Bode Plots, 9.3 Analog-to-Digital Conversion 446 and Resonance 278 9.4 LabVIEW 449 Summary 462 6.1 Fourier Analysis, Filters, and Transfer Problems 463 Functions 279 6.2 First-Order Lowpass Filters 287 6.3 Decibels, the Cascade Connection, and Logarithmic Frequency Scales 292 10 6.4 Bode Plots 296 Diodes 467 6.5 First-Order Highpass Filters 299 10.1 Basic Diode Concepts 468 6.6 Series Resonance 303 10.2 Load-Line Analysis of Diode 6.7 Parallel Resonance 308 Circuits 471 6.8 Ideal and Second-Order Filters 311 10.3 Zener-Diode Voltage-Regulator 6.9 Transfer Functions and Bode Plots Circuits 474 with MATLAB 317 10.4 Ideal-Diode Model 478 6.10 Digital Signal Processing 322 10.5 Piecewise-Linear Diode Models 480 Summary 331 10.6 Rectiﬁer Circuits 483 Problems 333 10.7 Wave-Shaping Circuits 488 10.8 Linear Small-Signal Equivalent Circuits 493 7 Summary 499 Logic Circuits 347 Problems 499 7.1 Basic Logic Circuit Concepts 348 7.2 Representation of Numerical Data in Binary Form 351 11 7.3 Combinatorial Logic Circuits 359 Ampliﬁers: Speciﬁcations and External 7.4 Synthesis of Logic Circuits 366 Characteristics 511 7.5 Minimization of Logic Circuits 373 11.1 Basic Ampliﬁer Concepts 512 7.6 Sequential Logic Circuits 377 11.2 Cascaded Ampliﬁers 517 Summary 388 11.3 Power Supplies and Efﬁciency 520 Problems 389 11.4 Additional Ampliﬁer Models 523 11.5 Importance of Ampliﬁer Impedances 8 11.6 in Various Applications 526 Ideal Ampliﬁers 529 Computers and Microcontrollers 400 11.7 Frequency Response 530 8.1 Computer Organization 401 11.8 Linear Waveform Distortion 535 8.2 Memory Types 404 11.9 Pulse Response 539 8.3 Digital Process Control 406 11.10 Transfer Characteristic and Nonlinear 8.4 Programming Model for the HCS12/9S12 Distortion 542 Family 409 11.11 Differential Ampliﬁers 544 8.5 The Instruction Set and Addressing 11.12 Offset Voltage, Bias Current, Modes for the CPU12 413 and Offset Current 548 8.6 Assembly-Language Programming 422 Summary 553 Summary 427 Problems 554 Problems 428 Contents ix 12 Field-Effect Transistors 566 15 12.1 NMOS and PMOS Transistors 567 Magnetic Circuits and 12.2 Load-Line Analysis of a Simple NMOS Transformers 708 Ampliﬁer 574 15.1 Magnetic Fields 709 12.3 Bias Circuits 577 15.2 Magnetic Circuits 718 12.4 Small-Signal Equivalent Circuits 580 15.3 Inductance and Mutual Inductance 723 12.5 Common-Source Ampliﬁers 585 15.4 Magnetic Materials 727 12.6 Source Followers 588 15.5 Ideal Transformers 731 12.7 CMOS Logic Gates 593 15.6 Real Transformers 738 Summary 598 Summary 743 Problems 599 Problems 743 16 13 DC Machines 754 Bipolar Junction Transistors 607 16.1 Overview of Motors 755 13.1 Current and Voltage Relationships 608 16.2 Principles of DC Machines 764 13.2 Common-Emitter Characteristics 611 16.3 Rotating DC Machines 769 13.3 Load-Line Analysis of a 16.4 Shunt-Connected and Separately Excited Common-Emitter Ampliﬁer 612 DC Motors 775 13.4 pnp Bipolar Junction Transistors 618 16.5 Series-Connected DC Motors 780 13.5 Large-Signal DC Circuit Models 620 16.6 Speed Control of DC Motors 784 13.6 Large-Signal DC Analysis of BJT 16.7 DC Generators 788 Circuits 623 Summary 793 13.7 Small-Signal Equivalent Circuits 630 Problems 794 13.8 Common-Emitter Ampliﬁers 633 13.9 Emitter Followers 638 Summary 644 17 Problems 645 AC Machines 803 17.1 Three-Phase Induction Motors 804 17.2 Equivalent-Circuit and Performance Calculations for Induction 14 Motors 812 Operational Ampliﬁers 655 17.3 Synchronous Machines 821 14.1 Ideal Operational Ampliﬁers 656 17.4 Single-Phase Motors 833 14.2 Inverting Ampliﬁers 657 17.5 Stepper Motors and Brushless 14.3 Noninverting Ampliﬁers 664 DC Motors 836 14.4 Design of Simple Ampliﬁers 667 Summary 838 14.5 Op-Amp Imperfections in the Linear Problems 839 Range of Operation 672 14.6 Nonlinear Limitations 676 14.7 DC Imperfections 681 APPENDICES 14.8 Differential and Instrumentation Ampliﬁers 685 14.9 Integrators and Differentiators 687 A Complex Numbers 845 14.10 Active Filters 690 Summary 694 Summary 852 Problems 695 Problems 852 x Contents B D Nominal Values and the Color Code for Answers for the Practice Tests 860 Resistors 854 E On-Line Student Resources 868 C The Fundamentals of Engineering Examination 856 Index 869 Preface As in the previous editions, my guiding philosophy in writing this book has three elements. The ﬁrst element is my belief that in the long run students are best served by learning basic concepts in a general setting. Second, I believe that students need to be motivated by seeing how the principles apply to speciﬁc and interesting problems in their own ﬁelds. The third element of my philosophy is to take every opportunity to make learning free of frustration for the student. This book covers circuit analysis, digital systems, electronics, and electromechan- ics at a level appropriate for either electrical-engineering students in an introductory course or nonmajors in a survey course. The only essential prerequisites are basic physics and single-variable calculus. Teaching a course using this book offers opportu- nities to develop theoretical and experimental skills and experiences in the following areas: Basic circuit analysis and measurement First- and second-order transients Steady-state ac circuits Resonance and frequency response Digital logic circuits Microcontrollers Computer-based instrumentation, including LabVIEW Diode circuits Electronic ampliﬁers Field-effect and bipolar junction transistors Operational ampliﬁers Transformers Ac and dc machines Computer-aided circuit analysis using MATLAB While the emphasis of this book is on basic concepts, a key feature is the inclusion of short articles scattered throughout showing how electrical-engineering concepts are applied in other ﬁelds. The subjects of these articles include anti-knock signal processing for internal combustion engines, a cardiac pacemaker, active noise control, and the use of RFID tags in ﬁsheries research, among others. I welcome comments from users of this book. Information on how the book could be improved is especially valuable and will be taken to heart in future revisions. My e-mail address is [email protected] xi xiv Preface ON-LINE STUDENT RESOURCES MasteringEngineering. Tutorial homework problems emulate the instructor’s ofﬁce-hour environment, guiding students through engineering concepts with self-paced individualized coaching. These in-depth tutorial homework problems are designed to coach students with feedback speciﬁc to their errors and optional hints that break problems down into simpler steps. Access can be purchased bundled with the textbook or online at www.masteringengineering.com. The Companion Website. Access is included with the purchase of every new book or can be purchased at www.pearsonhighered.com/hambley The Companion Website includes: Pearson eText, which is a complete on-line version of the book that includes highlighting, note-taking, and search capabilities. Video Solutions that provide complete, step-by-step solution walkthroughs of representative homework problems from each chapter. A Student Solutions Manual. A PDF ﬁle for each chapter includes full solutions for the in-chapter exercises, answers for the end-of-chapter problems that are marked with asterisks, and full solutions for the Practice Tests. A MATLAB folder that contains the m-ﬁles discussed in the book. A Multisim folder that contains tutorials on the basic features of Multisim and circuit simulations for a wide variety of circuits from the book. A Virtual Instruments folder, which contains the LabVIEW programs dis- cussed in Section 9.4. INSTRUCTOR RESOURCES Resources for instructors include: MasteringEngineering. This online Tutorial Homework program allows you to integrate dynamic homework with automatic 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. A complete Instructor’s Solutions Manual PowerPoint slides with all the ﬁgures from the