Introductory Circuit Analysis PDF, 12th Edition

Introductory Circuit Analysis Robert L Boylestad Twelfth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights res...

Introductory Circuit Analysis Robert L Boylestad Twelfth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 10: 1-292-02400-3 ISBN 13: 978-1-292-02400-4 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America  P E A R S O N C U S T O M L I B R A R Y Table of Contents 1. Introduction Robert L. Boylestad 1 2. Voltage and Current Robert L. Boylestad 33 3. Resistance Robert L. Boylestad 65 4. Ohm’s Law, Power, and Energy Robert L. Boylestad 103 5. Series dc Circuits Robert L. Boylestad 137 6. Parallel dc Circuits Robert L. Boylestad 191 7. Series-Parallel Circuits Robert L. Boylestad 249 8. Methods of Analysis and Selected Topics (dc) Robert L. Boylestad 289 9. Network Theorems Robert L. Boylestad 349 10. Capacitors Robert L. Boylestad 401 11. Inductors Robert L. Boylestad 467 12. Magnetic Circuits Robert L. Boylestad 517 13. Sinusoidal Alternating Waveforms Robert L. Boylestad 545 I  14. The Basic Elements and Phasors Robert L. Boylestad 595 15. Series and Parallel ac Circuits Robert L. Boylestad 645 16. Series-Parallel ac Networks Robert L. Boylestad 721 17. Methods of Analysis and Selected Topics (ac) Robert L. Boylestad 751 18. Network Theorems (ac) Robert L. Boylestad 793 19. Power (ac) Robert L. Boylestad 841 20. Resonance Robert L. Boylestad 879 21. Transformers Robert L. Boylestad 925 22. Polyphase Systems Robert L. Boylestad 969 23. Pulse Waveforms and the R-C Response Robert L. Boylestad 1005 24. Nonsinusoidal Circuits Robert L. Boylestad 1033 Appendix: Conversion Factors Robert L. Boylestad 1057 Appendix: PSpice and Multisim Robert L. Boylestad 1061 Appendix: Determinants Robert L. Boylestad 1063 Appendix: Magnetic Parameter Conversions Robert L. Boylestad 1073 Appendix: Maximum Power Transfer Conditions Robert L. Boylestad 1075 Summary of Equations Robert L. Boylestad 1079 Index 1083 II  Introduction Become aware of the rapid growth of the Objectives electrical/electronics industry over the past century. Understand the importance of applying a unit of measurement to a result or measurement and to ensuring that the numerical values substituted into an equation are consistent with the unit of measurement of the various quantities. Become familiar with the SI system of units used throughout the electrical/electronics industry. Understand the importance of powers of ten and how to work with them in any numerical calculation. Be able to convert any quantity, in any system of units, to another system with confidence. 1 THE ELECTRICAL/ELECTRONICS INDUSTRY Over the past few decades, technology has been changing at an ever-increasing rate. The pres- sure to develop new products, improve the performance of existing systems, and create new markets will only accelerate that rate. This pressure, however, is also what makes the field so exciting. New ways of storing information, constructing integrated circuits, and developing hardware that contains software components that can “think” on their own based on data input are only a few possibilities. Change has always been part of the human experience, but it used to be gradual. This is no longer true. Just think, for example, that it was only a few years ago that TVs with wide, flat screens were introduced. Already, these have been eclipsed by high-definition TVs with im- ages so crystal clear that they seem almost three-dimensional. Miniaturization has also made possible huge advances in electronic systems. Cell phones that originally were the size of notebooks are now smaller than a deck of playing cards. In addition, these new versions record videos, transmit photos, send text messages, and have calendars, reminders, calculators, games, and lists of frequently called numbers. Boom boxes playing audio cassettes have been replaced by pocket-sized iPods® that can store 30,000 songs or 25,000 photos. Hearing aids with higher power levels that are almost invisible in the ear, TVs with 1-inch screens—the list of new or improved products continues to expand because significantly smaller electronic systems have been developed. This reduction in size of electronic systems is due primarily to an important innovation introduced in 1958—the integrated circuit (IC). An integrated circuit can now contain features less than 50 nanometers across. The fact that measurements are now being made in nanome- ters has resulted in the terminology nanotechnology to refer to the production of integrated circuits called nanochips. To understand nanometers, consider drawing 100 lines within  S the boundaries of 1 inch. Then attempt drawing 1000 lines within the same length. Cutting I 50-nanometer features would require drawing over 500,000 lines in 1 inch. The integrated circuit shown in Fig. 1 is an Intel® Core 2 Extreme quad-core processor that has 291 million From Chapter 1 of Introductory Circuit Analysis, Twelfth Edition, Robert L. Boylestad. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Prentice Hall. All rights reserved. 1  INTRODUCTION Integrated Heat Spreader (IHS): The integrated metal heat spreader USA spreads heat from the silicon chips and protects them. D C25019 Core 1 Silicon chips (dies): The two dies inside the Intel® Core™ 2 Extreme Core 2 01 Core 3 Core 4 Advanc Smart Ca ed quad-core processor are 143 mm2 in che 1 Advanc Smart Ca ed che 2 size and utilize 291 million transistors each. Substrate: The dies are mounted (b) directly to the substrate which facilitates the contact to the motherboard and chipset of the PC via 775 contacts and electrical (a) connections. FIG. 1 Intel® Core™ 2 Extreme quad-core processer: (a) surface appearance, (b) internal chips. transistors in each dual-core chip. The result is that the entire package, which is about the size of three postage stamps, has almost 600 million transistors—a number hard to comprehend. However, before a decision is made on such dramatic reductions in size, the system must be designed and tested to determine if it is worth constructing as an integrated circuit. That design process requires engi- neers who know the characteristics of each device used in the system, including undesirable characteristics that are part of any electronic element. In other words, there are no ideal (perfect) elements in an elec- tronic design. Considering the limitations of each component is neces- sary to ensure a reliable response under all conditions of temperature, vibration, and effects of the surrounding environment. To develop this awareness requires time and must begin with understanding the basic characteristics of the device, as covered in this text. One of the objec- tives of this text is to explain how ideal components work and their func- tion in a network. Another is to explain conditions in which components may not be ideal. One of the very positive aspects of the learning process associated with electric and electronic circuits is that once a concept or procedure is clearly and correctly understood, it will be useful throughout the career of the individual at any level in the industry. Once a law or equation is understood, it will not be replaced by another equation as the material becomes more advanced and complicated. For instance, one of the first laws to be introduced is Ohm’s law. This law provides a relationship be- tween forces and components that will always be true, no matter how complicated the system becomes. In fact, it is an equation that will be applied in various forms throughout the design of the entire system. The use of the basic laws may change, but the laws will not change and will always be applicable. It is vitally important to understand that the learning process for cir- cuit analysis is sequential. Your beginning studies will establish the foundation for the material that follows. Failure to properly understand the early material will only lead to difficulties understanding the mate- rial later in this course. This chapter provides a brief history of the field followed by a review of mathematical concepts necessary to understand the rest of the material. 