Robbins - Circuit Analysis - Theory and Practice PDF 2003

1 Introduction OBJECTIVES Meter After studying this chapter, you will be Newton able to Pictorial Diagram describe the SI system of measurement, Power of Ten Notation convert between various...

1 Introduction OBJECTIVES Meter After studying this chapter, you will be Newton able to Pictorial Diagram describe the SI system of measurement, Power of Ten Notation convert between various sets of units, Prefixes use power of ten notation to simplify Programming Language handling of large and small numbers, Resistance express electrical units using standard Schematic Diagram prefix notation such as mA, kV, mW, etc., Scientific Notation use a sensible number of significant dig- SI Units its in calculations, Significant Digits describe what block diagrams are and SPICE why they are used, Volt convert a simple pictorial circuit to its schematic representation, Watt describe generally how computers fit in the electrical circuit analysis picture. OUTLINE Introduction KEY TERMS The SI System of Units Ampere Converting Units Block Diagram Power of Ten Notation Circuit Prefixes Conversion Factor Significant Digits and Numerical Accuracy Current Circuit Diagrams Energy Circuit Analysis Using Computers Joule A n electrical circuit is a system of interconnected components such as resis- tors, capacitors, inductors, voltage sources, and so on. The electrical behav- ior of these components is described by a few basic experimental laws. These CHAPTER PREVIEW laws and the principles, concepts, mathematical relationships, and methods of analysis that have evolved from them are known as circuit theory. Much of circuit theory deals with problem solving and numerical analysis. When you analyze a problem or design a circuit, for example, you are typically required to compute values for voltage, current, and power. In addition to a numerical value, your answer must include a unit. The system of units used for this purpose is the SI system (Systéme International). The SI system is a unified system of metric measurement; it encompasses not only the familiar MKS (meters, kilograms, seconds) units for length, mass, and time, but also units for electrical and magnetic quantities as well. Quite frequently, however, the SI units yield numbers that are either too large or too small for convenient use. To handle these, engineering notation and a set of standard prefixes have been developed. Their use in representation and computation is described and illustrated. The question of significant digits is also investigated. Since circuit theory is somewhat abstract, diagrams are used to help present ideas. We look at several types—schematic, pictorial, and block diagrams—and show how to use them to represent circuits and systems. We conclude the chapter with a brief look at computer usage in circuit analy- sis and design. Several popular application packages and programming languages are described. Special emphasis is placed on OrCAD PSpice and Electronics Workbench, the two principal software packages used throughout this book. Hints on Problem Solving PUTTING IT IN DURING THE ANALYSIS of electric circuits, you will find yourself solving quite a few PERSPECTIVE problems.An organized approach helps. Listed below are some useful guidelines: 1. Make a sketch (e.g., a circuit diagram), mark on it what you know, then iden- tify what it is that you are trying to determine. Watch for “implied data” such as the phrase “the capacitor is initially uncharged”. (As you will find out later, this means that the initial voltage on the capacitor is zero.) Be sure to convert all implied data to explicit data. 2. Think through the problem to identify the principles involved, then look for relationships that tie together the unknown and known quantities. 3. Substitute the known information into the selected equation(s) and solve for the unknown. (For complex problems, the solution may require a series of steps involving several concepts. If you cannot identify the complete set of steps before you start, start anyway. As each piece of the solution emerges, you are one step closer to the answer. You may make false starts. However, even experienced people do not get it right on the first try every time. Note also that there is seldom one “right” way to solve a problem. You may therefore come up with an entirely different correct solution method than the authors do.) 4. Check the answer to see that it is sensible—that is, is it in the “right ball- park”? Does it have the correct sign? Do the units match? 3 4 Chapter 1 Introduction 1.1 Introduction Technology is rapidly changing the way we do things; we now have comput- ers in our homes, electronic control systems in our cars, cellular phones that can be used just about anywhere, robots that assemble products on produc- tion lines, and so on. A first step to understanding these technologies is electric circuit theory. Circuit theory provides you with the knowledge of basic principles that you need to understand the behavior of electric and electronic devices, circuits, and systems. In this book, we develop and explore its basic ideas. Before We Begin Before we begin, let us look at a few examples of the technology at work. (As you go through these, you will see devices, components, and ideas that have not yet been discussed. You will learn about these later. For the moment, just concentrate on the general ideas.) As a first example, consider Figure 1–1, which shows a VCR. Its design is based on electrical, electronic, and magnetic circuit principles. For exam- ple, resistors, capacitors, transistors, and integrated circuits are used to con- trol the voltages and currents that operate its motors and amplify the audio and video signals that are the heart of the system. A magnetic circuit (the read/write system) performs the actual tape reads and writes. It creates, shapes, and controls the magnetic field that records audio and video signals on the tape. Another magnetic circuit, the power transformer, transforms the ac voltage from the 120-volt wall outlet voltage to the lower voltages required by the system. FIGURE 1–1 A VCR is a familiar example of an electrical/electronic system.  