book Instructor Resources are available for download by adopters of this book at the Pearson Higher Education website: www.pearsonhighered.com. If you are in need of a login and password, please contact your local Pearson representative. WHAT’S NEW IN THIS EDITION We have continued the popular Practice Tests that students can use in preparing for course exams at the end of each chapter. Answers for the Practice Tests appear in Appendix D and complete solutions are included in the on-line Student Solutions Manual ﬁles. Preface xv We have updated the coverage of MATLAB and the Symbolic Toolbox for network analysis in Chapters 2 through 6. Approximately 200 problems are new to this edition, replacing some of the problems from the previous edition, and many other problems have been modiﬁed. In Chapter 2, we have added an explanation of how the Wheatstone bridge is used in strain measurements. Sections 3.8 and 4.6 have been updated, deleting the coverage of piecewise linear functions which are problematic with recent versions of the Symbolic Toolbox. Chapter 8 has been extensively updated and now uses the Freescale Semi- conductor HCS12/9S12 family as an example of microcontrollers. Section 9.4 has been updated to the most recent version of LabVIEW. Relatively minor corrections and improvements appear throughout the book. PREREQUISITES The essential prerequisites for a course from this book are basic physics and single- variable calculus. A prior differential equations course would be helpful but is not essential. Differential equations are encountered in Chapter 4 on transient analysis, but the skills needed are developed from basic calculus. PEDAGOGICAL FEATURES The book includes various pedagogical features designed with the goal of stimulat- ing student interest, eliminating frustration, and engendering an awareness of the relevance of the material to their chosen profession. These features are: Statements of learning objectives open each chapter. Comments in the margins emphasize and summarize important points or indicate common pitfalls that students need to avoid. Short boxed articles demonstrate how electrical-engineering principles are applied in other ﬁelds of engineering. For example, see the articles on active noise cancellation (page 287) and electronic pacemakers (starting on page 385). Step-by-step problem solving procedures. For example, see the step-by-step sum- mary of node-voltage analysis (on pages 76–77) or the summary of Thévenin equivalents (on page 95). A Practice Test at the end of each chapter gives students a chance to test their knowledge. Answers appear in Appendix D. Complete solutions to the in-chapter exercises and Practice Tests, included as PDF ﬁles on-line, build student conﬁdence and indicate where additional study is needed. Summaries of important points at the end of each chapter provide references for students. Key equations are highlighted in the book to draw attention to important results. xvi Preface MEETING ABET-DIRECTED OUTCOMES Courses based on this book provide excellent opportunities to meet many of the directed outcomes for accreditation. The Criteria for Accrediting Engineering Pro- grams require that graduates of accredited programs have “an ability to apply knowledge of mathematics, science, and engineering” and “an ability to identify, formulate, and solve engineering problems.” This book, in its entirety, is aimed at developing these abilities. Also, graduates must have “an ability to design and conduct experiments, as well as analyze and interpret data.” Chapter 9, Computer-Based Instrumentation Systems, helps to develop this ability. If the course includes a laboratory, this ability can be developed even further. Furthermore, the criteria require “an ability to function on multi-disciplinary teams” and “an ability to communicate effectively.” Courses based on this book contribute to these abilities by giving nonmajors the knowledge and vocabu- lary to communicate effectively with electrical engineers. The book also helps to inform electrical engineers about applications in other ﬁelds of engineering. To aid in communication skills, end-of-chapter problems that ask students to explain electrical-engineering concepts in their own words are included. CONTENT AND ORGANIZATION Basic Circuit Analysis Chapter 1 deﬁnes current, voltage, power, and energy. Kirchhoff’s laws are introduced. Voltage sources, current sources, and resistance are deﬁned. Chapter 2 treats resistive circuits. Analysis by network reduction, node volt- ages, and mesh currents is covered. Thévenin equivalents, superposition, and the Wheatstone bridge are treated. Capacitance, inductance, and mutual inductance are treated in Chapter 3. Transients in electrical circuits are discussed in Chapter 4. First-order RL and RC circuits and time constants are covered, followed by a discussion of second-order circuits. Chapter 5 considers sinusoidal steady-state circuit behavior. (A review of com- plex arithmetic is included in Appendix A.) Power calculations, ac Thévenin and Norton equivalents, and balanced three-phase circuits are treated. Chapter 6 covers frequency response, Bode plots, resonance, ﬁlters, and digital signal processing. The basic concept of Fourier theory (that signals are composed of sinusoidal components having various amplitudes, phases, and frequencies) is qualitatively discussed. Digital Systems Chapter 7 introduces logic gates and the representation of numerical data in binary form. It then proceeds to discuss combinatorial and sequential logic. Boolean algebra, De Morgan’s laws, truth tables, Karnaugh maps, coders, decoders, ﬂip-ﬂops, and registers are discussed. Chapter 8 treats microcomputers with emphasis on embedded systems using the Freescale Semiconductor HCS12/9S12 as the primary example. Computer organiza- tion and memory types are discussed. Digital process control using microcontrollers Preface xvii is described in general terms. Finally, selected instructions and addressing modes for the CPU12 are described. Assembly language programming is treated very brieﬂy. Chapter 9 discusses computer-based instrumentation systems including mea- surement concepts, sensors, signal conditioning, and analog-to-digital conversion. The chapter ends with a discussion of LabVIEW, including an example virtual instrument that students can duplicate using an evaluation version on their own computers. Electronic Devices and Circuits Chapter 10 presents the diode, its various models, load-line analysis, and diode circuits, such as rectiﬁers, Zener-diode regulators, and wave shapers. In Chapter 11, the speciﬁcations and imperfections of ampliﬁers that need to be considered in applications are discussed from a users perspective. These include gain, input impedance, output impedance, loading effects, frequency response, pulse response, nonlinear distortion, common-mode rejection, and dc offsets. Chapter 12 covers the MOS ﬁeld-effect transistor, its characteristic curves, load- line analysis, large-signal and small-signal models, bias circuits, the common-source ampliﬁer, and the source follower. Chapter 13 gives a similar treatment for bipolar transistors. If desired, the order of Chapters 12 and 13 can be reversed. Another possibility is to skip most of both chapters so more time can be devoted to other topics. Chapter 14 treats the operational ampliﬁer and many of its applications. Non- majors can learn enough from this chapter to design and use op-amp circuits for instrumentation applications in their own ﬁelds. Electromechanics Chapter 15 reviews basic magnetic ﬁeld theory, analyzes magnetic circuits, and presents transformers. DC machines and ac machines are treated in Chapters 16 and 17, respectively. The emphasis is on motors rather than generators because the nonelectrical engineer applies motors much more often than generators. In Chapter 16, an overall