2  INTRODUCTION 2 A BRIEF HISTORY In the sciences, once a hypothesis is proven and accepted, it becomes one of the building blocks of that area of study, permitting additional in- vestigation and development. Naturally, the more pieces of a puzzle available, the more obvious is the avenue toward a possible solution. In fact, history demonstrates that a single development may provide the key that will result in a mushrooming effect that brings the science to a new plateau of understanding and impact. If the opportunity presents itself, read one of the many publications reviewing the history of this field. Space requirements are such that only a brief review can be provided here. There are many more contributors than could be listed, and their efforts have often provided important keys to the solution of some very important concepts. Throughout history, some periods were characterized by what ap- peared to be an explosion of interest and development in particular areas. As you will see from the discussion of the late 1700s and the early 1800s, inventions, discoveries, and theories came fast and furiously. Each new concept broadens the possible areas of application until it be- comes almost impossible to trace developments without picking a par- ticular area of interest and following it through. In the review, as you read about the development of radio, television, and computers, keep in mind that similar progressive steps were occurring in the areas of the telegraph, the telephone, power generation, the phonograph, appliances, and so on. There is a tendency when reading about the great scientists, inventors, and innovators to believe that their contribution was a totally individual effort. In many instances, this was not the case. In fact, many of the great contributors had friends or associates who provided support and encour- agement in their efforts to investigate various theories. At the very least, they were aware of one another’s efforts to the degree possible in the days when a letter was often the best form of communication. In partic- ular, note the closeness of the dates during periods of rapid development. One contributor seemed to spur on the efforts of the others or possibly provided the key needed to continue with the area of interest. In the early stages, the contributors were not electrical, electronic, or computer engineers as we know them today. In most cases, they were physicists, chemists, mathematicians, or even philosophers. In addition, they were not from one or two communities of the Old World. The home country of many of the major contributors introduced in the paragraphs to follow is provided to show that almost every established community had some impact on the development of the fundamental laws of electri- cal circuits. As you proceed through your studies, you will find that a number of the units of measurement bear the name of major contributors in those areas—volt after Count Alessandro Volta, ampere after André Ampère, ohm after Georg Ohm, and so forth—fitting recognition for their impor- tant contributions to the birth of a major field of study. Time charts indicating a limited number of major developments are provided in Fig. 2, primarily to identify specific periods of rapid devel- opment and to reveal how far we have come in the last few decades. In essence, the current state of the art is a result of efforts that began in earnest some 250 years ago, with progress in the last 100 years being al- most exponential. 3  INTRODUCTION Development A.D. Gilbert 0 1000 1600 1750s 1900 2000 Fundamentals (a) Wi-Fi (1996) Electronic Floppy disk (1970) Vacuum computers (1945) Pentium 4 chip Electronics tube 1.5 GHz (2001) amplifiers B&W Solid-state Apple’s era TV era (1947) mouse Intel® Core™ 2 (1932) (1983) processor 3 GHz (2006) i Phone (2007) 1900 1950 2000 Memristor Nanotechnology ICs GPS (1993) Fundamentals FM (1958) radio Cell phone (1991) (1929) Mobile First laptop telephone (1946) computer (1979) First assembled Color TV (1940) PC (Apple II in 1977) (b) FIG. 2 Time charts: (a) long-range; (b) expanded. As you read through the following brief review, try to sense the grow- ing interest in the field and the enthusiasm and excitement that must have accompanied each new revelation. Although you may find some of the terms used in the review new and essentially meaningless, the re- maining chapters will explain them thoroughly. The Beginning The phenomenon of static electricity has intrigued scholars throughout history. The Greeks called the fossil resin substance so often used to demonstrate the effects of static electricity elektron, but no extensive study was made of the subject until William Gilbert researched the phe- nomenon in 1600. In the years to follow, there was a continuing investi- gation of electrostatic charge by many individuals, such as Otto von Guericke, who developed the first machine to generate large amounts of charge, and Stephen Gray, who was able to transmit electrical charge over long distances on silk threads. Charles DuFay demonstrated that charges either attract or repel each other, leading him to believe that there were two types of charge—a theory we subscribe to today with our defined positive and negative charges. There are many who believe that the true beginnings of the electrical era lie with the efforts of Pieter van Musschenbroek and Benjamin Franklin. In 1745, van Musschenbroek introduced the Leyden jar for the storage of electrical charge (the first capacitor) and demonstrated electrical shock (and therefore the power of this new form of energy). Franklin used the Leyden jar some 7 years later to establish that light- ning is simply an electrical discharge, and he expanded on a number of other important theories, including the definition of the two types of charge as positive and negative. From this point on, new discoveries and theories seemed to occur at an increasing rate as the number of individu- als performing research in the area grew. 4  INTRODUCTION In 1784, Charles Coulomb demonstrated in Paris that the force be- tween charges is inversely related to the square of the distance between the charges. In 1791, Luigi Galvani, professor of anatomy at the Univer- sity of Bologna, Italy, performed experiments on the effects of electricity on animal nerves and muscles. The first voltaic cell, with its ability to produce electricity through the chemical action of a metal dissolving in an acid, was developed by another Italian, Alessandro Volta, in 1799. The fever pitch continued into the early 1800s, with Hans Christian Oersted, a Danish professor of physics, announcing in 1820 a relation- ship between magnetism and electricity that serves as the foundation for the theory of electromagnetism as we know it today. In the same year, a French physicist, André Ampère, demonstrated that there are magnetic effects around every current-carrying conductor and that current-carrying conductors can attract and repel each other just like magnets. In the period 1826 to 1827, a German physicist, Georg Ohm, introduced an important relationship between potential, current, and re- sistance that we now refer to as Ohm’s law. In 1831, an English physi- cist, Michael Faraday, demonstrated his theory of electromagnetic induction, whereby a changing current in one coil can induce a changing current in another coil, even though the two coils are not directly con- nected. Faraday also did extensive work on a storage device he called the condenser, which we refer to today as a capacitor. He introduced the idea of adding a dielectric between the plates of a capacitor to increase the storage capacity. James Clerk Maxwell, a Scottish professor of natu- ral philosophy, performed extensive mathematical analyses to develop what are currently called Maxwell’s