Section 1.1 Introduction 5 Figure 1–2 shows another example. In this case, a designer, using a per- sonal computer, is analyzing the performance of a power transformer. The transformer must meet not only the voltage and current requirements of the application, but safety- and efficiency-related concerns as well. A software application package, programmed with basic electrical and magnetic circuit fundamentals, helps the user perform this task. Figure 1–3 shows another application, a manufacturing facility where fine pitch surface-mount (SMT) components are placed on printed circuit boards at high speed using laser centering and optical verification. The bot- tom row of Figure 1–4 shows how small these components are. Computer control provides the high precision needed to accurately position parts as tiny as these. Before We Move On Before we move on, we should note that, as diverse as these applications are, they all have one thing in common: all are rooted in the principles of circuit theory. FIGURE 1–2 A transformer designer using a 3-D electromagnetic analysis program to check the design and operation of a power transformer. Upper inset: Magnetic field pat- tern. (Courtesy Carte International Inc.) 6 Chapter 1 Introduction FIGURE 1–3 Laser centering and optical verification in a manufacturing process. (Courtesy Vansco Electronics Ltd.) FIGURE 1–4 Some typical elec- tronic components. The small compo- nents at the bottom are surface mount parts that are installed by the machine shown in Figure 1–3. Surface mount parts  Section 1.2 The SI System of Units 7 1.2 The SI System of Units TABLE 1–1 Common Quantities The solution of technical problems requires the use of units. At present, two 1 meter ⫽ 100 centimeters ⫽ 39.37 major systems—the English (US Customary) and the metric—are in everyday inches 1 millimeter ⫽ 39.37 mils use. For scientific and technical purposes, however, the English system has 1 inch ⫽ 2.54 centimeters been largely superseded. In its place the SI system is used. Table 1–1 shows a 1 foot ⫽ 0.3048 meter few frequently encountered quantities with units expressed in both systems. 1 yard ⫽ 0.9144 meter The SI system combines the MKS metric units and the electrical units 1 mile ⫽ 1.609 kilometers into one unified system: See Tables 1–2 and 1–3. (Do not worry about the 1 kilogram ⫽ 1000 grams ⫽ electrical units yet. We define them later, starting in Chapter 2.) The units in 2.2 pounds Table 1–2 are defined units, while the units in Table 1–3 are derived units, 1 gallon (US) ⫽ 3.785 liters obtained by combining units from Table 1–2. Note that some symbols and abbreviations use capital letters while others use lowercase letters. A few non-SI units are still in use. For example, electric motors are commonly rated in horsepower, and wires are frequently specified in AWG sizes (American Wire Gage, Section 3.2). On occasion, you will need to con- vert non-SI units to SI units. Table 1–4 may be used for this purpose. Definition of Units When the metric system came into being in 1792, the meter was defined as one ten-millionth of the distance from the north pole to the equator and the second as 1/60 ⫻ 1/60 ⫻ 1/24 of the mean solar day. Later, more accurate def- initions based on physical laws of nature were adopted. The meter is now TABLE 1–2 Some SI Base Units Quantity Symbol Unit Abbreviation Length ᐉ meter m Mass m kilogram kg Time t second s Electric current I, i ampere A Temperature T kelvin K TABLE 1–3 Some SI Derived Units* Quantity Symbol Unit Abbreviation Force F newton N Energy W joule J Power P, p watt W Voltage V, v, E, e volt V Charge Q, q coulomb C Resistance R ohm ⍀ Capacitance C farad F Inductance L henry H Frequency f hertz Hz Magnetic flux F weber Wb Magnetic flux density B tesla T *Electrical and magnetic quantities will be explained as you progress through the book. As in Table 1–2, the distinction between capitalized and lowercase letters is important. 8 Chapter 1 Introduction TABLE 1–4 Conversions When You Know Multiply By To Find Length inches (in) 0.0254 meters (m) feet (ft) 0.3048 meters (m) miles (mi) 1.609 kilometers (km) Force pounds (lb) 4.448 newtons (N) Power horsepower (hp) 746 watts (W) Energy kilowatthour (kWh) 3.6 ⫻ 106 joules* (J) foot-pound (ft-lb) 1.356 joules* (J) Note: 1 joule ⫽ 1 newton-meter. defined as the distance travelled by light in a vacuum in 1/299 792 458 of a second, while the second is defined in terms of the period of a cesium-based atomic clock. The definition of the kilogram is the mass of a specific plat- inum-iridium cylinder (the international prototype), preserved at the Interna- tional Bureau of Weights and Measures in France. Relative Size of the Units* To gain a feel for the SI units and their relative size, refer to Tables 1–1 and 1–4. Note that 1 meter is equal to 39.37 inches; thus, 1 inch equals 1/39.37 ⫽ 0.0254 meter or 2.54 centimeters. A force of one pound is equal to 4.448 newtons; thus, 1 newton is equal to 1/4.448 ⫽ 0.225 pound of force, which is about the force required to lift a 1⁄ 4-pound weight. One joule is the work done in moving a distance of one meter against a force of one newton. This is about equal to the work required to raise a quarter-pound weight one meter. Raising the weight one meter in one second requires about one watt of power. The watt is also the SI unit for electrical power. A typical electric lamp, for example, dissipates power at the rate of 60 watts, and a toaster at a rate of about 1000 watts. The link between electrical and mechanical units can be easily estab- lished. Consider an electrical generator. Mechanical power input produces electrical power output. If the generator were 100% efficient, then one watt of mechanical power input would yield one watt of electrical power output. This clearly ties the electrical and mechanical systems of units together. However, just how big is a watt? While the above examples suggest that the watt is quite small, in terms of the rate at which a human can work it is actually quite large. For example, a person can do manual labor at a rate of about 60 watts when averaged over an 8-hour day—just enough to power a standard 60-watt electric lamp continuously over this time! A horse can do considerably better. Based on experiment, Isaac Watt determined that a strong dray horse could average 746 watts. From this, he defined the horsepower (hp) as 1 horsepower ⫽ 746 watts. This is the figure that we still use today. *Paraphrased from Edward C. Jordan and Keith Balmain, Electromagnetic Waves and Radiating Systems, Second Edition. (Englewood Cliffs, New Jersey: Prentice-Hall, Inc, 1968).  