view of motors in general is presented before considering DC machines, their equivalent circuits, and performance calculations. The universal motor and its applications are discussed. Chapter 17 deals with AC motors, starting with the three-phase induction motor. Synchronous motors and their advantages with respect to power-factor correction are analyzed. Small motors including single-phase induction motors are also discussed. A section on stepper motors and brushless dc motors ends the chapter. ACKNOWLEDGMENTS I wish to thank my colleagues, past and present, in the Electrical and Computer Engineering Department at Michigan Technological University, all of whom have given me help and encouragement at one time or another in writing this book and in my other projects. I have received much excellent advice from professors at other institutions who reviewed the manuscript in various stages over the years. This advice has improved the ﬁnal result a great deal, and I am grateful for their help. xviii Preface Current and past reviewers include: Ibrahim Abdel-Motaled, Northwestern University William Best, Lehigh University Steven Bibyk, Ohio State University D. B. Brumm, Michigan Technological University Karen Butler-Purry, Texas A&M University Robert Collin, Case Western University Joseph A. Coppola, Syracuse University Norman R. Cox, University of Missouri at Rolla W.T. Easter, North Carolina State University Zoran Gajic, Rutgers University Edwin L. Gerber, Drexel University Victor Gerez, Montana State University Walter Green, University of Tennessee Elmer Grubbs, New Mexico Highlands University Jasmine Henry, University of Western Australia Ian Hutchinson, MIT David Klemer, University of Wisconsin, Milwaukee Richard S. Marleau, University of Wisconsin Sunanda Mitra, Texas Tech University Phil Noe, Texas A&M University Edgar A. O’Hair, Texas Tech University John Pavlat, Iowa State University Clifford Pollock, Cornell University Michael Reed, Carnegie Mellon University Gerald F. Reid, Virginia Polytechnic Institute Selahattin Sayil, Lamar University William Sayle II, Georgia Institute of Technology Len Trombetta, University of Houston John Tyler, Texas A&M University Belinda B. Wang, University of Toronto Carl Wells, Washington State University Al Wicks, Virginia Tech Edward Yang, Columbia University Subbaraya Yuvarajan, North Dakota State University Rodger E. Ziemer, University of Colorado, Colorado Springs Over the years, many students and faculty using my books at MichiganTechnolog- ical University and elsewhere have made many excellent suggestions for improving the books and correcting errors. I thank them very much. I am indebted to Andrew Gilﬁllan and Tom Robbins, my present and past editors at Pearson, for keeping me pointed in the right direction and for many excellent suggestions that have improved my books a great deal. A very special thank you, also, to Scott Disanno for a great job of managing the production of this and past editions of this book. Thanks are extended to National Instruments which provided many excellent suggestions. Thanks are also extended to Pavithra Jayapaul of Jouve India for her excellent work on this edition. Also, I want to thank Tony and Pam for their continuing encouragement and valuable insights. I thank Judy for many good things much too extensive to list. ALLAN R. HAMBLEY Chapter 1 Introduction Study of this chapter will enable you to: Recognize interrelationships between electrical State and apply Kirchhoff’s current and voltage engineering and other ﬁelds of science and laws. engineering. Recognize series and parallel connections. List the major subﬁelds of electrical engineering. Identify and describe the characteristics of voltage List several important reasons for studying elec- and current sources. trical engineering. State and apply Ohm’s law. Deﬁne current, voltage, and power, including Solve for currents, voltages, and powers in simple their units. circuits. Calculate power and energy and determine whether energy is supplied or absorbed by a circuit element. Introduction to this chapter: n this chapter, we introduce electrical engineer- variables obey, and meet several circuit elements I ing, deﬁne circuit variables (current, voltage, power, and energy), study the laws that these circuit (current sources, voltage sources, and resistors). 1 2 Chapter 1 Introduction 1.1 OVERVIEW OF ELECTRICAL ENGINEERING Electrical engineers design systems that have two main objectives: 1. To gather, store, process, transport, and present information. 2. To distribute, store, and convert energy between various forms. In many electrical systems, the manipulation of energy and the manipulation of information are interdependent. For example, numerous aspects of electrical engineering relating to information are applied in weather prediction. Data about cloud cover, precipitation, wind speed, and so on are gathered electronically by weather satellites, by land-based radar sta- tions, and by sensors at numerous weather stations. (Sensors are devices that convert physical measurements to electrical signals.) This information is transported by elec- tronic communication systems and processed by computers to yield forecasts that are disseminated and displayed electronically. In electrical power plants, energy is converted from various sources to electrical form. Electrical distribution systems transport the energy to virtually every factory, home, and business in the world, where it is converted to a multitude of useful forms, such as mechanical energy, heat, and light. No doubt you can list scores of electrical engineering applications in your daily life. Increasingly, electrical and electronic features are integrated into new products. Automobiles and trucks provide just one example of this trend. The electronic content of the average automobile is growing rapidly in value. Auto designers realize that electronic technology is a good way to provide increased functionality at lower cost. Table 1.1 shows some of the applications of electrical engineering in automobiles. You may ﬁnd it interesting to As another example, we note that many common household appliances contain search the web for sites keypads for operator control, sensors, electronic displays, and computer chips, as related to “mechatronics.” well as more conventional switches, heating elements, and motors. Electronics have become so intimately integrated with mechanical systems that the name mechatronics is used for the combination. Subdivisions of Electrical Engineering Next, we give you an overall picture of electrical engineering by listing and brieﬂy discussing eight of its major areas. 1. Communication systems transport information in electrical form. Cellular phone, radio, satellite television, and the Internet are examples of communication systems. It is possible for virtually any two people (or computers) on the globe to communicate almost instantaneously. A climber on a mountaintop in Nepal can call or send e-mail to friends whether they are hiking in Alaska or sitting in a New York City ofﬁce. This kind of connectivity affects the way we live, the way we conduct business, and the design of everything we use. For example, communication systems will change the design of highways because trafﬁc and road-condition information collected by roadside sensors can be transmitted to central locations and used to route trafﬁc. When an accident occurs, an electrical signal can be emitted automatically when the airbags deploy, giving the exact location of the vehicle, summoning help, and notifying trafﬁc-control computers. Computers that are part of 2. Computer systems process and store information in digital form. No doubt products such as appliances you have already encountered computer applications in your own ﬁeld. Besides the and automobiles are called embedded computers. computers of which you are aware, there are many in unobvious places, such as house- hold appliances and automobiles. A typical modern automobile contains several Section 1.1 Overview of Electrical Engineering 3 Table 1.1. Current and Emerging Electronic/Electrical Applications in Automobiles and Trucks Safety Antiskid brakes Inﬂatable restraints Collision warning and avoidance Blind-zone vehicle detection (especially for large trucks) Infrared night vision systems Heads-up displays Automatic accident notiﬁcation Rear-view cameras Communications and entertainment AM/FM radio Digital audio broadcasting CD/DVD player Cellular phone Computer/e-mail Satellite radio Convenience Electronic GPS navigation Personalized seat/mirror/radio settings Electronic door locks Emissions, performance, and fuel economy Vehicle instrumentation Electronic ignition Tire inﬂation sensors Computerized performance evaluation and maintenance scheduling Adaptable suspension systems Alternative propulsion systems Electric vehicles Advanced batteries Hybrid vehicles dozen special-purpose computers. Chemical processes and railroad switching yards are routinely controlled through computers. 