equations, which support the efforts of Faraday linking electric and magnetic effects. Maxwell also devel- oped the electromagnetic theory of light in 1862, which, among other things, revealed that electromagnetic waves travel through air at the ve- locity of light (186,000 miles per second or 3 × 108 meters per second). In 1888, a German physicist, Heinrich Rudolph Hertz, through experi- mentation with lower-frequency electromagnetic waves (microwaves), substantiated Maxwell’s predictions and equations. In the mid-1800s, Gustav Robert Kirchhoff introduced a series of laws of voltages and currents that find application at every level and area of this field. In 1895, another German physicist, Wilhelm Röntgen, discovered electro- magnetic waves of high frequency, commonly called X-rays today. By the end of the 1800s, a significant number of the fundamental equations, laws, and relationships had been established, and various fields of study, including electricity, electronics, power generation and distribution, and communication systems, started to develop in earnest. The Age of Electronics Radio The true beginning of the electronics era is open to debate and is sometimes attributed to efforts by early scientists in applying potentials across evacuated glass envelopes. However, many trace the beginning to Thomas Edison, who added a metallic electrode to the vacuum of the tube and discovered that a current was established between the metal electrode and the filament when a positive voltage was applied to the metal electrode. The phenomenon, demonstrated in 1883, was referred to as the Edison effect. In the period to follow, the transmission of radio waves and the development of the radio received widespread attention. In 1887, Heinrich Hertz, in his efforts to verify Maxwell’s equations, 5  INTRODUCTION transmitted radio waves for the first time in his laboratory. In 1896, an Italian scientist, Guglielmo Marconi (often called the father of the radio), demonstrated that telegraph signals could be sent through the air over long distances (2.5 kilometers) using a grounded antenna. In the same year, Aleksandr Popov sent what might have been the first radio message some 300 yards. The message was the name “Heinrich Hertz” in respect for Hertz’s earlier contributions. In 1901, Marconi established radio communication across the Atlantic. In 1904, John Ambrose Fleming expanded on the efforts of Edison to develop the first diode, commonly called Fleming’s valve—actually the first of the electronic devices. The device had a profound impact on the design of detectors in the receiving section of radios. In 1906, Lee De Forest added a third element to the vacuum structure and created the first amplifier, the triode. Shortly thereafter, in 1912, Edwin Armstrong built the first regenerative circuit to improve receiver capabilities and then used the same contribution to develop the first nonmechanical oscillator. By 1915, radio signals were being transmitted across the United States, and in 1918 Armstrong applied for a patent for the superheterodyne cir- cuit employed in virtually every television and radio to permit amplifica- tion at one frequency rather than at the full range of incoming signals. The major components of the modern-day radio were now in place, and sales in radios grew from a few million dollars in the early 1920s to over $1 billion by the 1930s. The 1930s were truly the golden years of radio, with a wide range of productions for the listening audience. Television The 1930s were also the true beginnings of the television era, although development on the picture tube began in earlier years with Paul Nipkow and his electrical telescope in 1884 and John Baird and his long list of successes, including the transmission of television pictures over telephone lines in 1927 and over radio waves in 1928, and simulta- neous transmission of pictures and sound in 1930. In 1932, NBC in- stalled the first commercial television antenna on top of the Empire State Building in New York City, and RCA began regular broadcasting in 1939. World War 2 slowed development and sales, but in the mid-1940s the number of sets grew from a few thousand to a few million. Color tel- evision became popular in the early 1960s. Computers The earliest computer system can be traced back to Blaise Pascal in 1642 with his mechanical machine for adding and sub- tracting numbers. In 1673, Gottfried Wilhelm von Leibniz used the Leibniz wheel to add multiplication and division to the range of opera- tions, and in 1823 Charles Babbage developed the difference engine to add the mathematical operations of sine, cosine, logarithms, and several others. In the years to follow, improvements were made, but the system remained primarily mechanical until the 1930s when electromechanical systems using components such as relays were introduced. It was not until the 1940s that totally electronic systems became the new wave. It is interesting to note that, even though IBM was formed in 1924, it did not enter the computer industry until 1937. An entirely electronic system known as ENIAC was dedicated at the University of Pennsylvania in 1946. It contained 18,000 tubes and weighed 30 tons but was several times faster than most electromechanical systems. Although other vac- uum tube systems were built, it was not until the birth of the solid-state era that computer systems experienced a major change in size, speed, and capability. 6  INTRODUCTION The Solid-State Era In 1947, physicists William Shockley, John Bardeen, and Walter H. Brattain of Bell Telephone Laboratories demonstrated the point-contact transistor (Fig. 3), an amplifier constructed entirely of solid-state ma- terials with no requirement for a vacuum, glass envelope, or heater volt- age for the filament. Although reluctant at first due to the vast amount of material available on the design, analysis, and synthesis of tube net- works, the industry eventually accepted this new technology as the wave of the future. In 1958, the first integrated circuit (IC) was devel- oped at Texas Instruments, and in 1961 the first commercial integrated circuit was manufactured by the Fairchild Corporation. It is impossible to review properly the entire history of the electrical/ electronics field in a few pages. The effort here, both through the dis- cussion and the time graphs in Fig. 2, was to reveal the amazing progress of this field in the last 50 years. The growth appears to be truly exponential since the early 1900s, raising the interesting ques- tion, Where do we go from here? The time chart suggests that the next few decades will probably contain many important innovative contri- FIG. 3 butions that may cause an even faster growth curve than we are now The first transistor. experiencing. (Used with permission of Lucent Technologies Inc./ Bell Labs.) 3 UNITS OF MEASUREMENT One of the most important rules to remember and apply when working in any field of technology is to use the correct units when substituting numbers into an equation. Too often we are so intent on obtaining a nu- merical solution that we overlook checking the units associated with the numbers being substituted into an equation. Results obtained, therefore, are often meaningless. Consider, for example, the following very funda- mental physics equation: y  velocity d y d  distance (1) t t  time Assume, for the moment, that the following data are obtained for a mov- ing object: d  4000 ft t  1 min and y is desired in miles per hour. Often, without a second thought or consideration, the numerical values are simply substituted into the equa- tion, with the result here that d 4000 ft y   4000 mph t 1 min As indicated above, the solution is totally incorrect. If the result is de- sired in miles per hour, the unit of measurement for distance must be miles, and that for time, hours. In a moment, when the problem is ana- lyzed properly, the extent of the error will demonstrate the importance of ensuring that the numerical value substituted into an equation must have the unit of measurement specified by the equation. 