Section 1.3 Converting Units 9 1.3 Converting Units Often quantities expressed in one unit must be converted to another. For example, suppose you want to determine how many kilometers there are in ten miles. Given that 1 mile is equal to 1.609 kilometers, Table 1–1, you can write 1 mi ⫽ 1.609 km, using the abbreviations in Table 1–4. Now multiply both sides by 10. Thus, 10 mi ⫽ 16.09 km. This procedure is quite adequate for simple conversions. However, for complex conversions, it may be difficult to keep track of units. The proce- dure outlined next helps. It involves writing units into the conversion sequence, cancelling where applicable, then gathering up the remaining units to ensure that the final result has the correct units. To get at the idea, suppose you want to convert 12 centimeters to inches. From Table 1–1, 2.54 cm ⫽ 1 in. Since these are equivalent, you can write 2.54 cm 1 in ᎏᎏ ⫽ 1 or ᎏᎏ ⫽ 1 (1–1) 1 in 2.54 cm Now multiply 12 cm by the second ratio and note that unwanted units can- cel. Thus, 1 in 12 cm ⫻ ᎏᎏ ⫽ 4.72 in 2.54 cm The quantities in equation 1–1 are called conversion factors. Conver- sion factors have a value of 1 and you can multiply by them without chang- ing the value of an expression. When you have a chain of conversions, select factors so that all unwanted units cancel. This provides an automatic check on the final result as illustrated in part (b) of Example 1–1. EXAMPLE 1–1 Given a speed of 60 miles per hour (mph), a. convert it to kilometers per hour, b. convert it to meters per second. Solution a. Recall, 1 mi ⫽ 1.609 km. Thus, 1.609 km 1 ⫽ ᎏᎏ 1 mi Now multiply both sides by 60 mi/h and cancel units: 60 mi 1.609 km 60 mi/h ⫽ ᎏᎏ ⫻ ᎏᎏ ⫽ 96.54 km/h h 1 mi b. Given that 1 mi ⫽ 1.609 km, 1 km ⫽ 1000 m, 1 h ⫽ 60 min, and 1 min ⫽ 60 s, choose conversion factors as follows: 1.609 km 1000 m 1h 1 min 1 ⫽ ᎏᎏ, 1 ⫽ ᎏᎏ, 1 ⫽ ᎏᎏ, and 1 ⫽ ᎏᎏ 1 mi 1 km 60 min 60 s 10 Chapter 1 Introduction Thus, 60 mi 60 mi 1.609 km 1000 m 1h 1 min ᎏᎏ ⫽ ᎏᎏ ⫻ ᎏᎏ ⫻ ᎏᎏ ⫻ ᎏᎏ ⫻ ᎏᎏ ⫽ 26.8 m/s h h 1 mi 1 km 60 min 60 s You can also solve this problem by treating the numerator and denomi- nator separately. For example, you can convert miles to meters and hours to seconds, then divide (see Example 1–2). In the final analysis, both methods are equivalent. EXAMPLE 1–2 Do Example 1–1(b) by expanding the top and bottom sepa- rately. Solution 1.609 km 1000 m 60 mi ⫽ 60 mi ⫻ ᎏᎏ ⫻ ᎏᎏ ⫽ 96 540 m 1 mi 1 km 60 min 60 s 1 h ⫽ 1 h ⫻ ᎏᎏ ⫻ ᎏᎏ ⫽ 3600 s 1h 1 min Thus, velocity ⫽ 96 540 m/3600 s ⫽ 26.8 m/s as above. PRACTICE 1. Area ⫽ pr 2. Given r ⫽ 8 inches, determine area in square meters (m2). PROBLEMS 1 2. A car travels 60 feet in 2 seconds. Determine a. its speed in meters per second, b. its speed in kilometers per hour. For part (b), use the method of Example 1–1, then check using the method of Example 1–2. Answers: 1. 0.130 m2 2. a. 9.14 m/s b. 32.9 km/h 1.4 Power of Ten Notation Electrical values vary tremendously in size. In electronic systems, for example, voltages may range from a few millionths of a volt to several thousand volts, while in power systems, voltages of up to several hundred thousand are com- mon. To handle this large range, the power of ten notation (Table 1–5) is used. To express a number in power of ten notation, move the decimal point to where you want it, then multiply the result by the power of ten needed to restore the number to its original value. Thus, 247 000 ⫽ 2.47 ⫻ 105. (The number 10 is called the base, and its power is called the exponent.) An easy way to determine the exponent is to count the number of places (right or left) that you moved the decimal point. Thus, 247 000 ⫽ 2 4 7 0 0 0 ⫽ 2.47 ⫻ 105 54321  Section 1.4 Power of Ten Notation 11 TABLE 1–5 Common Power of Ten Multipliers 1 000 000 ⫽ 106 0.000001 ⫽ 10⫺6 100 000 ⫽ 105 0.00001 ⫽ 10⫺5 10 000 ⫽ 104 0.0001 ⫽ 10⫺4 1 000 ⫽ 103 0.001 ⫽ 10⫺3 100 ⫽ 102 0.01 ⫽ 10⫺2 10 ⫽ 101 0.1 ⫽ 10⫺1 1 ⫽ 100 1 ⫽ 100 Similarly, the number 0.003 69 may be expressed as 3.69 ⫻ 10⫺3 as illus- trated below. 0.003 69 ⫽ 0.0 0 3 6 9 ⫽ 3.69 ⫻ 10⫺3 123 Multiplication and Division Using Powers of Ten To multiply numbers in power of ten notation, multiply their base numbers, then add their exponents. Thus, (1.2 ⫻ 103)(1.5 ⫻ 104) ⫽ (1.2)(1.5) ⫻ 10(3⫹4) ⫽ 1.8 ⫻ 107 For division, subtract the exponents in the denominator from those in the numerator. Thus, 4.5 ⫻ 102 4.5 ᎏᎏ ⫽ ᎏᎏ ⫻ 102⫺(⫺2) ⫽ 1.5 ⫻ 104 3 ⫻ 10⫺2 3 EXAMPLE 1–3 Convert the following numbers to power of ten notation, then perform the operation indicated: a. 276 ⫻ 0.009, b. 98 200/20. Solution a. 276 ⫻ 0.009 ⫽ (2.76 ⫻ 102)(9 ⫻ 10⫺3) ⫽ 24.8 ⫻ 10⫺1 ⫽ 2.48 98 200 9.82 ⫻ 104 b. ᎏᎏ ⫽ ᎏᎏ ⫽ 4.91 ⫻ 103 20 2 ⫻ 101 Addition and Subtraction Using Powers of Ten To add or subtract, first adjust all numbers to the same power of ten. It does not matter what exponent you choose, as long as all are the same. 12 Chapter 1 Introduction EXAMPLE 1–4 Add 3.25 ⫻ 102 and 5 ⫻ 103 a. using 102 representation, b. using 103 representation. Solution a. 5 ⫻ 103 ⫽ 50 ⫻ 102. Thus, 3.25 ⫻ 102 ⫹ 50 ⫻ 102 ⫽ 53.25 ⫻ 102 b. 3.25 ⫻ 102 ⫽ 0.325 ⫻ 103. Thus, 0.325 ⫻ 103 ⫹ 5 ⫻ 103 ⫽ 5.325 ⫻ 103, which is the same as 53.25 ⫻ 102 Powers NOTES... Raising a number to a power is a form of multiplication (or division if the Use common sense when han- exponent is negative). For example, dling numbers. With calculators, for example, it is often easier to (2 ⫻ 103)2 ⫽ (2 ⫻ 103)(2 ⫻ 103) ⫽ 4 ⫻ 106 work directly with numbers in In general, (N ⫻ 10n)m ⫽ Nm ⫻ 10nm. In this notation, (2 ⫻ 103)2 ⫽ 22 ⫻ their original form than to con- 103⫻2 ⫽ 4 ⫻ 106 as before. vert them to power of ten nota- Integer fractional powers represent roots. Thus, 41/2 ⫽ 兹4苶 ⫽ 2 and tion. (As an example, it is more 3 271/3 ⫽ 兹2苶7苶 ⫽ 3. sensible to multiply 276 ⫻ 0.009 directly than to convert to power of ten notation as we did in Example 1–3(a).) If the final result is needed as a power of EXAMPLE 1–5 Expand the following: ten, you can convert as a last a. (250)3 b. (0.0056)2 c. (141)⫺2 d. (60)1/3 step. Solution a. (250)3 ⫽ (2.5 ⫻ 102)3 ⫽ (2.5)3 ⫻ 102⫻3 ⫽ 15.625 ⫻ 106 b. (0.0056)2 ⫽ (5.6 ⫻ 10⫺3)2 ⫽ (5.6)2 ⫻ 10⫺6 ⫽ 31.36 ⫻ 10⫺6 c. (141)⫺2 ⫽ (1.41 ⫻ 102)⫺2 ⫽ (1.41)⫺2 ⫻ (102)⫺2 ⫽ 0.503 ⫻ 10⫺4 3 d. (60)1/3 ⫽ 兹6苶0苶 ⫽ 3.915 PRACTICE Determine the following: PROBLEMS 2 a. (6.9 ⫻ 105)(0.392 ⫻ 10⫺2) b. (23.9 ⫻ 1011)/(8.15 ⫻ 105) c. 14.6 ⫻ 102 ⫹ 11.2 ⫻ 101 (Express in 102 and 101 notation.) d. (29.6)3 e. (0.385)⫺2 Answers: a. 2.71 ⫻ 103 b. 2.93 ⫻ 106 c. 15.7 ⫻ 102 ⫽ 157 ⫻ 101 d. 25.9 ⫻ 103 e. 6.75  Section 1.5 Prefixes 13 1.5 Prefixes TABLE 1–6 Engineering Prefixes Power of 10 Prefix Symbol Scientific and Engineering Notation 1012 tera T If power of ten numbers are written with one digit to the left of the decimal 109 giga G 106 mega M place, they are said to be in scientific notation. Thus, 2.47 ⫻ 105 is in sci- 103 kilo k entific notation, while 24.7 ⫻ 104 and 0.247 ⫻ 106 are not. However, we 10⫺3 milli m are more interested in engineering notation. In engineering notation, pre- 10⫺6 micro m fixes are used to represent certain powers of ten; see Table 1–6. Thus, a 10⫺9 nano n quantity such as 0.045 A (amperes) can be expressed as 45 ⫻ 10⫺3 A, but it 10⫺12 pico p is preferable to express it as 45 mA. Here, we have substituted the prefix milli for the multiplier 10⫺3. It is usual to select a prefix that results in a base number between 0.1 and 999. Thus, 1.5 ⫻ 10⫺5 s would be expressed as 15 ms. EXAMPLE 1–6 Express the following in engineering notation: a. 10 ⫻ 104 volts b. 0.1 ⫻ 10⫺3 watts c. 250 ⫻ 10⫺7 seconds Solution a. 10 ⫻ 104 V ⫽ 100 ⫻ 103 V ⫽ 100 kilovolts ⫽ 100 kV b. 0.1 ⫻ 10⫺3 W ⫽ 0.1 milliwatts ⫽ 0.1 mW c. 250 ⫻ 10⫺7 s ⫽ 25 ⫻ 10⫺6 s ⫽ 25 microseconds ⫽ 25 ms EXAMPLE 1–7 Convert 0.1 MV to kilovolts (kV). Solution 0.1 MV ⫽ 0.1 ⫻ 106 V ⫽ (0.1 ⫻ 103) ⫻ 103 V ⫽ 100 kV Remember that a prefix represents a power of ten and thus the rules for power of ten computation apply. For example, when adding or subtracting, adjust to a common base, as illustrated in Example 1–8. EXAMPLE 1–8 Compute the sum of 1 ampere (amp) and 100 milli- amperes. Solution Adjust to a common base, either amps (A) or milliamps (mA). Thus, 1 A ⫹ 100 mA ⫽ 1 A ⫹ 100 ⫻ 10⫺3 A ⫽ 1 A ⫹ 0.1 A ⫽ 1.1 A Alternatively, 1 A ⫹ 100 mA ⫽ 1000 mA ⫹ 100 mA ⫽ 1100 mA. 14 Chapter 1 Introduction PRACTICE 1. Convert 1800 kV to megavolts (MV). PROBLEMS 3 2. In Chapter 4, we show that voltage is the product of current times resistance— that is, V ⫽ I ⫻ R, where V is in volts, I is in amperes, and R is in ohms. Given I ⫽ 25 mA and R ⫽ 4 k⍀, convert these to power of ten notation, then determine V. 3. If I1 ⫽ 520 mA, I2 ⫽ 0.157 mA, and I3 ⫽ 2.75 ⫻ 10⫺4 A, what is I1 ⫹ I2 ⫹ I3 in mA? Answers: 1. 1.8 MV 2. 100 V 3. 0.952 mA IN-PROCESS 1. All conversion factors have a value of what? LEARNING CHECK 1 2. Convert 14 yards to centimeters. 3. What units does the following reduce to? km m h min ᎏᎏ ⫻ ᎏᎏ ⫻ ᎏᎏ ⫻ ᎏᎏ h km min s 4. Express the following in engineering notation: a. 4270 ms b. 0.001 53 V c. 12.3 ⫻ 10⫺4 s 5. Express the result of each of the following computations as a number times 10 to the power indicated: a. 150 ⫻ 120 as a value times 104; as a value times 103. b. 300 ⫻ 6/0.005 as a value times 104; as a value times 105; as a value times 106. c. 430 ⫹ 15 as a value times 102; as a value times 101. d. (3 ⫻ 10⫺2)3 as a value times 10⫺6; as a value times 10⫺5. 6. Express each of the following as indicated. a. 752 mA in mA. b. 0.98 mV in mV. c. 270 ms ⫹ 0.13 ms in ms and in ms. (Answers are at the end of the chapter.) 1.6 Significant Digits and Numerical Accuracy The number of digits in a number that carry actual information are termed significant digits. Thus, if we say a piece of wire is 3.57 meters long, we mean that its length is closer to 3.57 m than it is to 3.56 m or 3.58 m and we have three significant digits. (The number of significant digits includes the first estimated digit.) If we say that it is 3.570 m, we mean that it is closer to 3.570 m than to 3.569 m or 3.571 m and we have four significant digits. When determining significant digits, zeros used to locate the decimal point are not counted. Thus, 0.004 57 has three significant digits; this can be seen if you express it as 4.57 ⫻ 10⫺3.  Section 1.6 Significant Digits and Numerical Accuracy 15 Most calculations that you will do in circuit theory will be done using a NOTES... hand calculator. An error that has become quite common is to show more digits of “accuracy” in an answer than are warranted, simply because the When working with numbers, numbers appear on the calculator display. The number of digits that you you will encounter exact num- should show is related to the number of significant digits in the numbers bers and approximate numbers. used in the calculation. Exact numbers are numbers that To illustrate, suppose you have two numbers, A ⫽ 3.76 and B ⫽ 3.7, to we know for certain, while be multiplied. Their product is 13.912. If the numbers 3.76 and 3.7 are exact approximate numbers are num- this answer is correct. However, if the numbers have been obtained by mea- bers that have some uncertainty. surement where values cannot be determined exactly, they will have some For example, when we say that uncertainty and the product must reflect this uncertainty. For example, sup- there are 60 minutes in one hour, pose A and B have an uncertainty of 1 in their first estimated digit—that is, the 60 here is exact. However, if A ⫽ 3.76 ⫾ 0.01 and B ⫽ 3.7 ⫾ 0.1. This means that A can be as small as we measure the length of a wire and state it as 60 m, the 60 in 3.75 or as large as 3.77, while B can be as small as 3.6 or as large as 3.8. this case carries some uncer- Thus, their product can be as small as 3.75 ⫻ 3.6 ⫽ 13.50 or as large as tainty (depending on how good 3.77 ⫻ 3.8 ⫽ 14.326. The best that we can say about the product is that it is our measurement is), and is thus 14, i.e., that you know it only to the nearest whole number. You cannot even an approximate number. When say that it is 14.0 since this implies that you know the answer to the nearest an exact number is included in a tenth, which, as you can see from the above, you do not. calculation, there is no limit to We can now give a “rule of thumb” for determining significant digits. how many decimal places you The number of significant digits in a result due to multiplication or division can associate with it—the accu- is the same as the number of significant digits in the number with the least racy of the result is affected only number of significant digits. In the previous calculation, for example, 3.7 has by the approximate numbers two significant digits so that the answer can have only two significant digits involved in the calculation. as well. This agrees with our earlier observation that the answer is 14, not Many numbers encountered in 14.0 (which has three). technical work are approximate, When