3. Control systems gather information with sensors and use electrical energy to control a physical process. A relatively simple control system is the heating/cooling system in a residence. A sensor (thermostat) compares the temperature with the desired value. Control circuits operate the furnace or air conditioner to achieve the desired temperature. In rolling sheet steel, an electrical control system is used to obtain the desired sheet thickness. If the sheet is too thick (or thin), more (or less) force is applied to the rollers. The temperatures and ﬂow rates in chemical processes are controlled in a similar manner. Control systems have even been installed in tall buildings to reduce their movement due to wind. 4. Electromagnetics is the study and application of electric and magnetic ﬁelds. The device (known as a magnetron) used to produce microwave energy in an oven is one application. Similar devices, but with much higher power levels, are employed in manufacturing sheets of plywood. Electromagnetic ﬁelds heat the glue between 4 Chapter 1 Introduction layers of wood so that it will set quickly. Cellular phone and television antennas are also examples of electromagnetic devices. 5. Electronics is the study and application of materials, devices, and circuits used in amplifying and switching electrical signals. The most important electronic devices are transistors of various kinds. They are used in nearly all places where electrical information or energy is employed. For example, the cardiac pacemaker is an elec- tronic circuit that senses heart beats, and if a beat does not occur when it should, applies a minute electrical stimulus to the heart, forcing a beat. Electronic instru- mentation and electrical sensors are found in every ﬁeld of science and engineering. Many of the aspects of electronic ampliﬁers studied later in this book have direct application to the instrumentation used in your ﬁeld of engineering. 6. Photonics is an exciting new ﬁeld of science and engineering that promises Electronic devices are based to replace conventional computing, signal-processing, sensing, and communica- on controlling electrons. tion devices based on manipulating electrons with greatly improved products Photonic devices perform similar functions by based on manipulating photons. Photonics includes light generation by lasers and controlling photons. light-emitting diodes, transmission of light through optical components, as well as switching, modulation, ampliﬁcation, detection, and steering light by electrical, acoustical, and photon-based devices. Current applications include readers for DVD disks, holograms, optical signal processors, and ﬁber-optic communication systems. Future applications include optical computers, holographic memories, and medi- cal devices. Photonics offers tremendous opportunities for nearly all scientists and engineers. 7. Power systems convert energy to and from electrical form and transmit energy over long distances. These systems are composed of generators, transformers, distri- bution lines, motors, and other elements. Mechanical engineers often utilize electrical motors to empower their designs. The selection of a motor having the proper torque– speed characteristic for a given mechanical application is another example of how you can apply the information in this book. 8. Signal processing is concerned with information-bearing electrical signals. Often, the objective is to extract useful information from electrical signals derived from sensors. An application is machine vision for robots in manufacturing. Another application of signal processing is in controlling ignition systems of internal combus- tion engines. The timing of the ignition spark is critical in achieving good performance and low levels of pollutants. The optimum ignition point relative to crankshaft rota- tion depends on fuel quality, air temperature, throttle setting, engine speed, and other factors. If the ignition point is advanced slightly beyond the point of best performance, engine knock occurs. Knock can be heard as a sharp metallic noise that is caused by rapid pressure ﬂuctuations during the spontaneous release of chemical energy in the combustion chamber. A combustion-chamber pressure pulse displaying knock is shown in Figure 1.1. At high levels, knock will destroy an engine in a very short time. Prior to the advent of practical signal-processing electronics for this application, engine timing needed to be adjusted for distinctly suboptimum performance to avoid knock under varying combinations of operating conditions. By connecting a sensor through a tube to the combustion chamber, an electrical signal proportional to pressure is obtained. Electronic circuits process this signal to determine whether the rapid pressure ﬂuctuations characteristic of knock are present. Then electronic circuits continuously adjust ignition timing for optimum performance while avoiding knock. Section 1.1 Overview of Electrical Engineering 5 Pressure (psi) 800 Knock 600 400 Figure 1.1 Pressure versus time for an internal combustion engine experiencing knock. Sensors convert 200 pressure to an electrical signal that is processed to adjust ignition timing for minimum pollution and good t (ms) performance. 1 2 3 4 5 6 7 8 Why You Need to Study Electrical Engineering As a reader of this book, you may be majoring in another ﬁeld of engineering or sci- ence and taking a required course in electrical engineering. Your immediate objective is probably to meet the course requirements for a degree in your chosen ﬁeld. How- ever, there are several other good reasons to learn and retain some basic knowledge of electrical engineering: 1. To pass the Fundamentals of Engineering (FE) Examination as a ﬁrst step in becoming a Registered Professional Engineer. In the United States, before per- forming engineering services for the public, you will need to become registered as a Professional Engineer (PE). This book gives you the knowledge to answer questions relating to electrical engineering on the registration examinations. Save this book Save this book and course and course notes to review for the FE examination. (See Appendix C for more on notes to review for the FE exam. the FE exam.) 2. To have a broad enough knowledge base so that you can lead design projects in your own ﬁeld. Increasingly, electrical engineering is interwoven with nearly all scientiﬁc experiments and design projects in other ﬁelds of engineering. Industry has repeatedly called for engineers who can see the big picture and work effectively in teams. Engineers or scientists who narrow their focus strictly to their own ﬁeld are destined to be directed by others. (Electrical engineers are somewhat fortunate in this respect because the basics of structures, mechanisms, and chemical processes are familiar from everyday life. On the other hand, electrical engineering concepts are somewhat more abstract and hidden from the casual observer.) 