7  INTRODUCTION The next question is normally, How do I convert the distance and time to the proper unit of measurement? A method is presented in Section 9 of this chapter, but for now it is given that 1 mi  5280 ft 4000 ft  0.76 mi 1 min  601 h  0.017 h Substituting into Eq. (1), we have d 0.76 mi y   44.71 mph t 0.017 h which is significantly different from the result obtained before. To complicate the matter further, suppose the distance is given in kilometers, as is now the case on many road signs. First, we must re- alize that the prefix kilo stands for a multiplier of 1000 (to be intro- duced in Section 5), and then we must find the conversion factor between kilometers and miles. If this conversion factor is not readily available, we must be able to make the conversion between units using the conversion factors between meters and feet or inches, as de- scribed in Section 9. Before substituting numerical values into an equation, try to mentally establish a reasonable range of solutions for comparison purposes. For instance, if a car travels 4000 ft in 1 min, does it seem reasonable that the speed would be 4000 mph? Obviously not! This self-checking procedure is particularly important in this day of the hand-held calculator, when ridiculous results may be accepted simply because they appear on the digital display of the instrument. Finally, if a unit of measurement is applicable to a result or piece of data, then it must be applied to the numerical value. To state that y  44.71 without including the unit of measurement mph is meaningless. Eq. (1) is not a difficult one. A simple algebraic manipulation will re- sult in the solution for any one of the three variables. However, in light of the number of questions arising from this equation, the reader may wonder if the difficulty associated with an equation will increase at the same rate as the number of terms in the equation. In the broad sense, this will not be the case. There is, of course, more room for a mathematical error with a more complex equation, but once the proper system of units is chosen and each term properly found in that system, there should be very little added difficulty associated with an equation requiring an in- creased number of mathematical calculations. In review, before substituting numerical values into an equation, be absolutely sure of the following: 1. Each quantity has the proper unit of measurement as defined by the equation. 2. The proper magnitude of each quantity as determined by the defining equation is substituted. 3. Each quantity is in the same system of units (or as defined by the equation). 4. The magnitude of the result is of a reasonable nature when compared to the level of the substituted quantities. 5. The proper unit of measurement is applied to the result. 8  INTRODUCTION 4 SYSTEMS OF UNITS In the past, the systems of units most commonly used were the English and metric, as outlined in Table 1. Note that while the English system is based on a single standard, the metric is subdivided into two interrelated standards: the MKS and the CGS. Fundamental quantities of these sys- tems are compared in Table 1 along with their abbreviations. The MKS and CGS systems draw their names from the units of measurement used with each system; the MKS system uses Meters, Kilograms, and Seconds, while the CGS system uses Centimeters, Grams, and Seconds. TABLE 1 Comparison of the English and metric systems of units. ENGLISH METRIC SI MKS CGS Length: Meter (m) Centimeter (cm) Meter (m) Yard (yd) (39.37 in.) (2.54 cm  1 in.) (0.914 m) (100 cm) Mass: Slug Kilogram (kg) Gram (g) Kilogram (kg) (14.6 kg) (1000 g) Force: Newton (N) Pound (lb) Newton (N) Dyne (4.45 N) (100,000 dynes) Temperature: Fahrenheit (°F) Celsius or Centigrade (°C) Kelvin (K) K  273.15  °C a °C  32 b 9 Centigrade (°C) 冢 5 冣 5  (°F  32) 9 Energy: Foot-pound (ft-lb) Newton-meter (N m) Dyne-centimeter or erg Joule (J) (1.356 joules) or joule (J) (1 joule  107 ergs) (0.7376 ft-lb) Time: Second (s) Second (s) Second (s) Second (s) Understandably, the use of more than one system of units in a world that finds itself continually shrinking in size, due to advanced technical developments in communications and transportation, would introduce unnecessary complications to the basic understanding of any technical data. The need for a standard set of units to be adopted by all nations has become increasingly obvious. The International Bureau of Weights and Measures located at Sèvres, France, has been the host for the General Conference of Weights and Measures, attended by representatives from all nations of the world. In 1960, the General Conference adopted a sys- tem called Le Système International d’Unités (International System of Units), which has the international abbreviation SI. It was adopted by the Institute of Electrical and Electronic Engineers (IEEE) in 1965 and by the United States of America Standards Institute (USASI) in 1967 as a standard for all scientific and engineering literature. For comparison, the SI units of measurement and their abbreviations appear in Table 1. These abbreviations are those usually applied to each unit of measurement, and they were carefully chosen to be the most ef- fective. Therefore, it is important that they be used whenever applicable 9  INTRODUCTION Length: 1 yard (yd) = 0.914 meter (m) = 3 feet (ft) 1 m = 100 cm = 39.37 in. 2.54 cm = 1 in. SI and MKS 1m English 1 in. Actual English 1 yd lengths CGS 1 cm English 1 ft Mass: Force: 1 slug = 14.6 kilograms English 1 pound (lb) 1 pound (lb) = 4.45 newtons (N) 1 kilogram = 1000 g 1 newton = 100,000 dynes (dyn) 1 slug English 1 kg 1g SI and SI and CGS MKS MKS 1 newton (N) 1 dyne (CGS) Temperature: MKS and English CGS SI (Boiling) 212˚F 373.15 K Energy: 100˚C English 1 ft-lb SI and MKS 1 ft-lb = 1.356 joules 7 (Freezing) 1 joule (J) 1 joule = 10 ergs 32˚F 0˚C 273.15 K 0˚F 9 ˚F = 5_ ˚C + 32˚ 1 erg (CGS) ˚C = _5 (˚F – 32˚) 9 K = 273.15 + ˚C (Absolute zero) – 459.7˚F –273.15˚C 0K Fahrenheit Celsius or Kelvin Centigrade FIG. 4 Comparison of units of the various systems of units. to ensure universal understanding. Note the similarities of the SI system to the MKS system. This text uses, whenever possible and practical, all of the major units and abbreviations of the SI system in an effort to sup- port the need for a universal system. Those readers requiring additional information on the SI system should contact the information office of the American Society for Engineering Education (ASEE).* Figure 4 should help you develop some feeling for the relative mag- nitudes of the units of measurement of each system of units. Note in the figure the relatively small magnitude of the units of measurement for the CGS system. A standard exists for each unit of measurement of each system. The standards of some units are quite interesting. The meter was originally defined in 1790 to be 1/10,000,000 the dis- tance between the equator and either pole at sea level, a length preserved *American Society for Engineering Education (ASEE), 1818 N Street N.W., Suite 600, Washington, D.C. 20036-2479; (202) 331-3500; http://www.asee.org/. 