adding or subtracting, you must also use common sense. For as they have been obtained by example, suppose two currents are measured as 24.7 A (one place known measurement. after the decimal point) and 123 mA (i.e., 0.123 A). Their sum is 24.823 A. However, the right-hand digits 23 in the answer are not significant. They cannot be, since, if you don’t know what the second digit after the decimal NOTES... point is for the first current, it is senseless to claim that you know their sum to the third decimal place! The best that you can say about the sum is that it In this book, given numbers are assumed to be exact unless oth- also has one significant digit after the decimal place, that is, erwise noted. Thus, when a value is given as 3 volts, take it 24.7 A (One place after decimal) to mean exactly 3 volts, not sim- ⫹ 0.123 A ply that it has one significant figure. Since our numbers are 24.823 A → 24.8 A (One place after decimal) assumed to be exact, all digits are significant, and we use as Therefore, when adding numbers, add the given data, then round the result to many digits as are convenient in examples and problems. Final the last column where all given numbers have significant digits. The process answers are usually rounded to 3 is similar for subtraction. digits. 16 Chapter 1 Introduction PRACTICE 1. Assume that only the digits shown in 8.75 ⫻ 2.446 ⫻ 9.15 are significant. Deter- PROBLEMS 4 mine their product and show it with the correct number of significant digits. 2. For the numbers of Problem 1, determine 8.75 ⫻ 2.446 ᎏᎏ 9.15 3. If the numbers in Problems 1 and 2 are exact, what are the answers to eight digits? 4. Three currents are measured as 2.36 A, 11.5 A, and 452 mA. Only the digits shown are significant. What is their sum shown to the correct number of sig- nificant digits? Answers: 1. 196 2. 2.34 3. 195.83288; 2.3390710 4. 14.3 A 1.7 Circuit Diagrams Electric circuits are constructed using components such as batteries, switches, resistors, capacitors, transistors, interconnecting wires, etc. To represent these circuits on paper, diagrams are used. In this book, we use three types: block diagrams, schematic diagrams, and pictorials. Block Diagrams Block diagrams describe a circuit or system in simplified form. The overall problem is broken into blocks, each representing a portion of the system or circuit. Blocks are labelled to indicate what they do or what they contain, then interconnected to show their relationship to each other. General signal flow is usually from left to right and top to bottom. Figure 1–5, for example, represents an audio amplifier. Although you have not covered any of its cir- cuits yet, you should be able to follow the general idea quite easily—sound is picked up by the microphone, converted to an electrical signal, amplified by a pair of amplifiers, then output to the speaker, where it is converted back to sound. A power supply energizes the system. The advantage of a block diagram is that it gives you the overall picture and helps you understand the general nature of a problem. However, it does not provide detail. Sound Power Sound Amplifier Amplifier Waves Waves Microphone Power Speaker Supply Amplification System FIGURE 1–5 An example block diagram. Pictured is a simplified representation of an audio amplification system.  Section 1.7 Circuit Diagrams 17 Current Switch  Lamp
(load) Interconnecting wire Jolt Battery (source) FIGURE 1–6 A pictorial diagram. The battery is referred to as a source while the lamp is referred to as a load. (The ⫹ and ⫺ on the battery are discussed in Chapter 2.) Switch Pictorial Diagrams Pictorial diagrams are one of the types of diagrams that provide detail. ⫹ They help you visualize circuits and their operation by showing components Battery ⫺ Lamp as they actually appear. For example, the circuit of Figure 1–6 consists of a battery, a switch, and an electric lamp, all interconnected by wire. Operation is easy to visualize—when the switch is closed, the battery causes current in the circuit, which lights the lamp. The battery is referred to as the source and (a) Schematic using lamp symbol the lamp as the load. Switch Schematic Diagrams While pictorial diagrams help you visualize circuits, they are cumbersome to draw. Schematic diagrams get around this by using simplified, standard symbols to represent components; see Table 1–7. (The meaning of these ⫹ symbols will be made clear as you progress through the book.) In Figure Battery ⫺ Resistance 1–7(a), for example, we have used some of these symbols to create a schematic for the circuit of Figure 1–6. Each component has been replaced by its corresponding circuit symbol. When choosing symbols, choose those that are appropriate to the occa- (b) Schematic using resistance symbol sion. Consider the lamp of Figure 1–7(a). As we will show later, the lamp FIGURE 1–7 Schematic representa- possesses a property called resistance that causes it to resist the passage of tion of Figure 1–6. The lamp has a cir- charge. When you wish to emphasize this property, use the resistance symbol cuit property called resistance (dis- rather than the lamp symbol, as in Figure 1–7(b). cussed in Chapter 3). 18 Chapter 1 Introduction TABLE 1–7 Schematic Circuit Symbols ⫹ ⫹ ⫹ ⫺ ⫺ ⫺ Single Multicell AC Current Fixed Variable Fixed Variable Air Iron Ferrite cell Voltage Source Core Core Core Source Batteries Resistors Capacitors Inductors SPST Earth SPDT Chassis Wires Wires Lamp Switches Microphone Speaker Joining Crossing Grounds Fuses V Voltmeter kV I Ammeter Air Core Iron Core Ferrite Core A Circuit Dependent Breakers Ammeter Transformers Source When you draw schematic diagrams, draw them with horizontal and ver- tical lines joined at right angles as in Figure 1–7. This is standard practice. (At this point you should glance through some later chapters, e.g., Chapter 7, and study additional examples.) 