3. To be able to operate and maintain electrical systems, such as those found in control systems for manufacturing processes. The vast majority of electrical-circuit malfunctions can be readily solved by the application of basic electrical-engineering principles. You will be a much more versatile and valuable engineer or scientist if you can apply electrical-engineering principles in practical situations. 4. To be able to communicate with electrical-engineering consultants. Very likely, you will often need to work closely with electrical engineers in your career. This book will give you the basic knowledge needed to communicate effectively. 6 Chapter 1 Introduction Content of This Book Electrical engineering is too vast to cover in one or two courses. Our objective is to introduce the underlying concepts that you are most likely to need. Circuit theory Circuit theory is the electrical is the electrical engineer’s fundamental tool. That is why the ﬁrst six chapters of this engineer’s fundamental tool. book are devoted to circuits. Embedded computers, sensors, and electronic circuits will be an increasingly important part of the products you design and the instrumentation you use as an engineer or scientist. Chapters 7, 8, and 9 treat digital systems with emphasis on embedded computers and instrumentation. Chapters 10 through 14 deal with electronic devices and circuits. As a mechanical, chemical, civil, industrial, or other engineer, you will very likely need to employ energy-conversion devices. The last three chapters relate to electrical energy systems treating transformers, generators, and motors. Because this book covers many basic concepts, it is also sometimes used in intro- ductory courses for electrical engineers. Just as it is important for other engineers and scientists to see how electrical engineering can be applied to their ﬁelds, it is equally important for electrical engineers to be familiar with these applications. 1.2 CIRCUITS, CURRENTS, AND VOLTAGES Overview of an Electrical Circuit Before we carefully deﬁne the terminology of electrical circuits, let us gain some basic understanding by considering a simple example: the headlight circuit of an automobile. This circuit consists of a battery, a switch, the headlamps, and wires connecting them in a closed path, as illustrated in Figure 1.2. The battery voltage is a Chemical forces in the battery cause electrical charge (electrons) to ﬂow through measure of the energy gained the circuit. The charge gains energy from the chemicals in the battery and delivers by a unit of charge as it moves through the battery. energy to the headlamps. The battery voltage (nominally, 12 volts) is a measure of the energy gained by a unit of charge as it moves through the battery. The wires are made of an excellent electrical conductor (copper) and are insu- lated from one another (and from the metal auto body) by electrical insulation Electrons readily move (plastic) coating the wires. Electrons readily move through copper but not through through copper but not the plastic insulation. Thus, the charge ﬂow (electrical current) is conﬁned to the through plastic insulation. wires until it reaches the headlamps. Air is also an insulator. The switch is used to control the ﬂow of current. When the conducting metal- lic parts of the switch make contact, we say that the switch is closed and current ﬂows through the circuit. On the other hand, when the conducting parts of the Electrons experience collisions switch do not make contact, we say that the switch is open and current does with the atoms of the not ﬂow. tungsten wires, resulting in heating of the tungsten. The headlamps contain special tungsten wires that can withstand high temper- atures. Tungsten is not as good an electrical conductor as copper, and the electrons experience collisions with the atoms of the tungsten wires, resulting in heating of the tungsten. We say that the tungsten wires have electrical resistance. Thus, energy is transferred by the chemical action in the battery to the electrons and then to the Energy is transferred by the tungsten, where it appears as heat. The tungsten becomes hot enough so that copi- chemical action in the battery ous light is emitted. We will see that the power transferred is equal to the product to the electrons and then to the tungsten. of current (rate of ﬂow of charge) and the voltage (also called electrical potential) applied by the battery. Section 1.2 Circuits, Currents, and Voltages 7 Switch Battery Wires Headlamps (a) Physical configuration Conductors representing wires Switch + 12 V − Resistances Voltage source representing representing battery headlamps (b) Circuit diagram Figure 1.2 The headlight circuit. (a) The actual physical layout of the circuit. (b) The circuit diagram. (Actually, the simple description of the headlight circuit we have given is most appropriate for older cars. In more modern automobiles, sensors provide information to an embedded computer about the ambient light level, whether or not the ignition is energized, and whether the transmission is in park or drive. The dashboard switch merely inputs a logic level to the computer, indicating the intention of the operator with regard to the headlights. Depending on these inputs, the computer controls the state of an electronic switch in the headlight circuit. When the ignition is turned off and if it is dark, the computer keeps the lights on for a few minutes so the passengers can see to exit and then turns them off to conserve energy in the battery. This is typical of the trend to use highly sophisticated electronic and computer technology to enhance the capabilities of new designs in all ﬁelds of engineering.) Fluid-Flow Analogy Electrical circuits are analogous to ﬂuid-ﬂow systems. The battery is analogous to a pump, and charge is analogous to the ﬂuid. Conductors (usually copper wires) correspond to frictionless pipes through which the ﬂuid ﬂows. Electrical current is The ﬂuid-ﬂow analogy can the counterpart of the ﬂow rate of the ﬂuid. Voltage corresponds to the pressure be very helpful initially in differential between points in the ﬂuid circuit. Switches are analogous to valves. understanding electrical Finally, the electrical resistance of a tungsten headlamp is analogous to a constriction circuits. in a ﬂuid system that results in turbulence and conversion of energy to heat. Notice that current is a measure of the ﬂow of charge through the cross section of a circuit element, whereas voltage is measured across the ends of a circuit element or between any other two points in a circuit. Now that we have gained a basic understanding of a simple electrical circuit, we will deﬁne the concepts and terminology more carefully. 