10  INTRODUCTION on a platinum–iridium bar at the International Bureau of Weights and Measures at Sèvres, France. The meter is now defined with reference to the speed of light in a vacuum, which is 299,792,458 m/s. The kilogram is defined as a mass equal to 1000 times the mass of 1 cubic centimeter of pure water at 4°C. This standard is preserved in the form of a platinum–iridium cylinder in Sèvres. The second was originally defined as 1/86,400 of the mean solar day. However, since Earth’s rotation is slowing down by almost 1 second every 10 years, the second was redefined in 1967 as 9,192,631,770 periods of the electromagnetic radiation emitted by a particular transition of the cesium atom. 5 SIGNIFICANT FIGURES, ACCURACY, AND ROUNDING OFF This section emphasizes the importance of knowing the source of a piece of data, how a number appears, and how it should be treated. Too often we write numbers in various forms with little concern for the for- mat used, the number of digits that should be included, and the unit of measurement to be applied. For instance, measurements of 22.1 in. and 22.10 in. imply different levels of accuracy. The first suggests that the measurement was made by an instrument accurate only to the tenths place; the latter was obtained with instrumentation capable of reading to the hundredths place. The use of zeros in a number, therefore, must be treated with care, and the impli- cations must be understood. In general, there are two types of numbers: exact and approximate. Exact numbers are precise to the exact number of digits presented, just as we know that there are 12 apples in a dozen and not 12.1. Through- out the text, the numbers that appear in the descriptions, diagrams, and examples are considered exact, so that a battery of 100 V can be writ- ten as 100.0 V, 100.00 V, and so on, since it is 100 V at any level of pre- cision. The additional zeros were not included for purposes of clarity. However, in the laboratory environment, where measurements are con- tinually being taken and the level of accuracy can vary from one in- strument to another, it is important to understand how to work with the results. Any reading obtained in the laboratory should be consid- ered approximate. The analog scales with their pointers may be difficult to read, and even though the digital meter provides only specific dig- its on its display, it is limited to the number of digits it can provide, leaving us to wonder about the less significant digits not appearing on the display. The precision of a reading can be determined by the number of significant figures (digits) present. Significant digits are those integers (0 to 9) that can be assumed to be accurate for the measurement being made. The result is that all nonzero numbers are considered significant, with zeros being significant in only some cases. For instance, the zeros in 1005 are considered significant because they define the size of the number and are surrounded by nonzero digits. For the number 0.4020, the zero to the left of the decimal point is not significant, but the other 11  INTRODUCTION two zeros are because they define the magnitude of the number and the fourth-place accuracy of the reading. When adding approximate numbers, it is important to be sure that the accuracy of the readings is consistent throughout. To add a quantity ac- curate only to the tenths place to a number accurate to the thousandths place will result in a total having accuracy only to the tenths place. One cannot expect the reading with the higher level of accuracy to improve the reading with only tenths-place accuracy. In the addition or subtraction of approximate numbers, the entry with the lowest level of accuracy determines the format of the solution. For the multiplication and division of approximate numbers, the result has the same number of significant figures as the number with the least number of significant figures. For approximate numbers (and exact numbers, for that matter), there is often a need to round off the result; that is, you must decide on the ap- propriate level of accuracy and alter the result accordingly. The accepted procedure is simply to note the digit following the last to appear in the rounded-off form, add a 1 to the last digit if it is greater than or equal to 5, and leave it alone if it is less than 5. For example, 3.186 ⬵ 3.19 ⬵ 3.2, depending on the level of precision desired. The symbol ⬵ means ap- proximately equal to. EXAMPLE 1 Perform the indicated operations with the following ap- proximate numbers and round off to the appropriate level of accuracy. a. 532.6  4.02  0.036  536.656 ⬵ 536.7 (as determined by 532.6) b. 0.04  0.003  0.0064  0.0494 ⬵ 0.05 (as determined by 0.04) EXAMPLE 2 Round off the following numbers to the hundredths place. a. 32.419  32.42 b. 0.05328  0.05 EXAMPLE 3 Round off the result 5.8764 to a. tenths-place accuracy. b. hundredths-place accuracy. c. thousands-place accuracy. Solution: a. 5.9 b. 5.88 c. 5.876 6 POWERS OF TEN It should be apparent from the relative magnitude of the various units of measurement that very large and very small numbers are frequently en- countered in the sciences. To ease the difficulty of mathematical operations with numbers of such varying size, powers of ten are usually employed. This notation takes full advantage of the mathematical properties of powers 12  INTRODUCTION of ten. The notation used to represent numbers that are integer powers of ten is as follows: 1  100 1/10  0.1  101 10  101 1/100  0.01  102 100  102 1/1000  0.001  103 1000  103 1/10,000  0.0001  104 In particular, note that 100  1, and, in fact, any quantity to the zero power is 1 (x0  1, 10000  1, and so on). Numbers in the list greater than 1 are associated with positive powers of ten, and numbers in the list less than 1 are associated with negative powers of ten. A quick method of determining the proper power of ten is to place a caret mark to the right of the numeral 1 wherever it may occur; then count from this point to the number of places to the right or left before arriving at the decimal point. Moving to the right indicates a positive power of ten, whereas moving to the left indicates a negative power. For example, 10,000.0  1 0 , 0 0 0.  104 1 2 3 4 0.00001  0. 0 0 0 0 1  105 5 4 3 2 1 Some important mathematical equations and relationships pertaining to powers of ten are listed below, along with a few examples. In each case, n and m can be any positive or negative real number. 1 1  10n  10n (2) 10n 10n Eq. (2) clearly reveals that shifting a power of ten from the denomi- nator to the numerator, or the reverse, requires simply changing the sign of the power. EXAMPLE 4 1 1 a.  3  103 1000 10 1 1 b.  5  10 5 0.00001 10 The product of powers of ten: 110n 2 110m 2  1102 1nm2 (3) EXAMPLE 5 a. (1000)(10,000)  (103)(104)  10(34)  107 b. (0.00001)(100)  (105)(102)  10(52)  103 The division of powers of ten: 10n  101nm2 (4) 10m 13  INTRODUCTION EXAMPLE 6 105  2  101522  103 100,000 a. 100 10 103  4  10131422  101342  107 1000 b. 0.0001 10 Note the use of parentheses in part (b) to ensure that the proper sign is established between operators. The power of powers of ten: 110n 2 m  10nm (5) EXAMPLE 7 a. (100)4  (102)4  10(2)(4)  108 b. (1000)2  (103)2  10(3)(2)  106 c. (0.01)3  (102)3  10(2)(3)  106 Basic Arithmetic Operations Let us now examine the use of powers of ten to perform some basic arithmetic operations using numbers that are not just powers of ten. The number 5000 can be written as 5  1000 = 5  103, and the number 0.0004 can be written as 4  0.0001  4  104. Of course, 105 can also be written as 1  105 if it clarifies the operation to be performed. Addition and Subtraction To perform addition or subtraction using powers of ten, the power of ten must be the same for each term; that is, A  10n  B  10n  1A  B2  10n (6) Eq. (6) covers all possibilities, but students often prefer to remember a verbal description of how to perform the operation. Eq. (6) states when adding or subtracting numbers in a power-of-ten format, be sure that the power of ten is the same for each number. Then separate the multipliers, perform the required operation, and apply the same power of ten to the result. EXAMPLE 8 a. 6300  75,000  (6.3)(1000)  (75)(1000)  6.3  103  75  103  (6.3  75)  103  81.3  103 b. 0.00096  0.000086  (96)(0.00001)  (8.6)(0.00001)  96  105  8.6  105  (96  8.6)  105  87.4  105 14  INTRODUCTION Multiplication In general, 1A  10n 2 1B  10m 2  1A2 1B2  10nm (7) revealing that the operations with the power of ten can be separated from the operation with the multipliers. Eq. (7) states when multiplying numbers in the power-of-ten format, first find the product of the multipliers and then determine the power of ten for the result