1.8 Circuit Analysis Using Computers Personal computers are used extensively for analysis and design. Software tools available for such tasks fall into two broad categories: prepackaged application programs (application packages) and programming languages. Application packages solve problems without requiring programming on the part of the user, while programming languages require the user to write code for each type of problem to be solved. Circuit Simulation Software Simulation software is application software; it solves problems by simulating the behavior of electrical and electronic circuits rather than by solving sets of equations. To analyze a circuit, you “build” it on your screen by selecting components (resistors, capacitors, transistors, etc.) from a library of parts, which you then position and interconnect to form the desired circuit. You can  Section 1.8 Circuit Analysis Using Computers 19 FIGURE 1–8 Computer screen showing circuit analysis using Electronics Workbench. change component values, connections, and analysis options instantly with the click of a mouse. Figures 1–8 and 1–9 show two examples. Most simulation packages use a software engine called SPICE, an acro- nym for Simulation Program with Integrated Circuit Emphasis. Popular products are PSpice, Electronics Workbench® (EWB) and Circuit Maker. In this text, we use Electronics Workbench and OrCAD PSpice, both of which have either evaluation or student versions (see the Preface for more details). Both products have their strong points. Electronics Workbench, for instance, more closely models an actual workbench (complete with realistic meters) than does PSpice and is a bit easier to learn. On the other hand, PSpice has a FIGURE 1–9 Computer screen showing circuit analysis using OrCAD PSpice. 20 Chapter 1 Introduction more complete analysis capability; for example, it determines and displays important information (such as phase angles in ac analyses and current waveforms in transient analysis) that Electronics Workbench, as of this writ- ing, does not. Prepackaged Math Software Math packages also require no programming. A popular product is Mathcad from Mathsoft Inc. With Mathcad, you enter equations in standard mathe- matical notation. For example, to find the first root of a quadratic equation, you would use ⫺b ⫹ 兹苶b2苶苶 ⫺苶4苶⭈苶a苶⭈苶c x: ⫽ ᎏᎏᎏ 2⭈a Mathcad is a great aid for solving simultaneous equations such as those encountered during mesh or nodal analysis (Chapters 8 and 19) and for plot- ting waveforms. (You simply enter the formula.) In addition, Mathcad incor- porates a built-in Electronic Handbook that contains hundreds of useful for- mulas and circuit diagrams that can save you a great deal of time. Programming Languages Many problems can also be solved using programming languages such as BASIC, C, or FORTRAN. To solve a problem using a programming lan- guage, you code its solution, step by step. We do not consider programming languages in this book. A Word of Caution With the widespread availability of inexpensive software tools, you may wonder why you are asked to solve problems manually throughout this book. The reason is that, as a student, your job is to learn principles and concepts. Getting correct answers using prepackaged software does not necessarily mean that you understand the theory—it may mean only that you know how to enter data. Software tools should always be used wisely. Before you use PSpice, Electronics Workbench, or any other application package, be sure that you understand the basics of the subject that you are studying. This is why you should solve problems manually with your calculator first. Follow- ing this, try some of the application packages to explore ideas. Most chapters (starting with Chapter 4) include a selection of worked-out examples and problems to get you started.  Problems 21 1.3 Converting Units PROBLEMS 1. Perform the following conversions: NOTES... a. 27 minutes to seconds b. 0.8 hours to seconds c. 2 h 3 min 47 s to s d. 35 horsepower to watts 1. Conversion factors may be found on the inside of the e. 1827 W to hp f. 23 revolutions to degrees front cover or in the tables of 2. Perform the following conversions: Chapter 1. a. 27 feet to meters b. 2.3 yd to cm 2. Difficult problems have their c. 36°F to degrees C d. 18 (US) gallons to liters question number printed in e. 100 sq. ft to m2 f. 124 sq. in. to m2 red. g. 47-pound force to newtons 3. Answers to odd-numbered problems are in Appendix D. 3. Set up conversion factors, compute the following, and express the answer in the units indicated. a. The area of a plate 1.2 m by 70 cm in m2. b. The area of a triangle with base 25 cm, height 0.5 m in m2. c. The volume of a box 10 cm by 25 cm by 80 cm in m3. d. The volume of a sphere with 10 in. radius in m3. 4. An electric fan rotates at 300 revolutions per minute. How many degrees is this per second? 5. If the surface mount robot machine of Figure 1–3 places 15 parts every 12 s, what is its placement rate per hour? 6. If your laser printer can print 8 pages per minute, how many pages can it print in one tenth of an hour? 7. A car gets 27 miles per US gallon. What is this in kilometers per liter? 8. The equatorial radius of the earth is 3963 miles. What is the earth’s circum- ference in kilometers at the equator? 9. A wheel rotates 18° in 0.02 s. How many revolutions per minute is this? 10. The height of horses is sometimes measured in “hands,” where 1 hand ⫽ 4 inches. How many meters tall is a 16-hand horse? How many centimeters? 11. Suppose s ⫽ vt is given, where s is distance travelled, v is velocity, and t is time. If you travel at v ⫽ 60 mph for 500 seconds, you get upon unthinking substitution s ⫽ vt ⫽ (60)(500) ⫽ 30,000 miles. What is wrong with this calculation? What is the correct answer? 12. How long does it take for a pizza cutter traveling at 0.12 m/s to cut diago- nally across a 15-in. pizza? 13. Joe S. was asked to convert 2000 yd/h to meters per second. Here is Joe’s work: velocity ⫽ 2000 ⫻ 0.9144 ⫻ 60/60 ⫽ 1828.8 m/s. Determine conver- sion factors, write units into the conversion, and find the correct answer. 14. The mean distance from the earth to the moon is 238 857 miles. Radio sig- nals travel at 299 792 458 m/s. How long does it take a radio signal to reach the moon? 22 Chapter 1 Introduction 15. Your plant manager asks you to investigate two machines. The cost of elec- tricity for operating machine #1 is 43 cents/minute, while that for machine #2 is $200.00 per 8-hour shift. The purchase price and production capacity for both machines are identical. Based on this information, which machine should you purchase and why? 16. Given that 1 hp ⫽ 550 ft-lb/s, 1 ft ⫽ 0.3048 m, 1 lb ⫽ 4.448 N, 1 J ⫽ 1 N- m, and 1 W ⫽ 1 J/s, show that 1 hp ⫽ 746 W. 1.4 Power of Ten Notation 17. Express each of the following in power of ten notation with one nonzero digit to the left of the decimal point: a. 8675 b. 0.008 72 c. 12.4 ⫻ 10 2 d. 37.2 ⫻ 10⫺2 e. 0.003 48 ⫻ 105 f. 0.000 215 ⫻ 10⫺3 g. 14.7 ⫻ 100 18. Express the answer for each of the following in power of ten notation with one nonzero digit to the left of the decimal point. a. (17.6)(100) b. (1400)(27 ⫻ 10⫺3) c. (0.15 ⫻ 106)(14 ⫻ 10⫺4) d. 1 ⫻ 10⫺7 ⫻ 10⫺4 ⫻ 10.65 e. (12.5)(1000)(0.01) f. (18.4 ⫻ 100)(100)(1.5 ⫻ 10⫺5)(0.001) 19. Repeat the directions in Question 18 for each of the following. 