8 Chapter 1 Introduction Resistances + − Inductance Voltage source Capacitance Conductors Figure 1.3 An electrical circuit consists of circuit elements, such as voltage sources, resistances, inductances, and capacitances, connected in closed paths by conductors. Electrical Circuits An electrical circuit consists of An electrical circuit consists of various types of circuit elements connected in closed various types of circuit paths by conductors. An example is illustrated in Figure 1.3. The circuit elements elements connected in closed paths by conductors. can be resistances, inductances, capacitances, and voltage sources, among others. The symbols for some of these elements are illustrated in the ﬁgure. Eventually, we will carefully discuss the characteristics of each type of element. Charge ﬂows easily through Charge ﬂows easily through conductors, which are represented by lines connect- conductors. ing circuit elements. Conductors correspond to connecting wires in physical circuits. Voltage sources create forces that cause charge to ﬂow through the conductors and other circuit elements. As a result, energy is transferred between the circuit elements, resulting in a useful function. Electrical Current Current is the time rate of ﬂow of electrical charge. Its Electrical current is the time rate of ﬂow of electrical charge through a conductor units are amperes (A), which or circuit element. The units are amperes (A), which are equivalent to coulombs per are equivalent to coulombs per second (C/s). second (C/s). (The charge on an electron is −1.602 × 10−19 C.) Conceptually, to ﬁnd the current for a given circuit element, we ﬁrst select a cross Reference direction section of the circuit element roughly perpendicular to the ﬂow of current. Then, we select a reference direction along the direction of ﬂow. Thus, the reference direction points from one side of the cross section to the other. This is illustrated in Figure 1.4. Next, suppose that we keep a record of the net charge ﬂow through the cross Cross section section. Positive charge crossing in the reference direction is counted as a positive Conductor or circuit element contribution to net charge. Positive charge crossing opposite to the reference is counted as a negative contribution. Furthermore, negative charge crossing in the ref- Figure 1.4 Current is the time rate of charge ﬂow erence direction is counted as a negative contribution, and negative charge against through a cross section of a the reference direction is a positive contribution to charge. conductor or circuit Thus, in concept, we obtain a record of the net charge in coulombs as a function element. of time in seconds denoted as q(t). The electrical current ﬂowing through the element in the reference direction is given by Colored shading is used to indicate key equations dq(t) i(t) = (1.1) throughout this book. dt A constant current of one ampere means that one coulomb of charge passes through the cross section each second. Section 1.2 Circuits, Currents, and Voltages 9 To ﬁnd charge given current, we must integrate. Thus, we have t q(t) = i(t) dt + q(t0 ) (1.2) t0 in which t0 is some initial time at which the charge is known. (Throughout this book, we assume that time t is in seconds unless stated otherwise.) Current ﬂow is the same for all cross sections of a circuit element. (We reexamine this statement when we introduce the capacitor in Chapter 3.) The current that enters one end ﬂows through the element and exits through the other end. Example 1.1 Determining Current Given Charge Suppose that charge versus time for a given circuit element is given by q(t) = 0 for t < 0 and q(t) = 2 − 2e−100t C for t > 0 Sketch q(t) and i(t) to scale versus time. Solution First we use Equation 1.1 to ﬁnd an expression for the current: dq(t) i(t) = dt =0 for t < 0 = 200e−100t A for t > 0 Plots of q(t) and i(t) are shown in Figure 1.5. Reference Directions In analyzing electrical circuits, we may not initially know the actual direction of current ﬂow in a particular circuit element. Therefore, we start by assigning current q (t) (C) i (t) (A) 2.0 200 1.0 100 0 t (ms) 0 t (ms) 0 10 20 30 40 0 10 20 30 40 Figure 1.5 Plots of charge and current versus time for Example 1.1. Note: The time scale is in milliseconds (ms). One millisecond is equivalent to 10−3 seconds. 10 Chapter 1 Introduction B D A C E Figure 1.6 In analyzing circuits, we frequently start by assigning current i2 i3 i1 variables i1 , i2 , i3 , and so forth. variables and arbitrarily selecting a reference direction for each current of interest. It is customary to use the letter i for currents and subscripts to distinguish different currents. This is illustrated by the example in Figure 1.6, in which the boxes labeled A, B, and so on represent circuit elements. After we solve for the current values, we may ﬁnd that some currents have negative values. For example, suppose that i1 = −2 A in the circuit of Figure 1.6. Because i1 has a negative value, we know that current actually ﬂows in the direction opposite to the reference initially selected for i1. Thus, the actual current is 2 A ﬂowing downward through element A. Direct Current and Alternating Current Dc currents are constant with When a current is constant with time, we say that we have direct current, abbreviated respect to time, whereas ac as dc. On the other hand, a current that varies with time, reversing direction peri- currents vary with time. odically, is called alternating current, abbreviated as ac. Figure 1.7 shows the values of a dc current and a sinusoidal ac current versus time. When ib (t) takes a negative value, the actual current direction is opposite to the reference direction for ib (t). The designation ac is used for other types of time-varying currents, such as the triangular and square waveforms shown in Figure 1.8. ia (t) ib (t) = 2 cos 2pt (A) (A) 2 t (s) t (s) 0.5 1.0 (a) Dc current (b) Ac current Figure 1.7 Examples of dc and ac currents versus time. Double-Subscript Notation for Currents So far we have used arrows alongside circuit elements or conductors to indicate reference directions for currents. Another way to indicate the current and refer- ence direction for a circuit element is to label the ends of the element and use double subscripts to deﬁne the reference direction for the current. For example, consider the resistance of Figure 1.9. The current denoted by iab is the current through the element with its reference direction pointing from a to b. Similarly, iba is the current with its reference directed from b to a. Of course, iab and iba are the same in magnitude and Section 1.2 Circuits, Currents, and Voltages 11 it (t) is (t) t t a (a) Triangular waveform (b) Square waveform iab iba Figure 1.8 Ac currents can have various waveforms. b Figure 1.9 Reference opposite in sign, because they denote the same current but with opposite reference directions can be indicated directions. Thus, we have by labeling the ends of iab = −iba circuit elements and using double subscripts on current variables. The reference Exercise 1.1 A constant current of 2 A ﬂows through a circuit element. In 10 seconds direction for iab points from a to b. On the other hand, (s), how much net charge passes through the element? the reference direction for Answer 20 C. iba points from b to a. Exercise 1.2 The charge that passes through a circuit element is given by q(t) = 0.01 sin(200t) C, in which the angle is in radians. Find the current as a function of time. Answer i(t) = 2 cos(200t) A. Exercise 1.3 In Figure 1.6, suppose that i2 = 1 A and i3 = −3 A. Assuming that the current consists of positive charge, in which direction (upward or downward) is charge moving in element C? In element E? Answer Downward in element C and upward in element E. Voltages When charge moves through circuit elements, energy can be transferred. In the case of automobile headlights, stored chemical energy is supplied by the battery and Voltage is a measure of the absorbed by the headlights where it appears as heat and light. The voltage associated energy transferred per unit of charge when charge moves with a circuit element is the energy transferred per unit of charge that ﬂows through from one point in an electrical the element. The units of voltage are volts (V), which are equivalent to joules per circuit to a second point. coulomb (J/C). For example, consider the storage battery in an automobile. The voltage across its terminals is (nominally) 12 V. This means that 12 J are transferred to or from the Notice that voltage is battery for each coulomb that ﬂows through it. When charge ﬂows in one direction, measured across the ends of a circuit element, whereas energy is supplied by the battery, appearing elsewhere in the circuit as heat or light current is a measure of charge or perhaps as mechanical energy at the starter motor. If charge moves through the ﬂow through the element. battery in the opposite direction, energy is absorbed by the battery, where it appears as stored chemical energy. Voltages are assigned polarities that indicate the direction of energy ﬂow. If positive charge moves from the positive polarity through the element toward the negative polarity, the element absorbs energy that appears as heat, mechanical energy, stored chemical energy, or as some other form. On the other hand, if positive charge moves from the negative polarity toward the positive polarity, the element supplies energy. This is illustrated in Figure 1.10. For negative charge, the direction of energy transfer is reversed. 