by adding the power-of-ten exponents. EXAMPLE 9 a. (0.0002)(0.000007)  [(2)(0.0001)][(7)(0.000001)]  (2  104)(7  106)  (2)(7)  (104)(106)  14  1010 b. (340,000)(0.00061)  (3.4  105)(61  105)  (3.4)(61)  (105)(105)  207.4  100  207.4 Division In general, A  10n A m   10nm (8) B  10 B revealing again that the operations with the power of ten can be sepa- rated from the same operation with the multipliers. Eq. (8) states when dividing numbers in the power-of-ten format, first find the result of dividing the mutipliers. Then determine the associated power for the result by subtracting the power of ten of the denominator from the power of ten of the numerator. EXAMPLE 10 47  105 105 a b a b  23.5  102 0.00047 47 a.    0.002 2  103 2 103 69  104 104 a b a b  5.31  1012 690,000 69 b.    0.00000013 13  108 13 108 Powers In general, 1A  10n 2 m  Am  10nm (9) which again permits the separation of the operation with the power of ten from the multiplier. Eq. (9) states when finding the power of a number in the power-of-ten format, first separate the multiplier from the power of ten and determine each separately. Determine the power-of-ten component by multiplying the power of ten by the power to be determined. 15  INTRODUCTION EXAMPLE 11 a. (0.00003)3  (3  105)3  (3)3  (105)3  27  1015 b. (90,800,000)2  (9.08  107)2  (9.08)2  (107)2  82.45  1014 In particular, remember that the following operations are not the same. One is the product of two numbers in the power-of-ten format, while the other is a number in the power-of-ten format taken to a power. As noted below, the results of each are quite different: (103)(103) ⬆ (103)3 (103)(103)  106  1,000,000 (103)3  (103)(103)(103)  109  1,000,000,000 7 FIXED-POINT, FLOATING-POINT, SCIENTIFIC, AND ENGINEERING NOTATION When you are using a computer or a calculator, numbers generally appear in one of four ways. If powers of ten are not employed, numbers are written in the fixed-point or floating-point notation. The fixed-point format requires that the decimal point appear in the same place each time. In the floating-point format, the decimal point appears in a location defined by the number to be displayed. Most computers and calculators permit a choice of fixed- or floating- point notation. In the fixed format, the user can choose the level of accu- racy for the output as tenths place, hundredths place, thousandths place, and so on. Every output will then fix the decimal point to one location, such as the following examples using thousandths-place accuracy: 1 1 2300  0.333  0.063  1150.000 3 16 2 If left in the floating-point format, the results will appear as follows for the above operations: 1 1 2300  0.333333333333  0.0625  1150 3 16 2 Powers of ten will creep into the fixed- or floating-point notation if the number is too small or too large to be displayed properly. Scientific (also called standard) notation and engineering notation make use of powers of ten, with restrictions on the mantissa (multiplier) or scale factor (power of ten). Scientific notation requires that the decimal point appear directly after the first digit greater than or equal to 1 but less than 10. A power of ten will then appear with the number (usually following the power notation E), even if it has to be to the zero power. A few examples: 1 1 2300  3.33333333333E1  6.25E2  1.15E3 3 16 2 Within scientific notation, the fixed- or floating-point format can be chosen. In the above examples, floating was employed. If fixed is chosen 16  INTRODUCTION and set at the hundredths-point accuracy, the following will result for the above operations: 1 1 2300  3.33E1  6.25E2  1.15E3 3 16 2 Engineering notation specifies that all powers of ten must be 0 or multiples of 3, and the mantissa must be greater than or equal to 1 but less than 1000. This restriction on the powers of ten is because specific powers of ten have been assigned prefixes that are introduced in the next few para- graphs. Using scientific notation in the floating-point mode results in the following for the above operations: 1 1 2300  333.333333333E3  62.5E3  1.15E3 3 16 2 Using engineering notation with two-place accuracy will result in the following: 1 1 2300  333.33E3  62.50E3  1.15E3 3 16 2 Prefixes Specific powers of ten in engineering notation have been assigned pre- fixes and symbols, as appearing in Table 2. They permit easy recognition of the power of ten and an improved channel of communication between technologists. TABLE 2 Multiplication SI SI Factors Prefix Symbol 1 000 000 000 000 000 000  1018 exa E 1 000 000 000 000 000  1015 peta P 1 000 000 000 000  1012 tera T 1 000 000 000  109 giga G 1 000 000  106 mega M 1 000  103 kilo k 0.001  103 milli m 0.000 001  106 micro M 0.000 000 001  109 nano n 0.000 000 000 001  1012 pico p 0.000 000 000 000 001  1015 femto f 0.000 000 000 000 000 001  1018 atto a EXAMPLE 12 a. 1,000,000 ohms  1  106 ohms  1 megohm  1 MΩ b. 100,000 meters  100  103 meters  100 kilometers  100 km 17  INTRODUCTION c. 0.0001 second  0.1  103 second  0.1 millisecond  0.1 ms d. 0.000001 farad  1  106 farad  1 microfarad  1 MF Here are a few examples with numbers that are not strictly powers of ten. EXAMPLE 13 a. 41,200 m is equivalent to 41.2  103 m  41.2 kilometers  41.2 km. b. 0.00956 J is equivalent to 9.56  103 J  9.56 millijoules  9.56 mJ. c. 0.000768 s is equivalent to 768  106 s  768 microseconds  768 Ms. 8.4  103 m 103  a b  a 2 b m 8400 m 8.4 d.  2 0.06 6  10 6 10  1.4 × 105 m  140  103 m  140 kilometers  140 km e. (0.0003) s  (3  104)4 s  81  1016 s 4  0.0081  1012 s  0.0081 picosecond  0.0081 ps 8 CONVERSION BETWEEN LEVELS OF POWERS OF TEN It is often necessary to convert from one power of ten to another. For in- stance, if a meter measures kilohertz (kHz—a unit of measurement for the frequency of an ac waveform), it may be necessary to find the corre- sponding level in megahertz (MHz). If time is measured in milliseconds (ms), it may be necessary to find the corresponding time in microsec- onds (␮s) for a graphical plot. The process is not difficult if we simply keep in mind that an increase or a decrease in the power of ten must be associated with the opposite effect on the multiplying factor. The proce- dure is best described by the following steps: 1. Replace the prefix by its corresponding power of ten. 2. Rewrite the expression, and set it equal to an unknown multiplier and the new power of ten. 3. Note the change in power of ten from the original to the new format. If it is an increase, move the decimal point of the original multiplier to the left (smaller value) by the same number. If it is a decrease, move the decimal point of the original multiplier to the right (larger value) by the same number. EXAMPLE 14 Convert 20 kHz to megahertz. Solution: In the power-of-ten format: 20 kHz  20  103 Hz The conversion requires that we find the multiplying factor to appear in the space below: Increase by 3 20  10 Hz 3  106 Hz Decrease by 3 18  INTRODUCTION Since the power of ten will be increased by a factor of three, the mul- tiplying factor must be decreased by moving the decimal point three places to the left, as shown below: 020.  0.02 3 and 20  103 Hz  0.02  106 Hz  0.02 MHz EXAMPLE 15 Convert 0.01 ms to microseconds. Solution: In the power-of-ten format: 0.01 ms  0.01  103 s Decrease by 3 3 and 0.01  10 s  106 s Increase by 3 Since the power of ten will be reduced by a factor of three, the multi- plying factor must be increased by moving the decimal point three places to the right, as follows: 0.010  10 3 and 0.01  103 s  10  106 s  10 Ms There is a tendency when comparing 3 to 6 to think that the power of ten has increased, but keep in mind when making your judg- ment about increasing or decreasing the magnitude of the multiplier that 106 is a great deal smaller than 103. EXAMPLE 16 Convert 0.002 km to millimeters. Solution: Decrease by 6 0.002  10 m 3  103 m Increase by 6 In this example we have to be very careful because the difference be- tween 3 and 3 is a factor of 6, requiring that the multiplying factor be modified as follows: 0.002000  2000 6 and 0.002  103 m  2000  103 m  2000 mm 9 CONVERSION WITHIN AND BETWEEN SYSTEMS OF UNITS The conversion within and between systems of units is a process that cannot be avoided in the study of any technical field. It is an operation, however, that is performed incorrectly so often that this section was in- cluded to provide one approach that, if applied properly, will lead to the correct result. 