125 8 ⫻ 104 a. ᎏᎏ b. ᎏᎏ 1000 (0.001) 3 ⫻ 10 4 (16 ⫻ 10⫺7)(21.8 ⫻ 106) c. ᎏᎏ d. ᎏᎏᎏ (1.5 ⫻ 10 ) 6 (14.2)(12 ⫻ 10⫺5) 20. Determine answers for the following a. 123.7 ⫹ 0.05 ⫹ 1259 ⫻ 10⫺3 b. 72.3 ⫻ 10⫺2 ⫹ 1 ⫻ 10⫺3 c. 86.95 ⫻ 10 ⫺ 383 2 d. 452 ⫻ 10⫺2 ⫹ (697)(0.01) 21. Convert the following to power of 10 notation and, without using your cal- culator, determine the answers. a. (4 ⫻ 103)(0.05)2 b. (4 ⫻ 103)(⫺0.05)2 (3 ⫻ 2 ⫻ 10)2 c. ᎏᎏ (2 ⫻ 5 ⫻ 10⫺1) (30 ⫹ 20)⫺2(2.5 ⫻ 106)(6000) d. ᎏᎏᎏᎏ (1 ⫻ 103)(2 ⫻ 10⫺1)2 (⫺0.027)1/3(⫺0.2)2 e. ᎏᎏ (23 ⫹ 1)0 ⫻ 10⫺3  Problems 23 22. For each of the following, convert the numbers to power of ten notation, then perform the indicated computations. Round your answer to four digits: a. (452)(6.73 ⫻ 104) b. (0.009 85)(4700) c. (0.0892)/(0.000 067 3) d. 12.40 ⫺ 236 ⫻ 10⫺2 e. (1.27)3 ⫹ 47.9/(0.8)2 f. (⫺643 ⫻ 10⫺3)3 g. [(0.0025)1/2][1.6 ⫻ 104] h. [(⫺0.027)1/3]/[1.5 ⫻ 10⫺4] 4 ⫺2 (3.5 ⫻ 10 ) ⫻ (0.0045) ⫻ (729) 2 1/3 i. ᎏᎏᎏᎏ [(0.008 72) ⫻ (47)3] ⫺ 356 23. For the following, a. convert numbers to power of ten notation, then perform the indicated computation, b. perform the operation directly on your calculator without conversion. What is your conclusion? 0.0352 i. 842 ⫻ 0.0014 ii. ᎏᎏ 0.007 91 24. Express each of the following in conventional notation: a. 34.9 ⫻ 104 b. 15.1 ⫻ 100 c. 234.6 ⫻ 10⫺4 d. 6.97 ⫻ 10⫺2 e. 45 786.97 ⫻ 10⫺1 f. 6.97 ⫻ 10⫺5 25. One coulomb (Chapter 2) is the amount of charge represented by 6 240 000 000 000 000 000 electrons. Express this quantity in power of ten notation. 26. The mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 899 9 kg. Express as a power of 10 with one non-zero digit to the left of the dec- imal point. 27. If 6.24 ⫻ 1018 electrons pass through a wire in 1 s, how many pass through it during a time interval of 2 hr, 47 min and 10 s? 28. Compute the distance traveled in meters by light in a vacuum in 1.2 ⫻ 10⫺8 second. 29. How long does it take light to travel 3.47 ⫻ 105 km in a vacuum? 30. How far in km does light travel in one light-year? 31. While investigating a site for a hydroelectric project, you determine that the flow of water is 3.73 ⫻ 104 m3/s. How much is this in liters/hour? m m2 32. The gravitational force between two bodies is F ⫽ 6.6726 ⫻ 10⫺11 ᎏ1ᎏ r2 N, where masses m1 and m2 are in kilograms and the distance r between gravitational centers is in meters. If body 1 is a sphere of radius 5000 miles and density of 25 kg/m3, and body 2 is a sphere of diameter 20 000 km and density of 12 kg/m3, and the distance between centers is 100 000 miles, what is the gravitational force between them? 1.5 Prefixes 33. What is the appropriate prefix and its abbreviation for each of the following multipliers ? a. 1000 b. 1 000 000 9 c. 10 d. 0.000 001 e. 10⫺3 f. 10⫺12 24 Chapter 1 Introduction 34. Express the following in terms of their abbreviations, e.g., microwatts as mW. Pay particular attention to capitalization (e.g., V, not v, for volts). a. milliamperes b. kilovolts c. megawatts d. microseconds e. micrometers f. milliseconds g. nanoamps 35. Express the following in the most sensible engineering notation (e.g., 1270 ms ⫽ 1.27 ms). a. 0.0015 s b. 0.000 027 s c. 0.000 35 ms 36. Convert the following: a. 156 mV to volts b. 0.15 mV to microvolts c. 47 kW to watts d. 0.057 MW to kilowatts e. 3.5 ⫻ 10 volts to kilovolts 4 f. 0.000 035 7 amps to microamps 37. Determine the values to be inserted in the blanks. a. 150 kV ⫽  ⫻ 103 V ⫽  ⫻ 106 V b. 330 mW ⫽  ⫻ 10⫺3 W ⫽  ⫻ 10⫺5 W 38. Perform the indicated operations and express the answers in the units indi- cated. a. 700 mA ⫺ 0.4 mA ⫽  mA ⫽  mA b. 600 MW ⫹ 300 ⫻ 104 W ⫽  MW 39. Perform the indicated operations and express the answers in the units indi- cated. a. 330 V ⫹ 0.15 kV ⫹ 0.2 ⫻ 103 V ⫽  V b. 60 W ⫹ 100 W ⫹ 2700 mW ⫽  W 40. The voltage of a high voltage transmission line is 1.15 ⫻ 105 V. What is its voltage in kV? 41. You purchase a 1500 W electric heater to heat your room. How many kW is this? 42. While repairing an antique radio, you come across a faulty capacitor desig- nated 39 mmfd. After a bit of research, you find that “mmfd” is an obsolete unit meaning “micromicrofarads”. You need a replacement capacitor of equal value. Consulting Table 1–6, what would 39 “micromicrofarads” be equivalent to? 43. A radio signal travels at 299 792.458 km/s and a telephone signal at 150 m/ms. If they originate at the same point, which arrives first at a destination 5000 km away? By how much? 44. a. If 0.045 coulomb of charge (Question 25) passes through a wire in 15 ms, how many electrons is this? b. At the rate of 9.36 ⫻ 1019 electrons per second, how many coulombs pass a point in a wire in 20 ms?  Problems 25 64 41 65 40 80 25 1 24 0.8 TYP 0.25 ⫾ 0.1 0.45 (b) (a) FIGURE 1–10 1.6 Significant Digits and Numerical Accuracy For each of the following, assume that the given digits are significant. 45. Determine the answer to three significant digits: 2.35 ⫺ 1.47 ⫻ 10⫺6 46. Given V ⫽ IR. If I ⫽ 2.54 and R ⫽ 52.71, determine V to the correct num- ber of significant digits. 47. If A ⫽ 4.05 ⫾ 0.01 is divided by B ⫽ 2.80 ⫾ 0.01, a. What is the smallest that the result can be? b. What is the largest that the result can be? c. Based on this, give the result A/B to the correct number of significant digits. 48. The large black plastic component soldered onto the printed circuit board of Figure 1–10(a) is an electronic device known as an integrated circuit. As indicated in (b), the center-to-center spacing of its leads (commonly called pins) is 0.8 ⫾ 0.1 mm. Pin diameters can vary from 0.25 to 0.45 mm. Con- sidering these uncertainties, a. What is the minimum distance between pins due to manufacturing toler- ances? b. What is the maximum distance? 1.7 Circuit Diagrams 49. Consider the pictorial diagram of Figure 1–11. Using the appropriate sym- bols from Table 1–7, draw this in schematic form. Hint: In later chapters, there are many schematic circuits containing resistors, inductors, and capac- itors. Use these as aids. 26 Chapter 1 Introduction Iron-core inductor Switch Resistor Resistor  Capacitor