12 Chapter 1 Introduction + ⊕ Energy supplied Energy absorbed by the element by the element Figure 1.10 Energy is transferred ⊕ when charge ﬂows through an element having a voltage across it. − + v2 − − v4 + Figure 1.11 If we do not know the voltage values and polarities in a 2 4 + + + circuit, we can start by assigning voltage variables choosing the v1 v3 v5 1 3 5 reference polarities arbitrarily. (The boxes represent unspeciﬁed circuit − − − elements.) Reference Polarities When we begin to analyze a circuit, we often do not know the actual polarities of some of the voltages of interest in the circuit. Then, we simply assign voltage variables choosing reference polarities arbitrarily. (Of course, the actual polarities are not arbitrary.) This is illustrated in Figure 1.11. Next, we apply circuit principles (discussed later), obtaining equations that are solved for the voltages. If a given voltage has an actual polarity opposite to our arbitrary choice for the reference polarity, we obtain a negative value for the voltage. For example, if we ﬁnd that In circuit analysis, we v3 = −5 V in Figure 1.11, we know that the voltage across element 3 is 5 V in frequently assign reference magnitude and its actual polarity is opposite to that shown in the ﬁgure (i.e., the polarities for voltages arbitrarily. If we ﬁnd at the actual polarity is positive at the bottom end of element 3 and negative at the top). end of the analysis that the We usually do not put much effort into trying to assign “correct” references value of a voltage is negative, for current directions or voltage polarities. If we have doubt about them, we make then we know that the true arbitrary choices and use circuit analysis to determine true directions and polarities polarity is opposite of the (as well as the magnitudes of the currents and voltages). polarity selected initially. Voltages can be constant with time or they can vary. Constant voltages are called dc voltages. On the other hand, voltages that change in magnitude and alternate in polarity with time are said to be ac voltages. For example, v1 (t) = 10 V is a dc voltage. It has the same magnitude and polarity for all time. On the other hand, v2 (t) = 10 cos(200π t)V + a − is an ac voltage that varies in magnitude and polarity. When v2 (t) assumes a negative value, the actual polarity is opposite the reference polarity. (We study sinusoidal ac currents and voltages in Chapter 5.) vab vba Double-Subscript Notation for Voltages − b + Another way to indicate the reference polarity of a voltage is to use double subscripts Figure 1.12 The voltage vab has a reference polarity that on the voltage variable. We use letters or numbers to label the terminals between is positive at point a and which the voltage appears, as illustrated in Figure 1.12. For the resistance shown in the negative at point b. ﬁgure, vab represents the voltage between points a and b with the positive reference Section 1.3 Power and Energy 13 at point a. The two subscripts identify the points between which the voltage appears, and the ﬁrst subscript is the positive reference. Similarly, vba is the voltage between a and b with the positive reference at point b. Thus, we can write vab = −vba (1.3) because vba has the same magnitude as vab but has opposite polarity. Still another way to indicate a voltage and its reference polarity is to use an arrow, as shown in Figure 1.13. The positive reference corresponds to the head of the arrow. v Figure 1.13 The positive Switches reference for v is at the head of the arrow. Switches control the currents in circuits. When an ideal switch is open, the current through it is zero and the voltage across it is determined by the remainder of the circuit. When an ideal switch is closed, the voltage across it is zero and the current through it is determined by the remainder of the circuit. Exercise 1.4 The voltage across a given circuit element is vab = 20 V. A positive charge of 2 C moves through the circuit element from terminal b to terminal a. How much energy is transferred? Is the energy supplied by the circuit element or absorbed by it? Answer 40 J are supplied by the circuit element. 1.3 POWER AND ENERGY Consider the circuit element shown in Figure 1.14. Because the current i is the rate i of ﬂow of charge and the voltage v is a measure of the energy transferred per unit of + charge, the product of the current and the voltage is the rate of energy transfer. In other words, the product of current and voltage is power: v p = vi (1.4) − Figure 1.14 When current The physical units of the quantities on the right-hand side of this equation are ﬂows through an element and voltage appears across volts × amperes = the element, energy is transferred. The rate of (joules/coulomb) × (coulombs/second) = energy transfer is p = vi. joules/second = watts Passive Reference Conﬁguration Now we may ask whether the power calculated by Equation 1.4 represents energy supplied by or absorbed by the element. Refer to Figure 1.14 and notice that the current reference enters the positive polarity of the voltage. We call this arrange- ment the passive reference conﬁguration. Provided that the references are picked in this manner, a positive result for the power calculation implies that energy is being absorbed by the element. On the other hand, a negative result means that the element is supplying energy to other parts of the circuit. 14 Chapter 1 Introduction If the current reference enters the negative end of the reference polarity, we compute the power as p = −vi (1.5) Then, as before, a positive value for p indicates that energy is absorbed by the element, and a negative value shows that energy is supplied by the element. If the circuit element happens to be an electrochemical battery, positive power means that the battery is being charged. In other words, the energy absorbed by the battery is being stored as chemical energy. On the other hand, negative power indicates that the battery is being discharged. Then the energy supplied by the battery is delivered to some other element in the circuit. Sometimes currents, voltages, and powers are functions of time. To emphasize this fact, we can write Equation 1.4 as p(t) = v(t)i(t) (1.6) Example 1.2 Power Calculations Consider the circuit elements shown in Figure 1.15. Calculate the power for each element. If each element is a battery, is it being charged or discharged? Solution In element A, the current reference enters the positive reference polarity. This is the passive reference conﬁguration. Thus, power is computed as pa = va ia = 12 V × 2 A = 24 W Because the power is positive, energy is absorbed by the device. If it is a battery, it is being charged. In element B, the current reference enters the negative reference polarity. (Recall that the current that enters one end of a circuit element must exit from the other end, and vice versa.) This is opposite to the passive reference conﬁguration. Hence, power is computed as pb = −vb ib = −(12 V) × 1 A = −12 W Since the power is negative, energy is supplied by the device. If it is a battery, it is being discharged. ia ib ic + + − va A vb B vc C − − + va = 12 V vb = 12 V vc = 12 V ia = 2 A ib = 1 A ic = −3 A (a) (b) (c) Figure 1.15 Circuit elements for Example 1.2. Section 1.3 Power and Energy 15 In element C, the current reference enters the positive reference polarity. This is the passive reference conﬁguration. Thus, we compute power as pc = vc ic = 12 V × (−3 A) = −36 W Since the result is negative, energy is supplied by the element. If it is a battery, it is being discharged. (Notice that since ic takes a negative value, current actually ﬂows downward through element C.) Energy Calculations To calculate the energy w delivered to a circuit element between time instants t1 and t2 , we integrate power: t2 w= p(t) dt (1.7) t1 Here we have explicitly indicated that power can be a function of time by using the notation p(t). Example 1.3 Energy Calculation Find an expression for the power for the voltage source shown in Figure 1.16. Compute the energy for the interval from t1 = 0 to t2 = ∞. Solution The current reference enters the positive reference polarity. Thus, we compute power as v(t) + − p(t) = v(t)i(t) i(t) = 12 × 2e−t v(t) = 12 V i(t) = 2e−t A = 24e−t W Figure 1.16 Circuit element for Example 1.3. Subsequently, the energy transferred is given by ∞ w= p(t) dt 0 ∞ = 24e−t dt 0 ∞ = −24e−t 0 = −24e−∞ − (−24e0 ) = 24 J Because the energy is positive, it is absorbed by the source. Preﬁxes In electrical engineering, we encounter a tremendous range of values for currents, voltages, powers, and other quantities. We use the preﬁxes shown in Table 1.2 when working with very large or small quantities. For example, 1 milliampere (1 mA) is equivalent to 10−3 A, 1 kilovolt (1 kV) is equivalent to 1000 V, and so on. 16 Chapter 1 Introduction Table 1.2. Preﬁxes Used for Large or Small Physical Quantities Preﬁx Abbreviation Scale Factor........................................................................................... giga- G 109 meg- or mega- M 106 kilo- k 103 milli- m 10−3 micro- μ 10−6 nano- n 10−9 pico- p 10−12 femto- f 10−15 ia (t) ib (t) + + va (t) A vb (t) B − − ia (t) = 2t ib (t) = 10 va (t) = 10t vb (t) = 20 − 2t Figure 1.17 See Exercise 1.6. (a) (b) Exercise 1.5 The ends of a circuit element are labeled a and b, respectively. Are the references for iab and vab related by the passive reference conﬁguration? Explain. Answer The reference direction for iab enters terminal a, which is also the posi- tive reference for vab. Therefore, the current reference direction enters the positive reference polarity, so we have the passive reference conﬁguration. Exercise 1.6 Compute the power as a function of time for each of the elements shown in Figure 1.17. Find the energy transferred between t1 = 0 and t2 = 10 s. In each case is energy supplied or absorbed by the element? Answer a. pa (t) = 20t 2 W, wa = 6667 J; since wa is positive, energy is absorbed by element A. b. pb (t) = 20t − 200 W, wb = −1000 J; since wb is negative, energy is supplied by element B. 1.4 KIRCHHOFF’S CURRENT LAW Kirchhoff’s current law states A node in an electrical circuit is a point at which two or more circuit elements are that the net current entering joined together. Examples of nodes are shown in Figure 1.18. a node is zero. An important principle of electrical circuits is Kirchhoff’s current law: The net current entering a node is zero. To compute the net current entering a node, we add the currents entering and subtract the currents leaving. For illustration, consider the nodes of Figure 1.18. Then, we can write: Node a : i1 + i2 − i3 = 0 Node b : i3 − i4 = 0 Node c : i5 + i6 + i7 = 0 Section 1.4 Kirchhoff’s Current Law 17 Node a Node b Node c i1 i3 i3 i5 i6 i4 i2 i7 (a) (b) (c) Figure 1.18 Partial circuits showing one node each to illustrate Kirchhoff’s current law. Notice that for node b, Kirchhoff’s current law requires that i3 = i4. In general, if only two circuit elements are connected at a node, their currents must be equal. The current ﬂows into the node through one element and out through the other. Usually, we will recognize this fact and assign a single current variable for both circuit elements. For node c, either all of the currents are zero or some are positive while others are negative. We abbreviate Kirchhoff’s current law as KCL. There are two other equivalent ways to state KCL. One way is: The net current leaving a node is zero. To compute the net current leaving a node, we add the currents leaving and subtract the currents entering. For the nodes of Figure 1.18, this yields the following: Node a : −i1 − i2 + i3 = 0 Node b : −i3 + i4 = 0 Node c : −i5 − i6 − i7 = 0 Of course, these equations are equivalent to those obtained earlier. Another way to state KCL is: The sum of the currents entering a node equals the An alternative way to state sum of the currents leaving a node. Applying this statement to Figure 1.18, we obtain Kirchhoff’s current law is that the sum of the currents the following set of equations: entering a node is equal to the sum of the currents Node a : i1 + i2 = i3 leaving a node. Node b : i3 = i4 Node c : i5 + i6 + i7 = 0 Again, these equations are equivalent to those obtained earlier. Physical Basis for Kirchhoff’s Current Law An appreciation of why KCL is true can be obtained by considering what would happen if it were violated. Suppose that we could have the situation shown in Figure 1.18(a), with i1 = 3 A, i2 = 2 A, and i3 = 4 A. Then, the net current entering the node would be i1 + i2 − i3 = 1 A = 1 C/s In this case, 1 C of charge would accumulate at the node during each second. After 1 s, we would have +1 C of charge at the node, and −1 C of charge somewhere else in the circuit. 18 Chapter 1 Introduction B ib ia Figure 1.19 Elements A, B, C, and D A D can be considered to be connected to a common node, because all points in id a circuit that are connected directly by C ic conductors are electrically equivalent to a single point. Suppose that these charges are separated by a distance of one meter (m). Recall that unlike charges experience a force of attraction. The resulting force turns out to be approximately 8.99 × 109 newtons (N) (equivalent to 2.02 × 109 pounds). Very large forces are generated when charges of this magnitude are separated by moderate distances. In effect, KCL states that such forces prevent charge from accumulating at the nodes of a circuit. All points in a circuit that All points in a circuit that are connected directly by conductors can be considered are connected directly by to be a single node. For example, in Figure 1.19, elements A, B, C, and D are connected conductors can be considered to be a single node. to a common node. Applying KCL, we can write ia + ic = ib + id Series Circuits We make frequent use of KCL in analyzing circuits. For example, consider the ele- ments A, B, and C shown in Figure 1.20. When elements are connected end to end, we ia say that they are connected in series. In order for elements A and B to be in series, no A 1 other path for current can be connected to the node joining A and B. Thus, all elements in a series circuit have identical currents. For example, writing Kirchhoff’s current law ib at node 1 for the circuit of Figure 1.20, we have B ia = ib C 2 ic At node 2, we have Figure 1.20 Elements A, ib = ic B, and C are connected in series. Thus, we have ia = ib = ic The current that enters a series circuit must ﬂow through each element in the circuit. Exercise 1.7 Use KCL to determine the values of the unknown currents shown in Figure 1.21. Answer ia = 4 A, ib = −2 A, ic = −8 A. Exercise 1.8 Consider the circuit of Figure 1.22. Identify the groups of circuit elements that are connected in series. Answer Elements A and B are in series; elements E, F, and G form another series combination. Section 1.5 Kirchhoff’s Voltage Law 19 1A 1A 3A 1A 3A 3A 2A ia ib ic 4A (a) (b) (c) Figure 1.21 See Exercise 1.7. B E A C D F

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