19  INTRODUCTION There is more than one method of performing the conversion process. In fact, some people prefer to determine mentally whether the conver- sion factor is multiplied or divided. This approach is acceptable for some elementary conversions, but it is risky with more complex operations. The procedure to be described here is best introduced by examining a relatively simple problem such as converting inches to meters. Specifi- cally, let us convert 48 in. (4 ft) to meters. If we multiply the 48 in. by a factor of 1, the magnitude of the quan- tity remains the same: 48 in.  48 in.112 (10) Let us now look at the conversion factor for this example: 1 m  39.37 in. Dividing both sides of the conversion factor by 39.37 in. results in the following format:  112 1m 39.37 in. Note that the end result is that the ratio 1 m/39.37 in. equals 1, as it should since they are equal quantities. If we now substitute this factor (1) into Eq. (10), we obtain 48 in.112  48 in. a b 1m 39.37 in. which results in the cancellation of inches as a unit of measure and leaves meters as the unit of measure. In addition, since the 39.37 is in the denominator, it must be divided into the 48 to complete the operation: 48 m  1.219 m 39.37 Let us now review the method: 1. Set up the conversion factor to form a numerical value of (1) with the unit of measurement to be removed from the original quantity in the denominator. 2. Perform the required mathematics to obtain the proper magnitude for the remaining unit of measurement. EXAMPLE 17 Convert 6.8 min to seconds. Solution: The conversion factor is 1 min  60 s Since the minute is to be removed as the unit of measurement, it must appear in the denominator of the (1) factor, as follows: a b  112 60 s Step 1: 1 min 6.8 min 112  6.8 min a b  16.82 160 2 s 60 s Step 2: 1 min  408 s 20  INTRODUCTION EXAMPLE 18 Convert 0.24 m to centimeters. Solution: The conversion factor is 1 m  100 cm Since the meter is to be removed as the unit of measurement, it must ap- pear in the denominator of the (1) factor as follows: a b 1 100 cm Step 1: 1m 0.24 m112  0.24 m a b  10.242 11002 cm 100 cm Step 2: 1m  24 cm The products (1)(1) and (1)(1)(1) are still 1. Using this fact, we can perform a series of conversions in the same operation. EXAMPLE 19 Determine the number of minutes in half a day. Solution: Working our way through from days to hours to minutes, always ensuring that the unit of measurement to be removed is in the denominator, results in the following sequence: 0.5 day a ba b  10.52 1242 1602 min 3h 60 min 1 day 1h  720 min EXAMPLE 20 Convert 2.2 yards to meters. Solution: Working our way through from yards to feet to inches to meters results in the following: 12.22 132 1122 2.2 yards a ba ba b  3 ft 12 in. 1m m 1 yard 1 ft 39.37 in. 39.37  2.012 m The following examples are variations of the above in practical situations. EXAMPLE 21 In Europe, Canada, and many other countries, the speed limit is posted in kilometers per hour. How fast in miles per hour is 100 km/h? Solution: a b 11 2 112 112 112 100 km h  a ba ba ba ba b 100 km 1000 m 39.37 in. 1 ft 1 mi h 1 km 1m 12 in. 5280 ft 11002 110002 139.372 mi  1122 152802 h  62.14 mph 21  INTRODUCTION TABLE 3 Many travelers use 0.6 as a conversion factor to simplify the math in- volved; that is, Symbol Meaning (100 km/h)(0.6) ⬵ 60 mph ⬆ Not equal to 6.12 ⬆ 6.13 > Greater than 4.78 > 4.20 and (60 km/h)(0.6) ⬵ 36 mph >> Much greater than 840 >> 16 < Less than 430 < 540 EXAMPLE 22 Determine the speed in miles per hour of a competitor 3 c. 10.022 2 e. 1 f. 0.1 d. 200,000 3 140002 2 4 33004 19. Using only those powers of ten listed in Table 2, express the following numbers in what seems to you the most logical e. form for future calculations: 2  104 a. 15,000 b. 0.005 f. [(0.000016)1>2] [(100,000)5] [0.02] c. 2,400,000 d. 60,000 3 10.0032 3 4 30.00007 4 2 3 11602 2 4 1a challenge2 e. 0.00040200 f. 0.0000000002 *g. 20. Perform the following operations: 3 12002 10.0008 2 4 1>2 a. 4200  48,000 b. 9  104  3.6  105 SECTION 7 Fixed-Point, Floating-Point, Scientific, c. 0.5  103 6  105 and Engineering Notation d. 1.2  103  50,000  103  400 21. Perform the following operations: 29. Write the following numbers in scientific and engineering a. (100)(1000) b. (0.01)(1000) notation to hundredths place: c. (103)(106) d. (100)(0.00001) a. 20.46 e. (106)(10,000,000) f. (10,000)(108) (1028) b. 50,420 c. 0.000674 22. Perform the following operations: d. 000.0460 a. (50,000) (0.002) b. 2200  0.002 30. Write the following numbers in scientific and engineering c. (0.000082) (1.2  106) notation to tenths place: d. (30  104) (0.004) (7  108) a. 5  102 23. Perform the following operations: b. 0.45  10 2 100 0.010 c. 1/32 a. b. d. p 10,000 1000 10,000 0.0000001 c. d. 0.001 100 SECTION 8 Conversion between Levels of 1038 11002 1>2 Powers of Ten e. f. 0.000100 0.01 31. Fill in the blanks of the following conversions: 24. Perform the following operations: a. 6  104  ______  106 2000 0.004 b. 0.4  103  ______  106 a. b. c. 50  105  ______  103  ______  106 0.00008 4  106  ______  109 0.000220 78  1018 c. d. d. 12  107  ______  103  ______  106 0.00005 4  106  ______  109 25. Perform the following operations: 32. Perform the following conversions: a. (100)3 b. (0.0001)1/2 a. 0.05 s to milliseconds 8 c. (10,000) d. (0.00000010)9 b. 2000 µs to milliseconds 26. Perform the following operations: c. 0.04 ms to microseconds a. (200)2 d. 8400 ps to microseconds b. (5  103)3 e. 100  103 mm to kilometers c. (0.004) (3  103)2 d. ((2  103) (0.8  104) (0.003  105))3 27. Perform the following operations: SECTION 9 Conversion within and between Systems 11002 1104 2 of Units a. (0.001)2 b. 1000 33. Perform the following conversions: 10.0012 1100 2 2 110 2 110,000 2 3 a. 1.5 min to seconds c. d. b. 2  102 h to seconds 10,000 1  104 c. 0.05 s to microseconds 10.00012 3 1100 2 3 1100 2 10.01 2 4 3 d. 0.16 m to millimeters e. *f. 3 11002 2 4 30.001 4 e. 0.00000012 s to nanoseconds 1  106 f. 4  108 s to days 29  INTRODUCTION 34. Perform the following metric conversions: 49. cos 21.87°  a. 80 mm to centimeters 3 b. 60 cm to kilometers *50. tan1  4 c. 12  103 m to micrometers d. 60 sq cm (cm2) to square meters (m2) 400 *51.  B 62  105 35. Perform the following conversions between systems: 8.2  103 a. 100 in. to meters *52. 1in engineering notation 2  b. 4 ft to meters 0.04  103 c. 6 lb to newtons 10.06  105 2 120  103 2 *53. 1in engineering notation 2  10.012 2 d. 60,000 dyn to pounds e. 150,000 cm to feet f. 0.002 mi to meters (5280 ft  1 mi) 4  104 1 *54. 3 5  36. What is a mile in feet, yards, meters, and kilometers? 2  10  400  10 2  10 6 37. Convert 60 mph to meters per second. 1in engineering notation 2  38. How long would it take a runner to complete a 10-km race if a pace of 6.5 min/mi were maintained? SECTION 13 Computer Analysis 39. Quarters are about 1 in. in diameter. How many would be required to stretch from one end of a football field to the 55. Investigate the availability of computer courses and com- other (100 yd)? puter time in your curriculum. Which languages are com- monly used, and which software packages are popular? 40. Compare the total time required to drive a long, tiring day of 500 mi at an average speed of 60 mph versus an average 56. Develop a list of three popular computer languages, includ- speed of 75 mph. Is the time saved for such a long trip ing a few characteristics of each. Why do you think some worth the added risk of the higher speed? languages are better for the analysis of electric circuits than others? *41. Find the distance in meters that a mass traveling at 600 cm/s will cover in 0.016 h. *42. Each spring there is a race up 86 floors of the 102-story Em- pire State Building in New York City. If you were able to GLOSSARY climb 2 steps/second, how long would it take in minutes to reach the 86th floor if each floor is 14 ft high and each step Cathode-ray tube (CRT) A glass enclosure with a relatively flat is about 9 in.? face (screen) and a vacuum inside that will display the light generated from the bombardment of the screen by electrons. *43. The record for the race in Problem 42 is 10.22 min. What CGS system The system of units employing the Centimeter, was the racer’s speed in min/mi for the race? Gram, and Second as its fundamental units of measure. *44. If the race of Problem 42 were a horizontal distance, how Difference engine One of the first mechanical calculators. long would it take a runner who can run 5-min miles to Edison effect Establishing a flow of charge between two ele- cover the distance? Compare this with the record speed of ments in an evacuated tube. Problem 43. Did gravity have a significant effect on the Electromagnetism The relationship between magnetic and overall time? electrical effects. Engineering notation A method of notation that specifies that all powers of ten used to define a number be multiples of 3 SECTION 11 Conversion Tables with a mantissa greater than or equal to 1 but less than 1000. 45. Determine the number of ENIAC The first totally electronic computer. a. Btu in 5 J of energy. Fixed-point notation Notation using a decimal point in a partic- b. cubic meters in 24 oz of a liquid. ular location to define the magnitude of a number. c. seconds in 1.4 days. Fleming’s valve The first of the electronic devices, the diode. d. pints in 1 m3 of a liquid. Floating-point notation Notation that allows the magnitude of a number to define where the decimal point should be placed. Integrated circuit (IC) A subminiature structure containing a SECTION 12 Calculators vast number of electronic devices designed to perform a par- Perform the following operations using a single sequence of cal- ticular set of functions. culator keys: Joule (J) A unit of measurement for energy in the SI or MKS system. Equal to 0.7378 foot-pound in the English system and 46. 6 (4  2  8)  107 ergs in the CGS system. 42  65 Kelvin (K) A unit of measurement for temperature in the SI sys- 47.  3 tem. Equal to 273.15  °C in the MKS and CGS systems. 2 2 52  a b  Kilogram (kg) A unit of measure for mass in the SI and MKS 48. systems. Equal to 1000 grams in the CGS system. B 3 30  INTRODUCTION Language A communication link between user and computer to Scientific notation A method for describing very large and very define the operations to be performed and the results to be dis- small numbers through the use of powers of ten, which played or printed. requires that the multiplier be a number between 1 and 10. Leyden jar One of the first charge-storage devices. Second (s) A unit of measurement for time in the SI, MKS, Menu A computer-generated list of choices for the user to deter- English, and CGS systems. mine the next operation to be performed. SI system The system of units adopted by the IEEE in 1965 and Meter (m) A unit of measure for length in the SI and MKS sys- the USASI in 1967 as the International System of Units tems. Equal to 1.094 yards in the English system and 100 cen- (Système International d’Unités). timeters in the CGS system. Slug A unit of measure for mass in the English system. Equal to MKS system The system of units employing the Meter, 14.6 kilograms in the SI or MKS system. Kilogram, and Second as its fundamental units of measure. Software package A computer program designed to perform Nanotechnology The production of integrated circuits in which specific analysis and design operations or generate results in a the nanometer is the typical unit of measurement. particular format. Newton (N) A unit of measurement for force in the SI and MKS Static electricity Stationary charge in a state of equilibrium. systems. Equal to 100,000 dynes in the CGS system. Transistor The first semiconductor amplifier. Pound (lb) A unit of measurement for force in the English sys- Voltaic cell A storage device that converts chemical to electrical tem. Equal to 4.45 newtons in the SI or MKS system. energy. Program A sequential list of commands, instructions, and so on, to perform a specified task using a computer. ANSWERS TO SELECTED ODD-NUMBERED PROBLEMS 5. 29.05 mph 25. (a) 1  106 (b) 10  103 35. (a) 2.54 m (b) 1.22 m 7. (a) 139.33 ft/s (b) 0.431 s (c) 100  1030 (d) 1  1063 (c) 26.7 N (d) 0.13 lb (c) 40.91 mph 27. (a) 1  106 (b) 1 105 (e) 4921.26 ft (f) 3.22 m 11. MKS, CGS  20°C; (c) 1  108 (d) 1  1011 37. 26.82 m/s SI, K  293.15 29. Scientific: (a) 2.05  101 39. 3600 quarters 13. 45.72 cm (b) 5.04  104 (c) 6.74  104 41. 345.6 m 15. (a) 14.6 (b) 56.0 (c) 1046.1 (d) 4.60  102 43. 44.82 min/mile (d) 0.1 (e) 3.1 Engineering: (a) 20.46  100 45. (a) 4.74  103 Btu 17. (a) 14.603 (b) 56.042 (b) 50.42  103 (b) 7.1  104 m3 (c) 1046.060 (d) 0.063 (c) 674.00  106 (c) 1.21  105 s (e) 3.142 (d) 46.00  103 (d) 2113.38 pints 19. (a) 15  103 (b) 5  103 31. (a) 0.06  106 47. 14.4 (c) 2.4  106 (d) 60  103 (b) 400  106 49. 0.93 (e) 4.02  104 (f) 2  1010 (c) 0.005  109 51. 3.24 21. (a) 100  103 (b) 10 (d) 1200  109 53. 1.20  1012 (c) 1  109 (d) 1  103 33. (a) 90 s (b) 72 s (e) 10 (f) 1  1024 (c) 50  103 ms (d) 160 mm 23. (a) 10  103 (b) 10  106 (e) 120 ns (f) 4629.63 days (c) 10  106 (d) 1  109 (e) 1  1042 (f) 1  103 31 This page intentionally left blank  Voltage and Current Become aware of the basic atomic structure of Objectives conductors such as copper and aluminum and understand why they are used so extensively in the field. Understand how the terminal voltage of a battery or any dc supply is established and how it creates a flow of charge in the system. Understand how current is established in a circuit and how its magnitude is affected by the charge flowing in the system and the time involved. Become familiar with the factors that affect the terminal voltage of a battery and how long a battery will remain effective. Be able to apply a voltmeter and ammeter correctly to measure the voltage and current of a network. 1 INTRODUCTION Now that the foundation for the study of electricity/electronics has been established, the con- cepts of voltage and current can be investigated. The term voltage is encountered practically every day. We have all replaced batteries in our flashlights, answering machines, calculators, automobiles, and so on, that had specific voltage ratings. We are aware that most outlets in our homes are 120 volts. Although current may be a less familiar term, we know what happens when we place too many appliances on the same outlet—the circuit breaker opens due to the excessive current that results. It is fairly common knowledge that current is something that moves through the wires and causes sparks and possibly fire if there is a “short circuit.” Cur- rent heats up the coils of an electric heater or the range of an electric stove; it generates light when passing through the filament of a bulb; it causes twists and kinks in the wire of an elec- tric iron over time; and so on. All in all, the terms voltage and current are part of the vocabu- lary of most individuals. In this chapter, the basic impact of current and voltage and the properties of each are intro- duced and discussed in some detail. Hopefully, any mysteries surrounding the general charac- teristics of each will be eliminated, and you will gain a clear understanding of the impact of each on an electric/electronics circuit. 2 ATOMS AND THEIR STRUCTURE A basic understanding of the fundamental concepts of current and voltage requires a degree of familiarity with the atom and its structure. The simplest of all atoms is the hydrogen atom, made up of two basic particles, the