Jolt Battery FIGURE 1–11 50. Draw the schematic diagram for a simple flashlight. 1.8 Circuit Analysis Using Computers 51. Many electronic and computer magazines carry advertisements for com- puter software tools such as PSpice, SpiceNet, Mathcad, MLAB, Matlab, Maple V, plus others. Investigate a few of these magazines in your school’s library; by studying such advertisements, you can gain valuable insight into what modern software packages are able to do.  Answers to In-Process Learning Checks 27 In-Process Learning Check 1 ANSWERS TO IN-PROCESS 1. One LEARNING CHECKS 2. 1280 cm 3. m/s 4. a. 4.27 s b. 1.53 mV c. 1.23 ms 5. a. 1.8 ⫻ 10 ⫽ 18 ⫻ 10 4 3 b. 36 ⫻ 104 ⫽ 3.6 ⫻ 105 ⫽ 0.36 ⫻ 106 c. 4.45 ⫻ 102 ⫽ 44.5 ⫻ 101 d. 27 ⫻ 10⫺6 ⫽ 2.7 ⫻ 10⫺5 6. a. 0.752 mA b. 980 mV c. 400 ms ⫽ 0.4 ms 2 Voltage and Current OBJECTIVES Circuit Breaker After studying this chapter, you will be Conductor able to Coulomb describe the makeup of an atom, Coulomb’s Law explain the relationships between Current valence shells, free electrons, and con- Electric Charge duction, Electron describe the fundamental (coulomb) Free Electrons force within an atom, and the energy Fuse required to create free electrons, Insulator describe what ions are and how they are created, Ion describe the characteristics of conduc- Neutron tors, insulators, and semiconductors, Polarity describe the coulomb as a measure of Potential Difference charge, Proton define voltage, Semiconductor describe how a battery “creates” volt- Shell age, Switch explain current as a movement of charge Valence and how voltage causes current in a con- Volt ductor, describe important battery types and their characteristics, OUTLINE describe how to measure voltage and Atomic Theory Review current. The Unit of Electrical Charge: The Coulomb KEY TERMS Voltage Current Ampere Practical DC Voltage Sources Atom Measuring Voltage and Current Battery Switches, Fuses, and Circuit Breakers Cell A basic electric circuit consisting of a source of electrical energy, a switch, a load, and interconnecting wire is shown in Figure 2–1. When the switch is closed, current in the circuit causes the light to come on. This circuit is represen- CHAPTER PREVIEW tative of many common circuits found in practice, including those of flashlights and automobile headlight systems. We will use it to help develop an understand- ing of voltage and current. Current Switch ⴑ ⴐ Lamp (load) Jolt Interconnecting wire Battery (source) FIGURE 2–1 A basic electric circuit. Elementary atomic theory shows that the current in Figure 2–1 is actually a flow of charges. The cause of their movement is the “voltage” of the source. While in Figure 2–1 this source is a battery, in practice it may be any one of a number of practical sources including generators, power supplies, solar cells, and so on. In this chapter we look at the basic ideas of voltage and current. We begin with a discussion of atomic theory. This leads us to free electrons and the idea of current as a movement of charge. The fundamental definitions of voltage and current are then developed. Following this, we look at a number of common volt- age sources. The chapter concludes with a discussion of voltmeters and amme- ters and the measurement of voltage and current in practice. 29 30 Chapter 2 Voltage and Current PUTTING IT IN The Equations of Circuit Theory PERSPECTIVE IN THIS CHAPTER you meet the first of the equations and formulas that we use to describe the relationships of circuit theory. Remembering formulas is made easier if you clearly understand the principles and concepts on which they are based. As you may recall from high school physics, formulas can come about in only one of three ways, through experiment, by definition, or by mathemati- cal manipulation. Experimental Formulas Circuit theory rests on a few basic experimental results. These are results that can be proven in no other way; they are valid solely because experiment has shown them to be true. The most fundamental of these are called “laws.” Four examples are Ohm’s law, Kirchhoff’s current law, Kirchhoff’s voltage law, and Faraday’s law. (These laws will be met in various chapters throughout the book.) When you see a formula referred to as a law or an experimental result, remember that it is based on experiment and cannot be obtained in any other way. Defined Formulas Some formulas are created by definition, i.e., we make them up. For example, there are 60 seconds in a minute because we define the second as 1/60 of a minute. From this we get the formula tsec ⫽ 60 ⫻ tmin. Derived Formulas This type of formula or equation is created mathematically by combining or manipulating other formulas. In contrast to the other two types of formulas, the only way that a derived relationship can be obtained is by mathematics. An awareness of where circuit theory formulas come from is important to you. This awareness not only helps you understand and remember formulas, it helps you understand the very foundations of the theory—the basic experimen- tal premises upon which it rests, the important definitions that have been made, and the methods by which these foundation ideas have been put together. This can help enormously in understanding and remembering concepts. 2.1 Atomic Theory Review The basic structure of an atom is shown symbolically in Figure 2–2. It con- sists of a nucleus of protons and neutrons surrounded by a group of orbiting electrons. As you learned in physics, the electrons are negatively charged (⫺), while the protons are positively charged (⫹). Each atom (in its normal state) has an equal number of electrons and protons, and since their charges are equal and opposite, they cancel, leaving the atom electrically neutral, i.e., with zero net charge. The nucleus, however, has a net positive charge, since it consists of positively charged protons and uncharged neutrons.  Section 2.1 Atomic Theory Review 31 Electron (negative charge) ⴑ ⴐ Proton (positive charge) Neutron (uncharged) FIGURE 2–2 Bohr model of the atom. Electrons travel around the nucleus at incredible speeds, making billions of trips in a fraction of a second. The force of attraction between the electrons and the protons in the nucleus keeps them in orbit. The basic structure of Figure 2–2 applies to all elements, but each ele- ment has its own unique combination of electrons, protons, and neutrons. For example, the hydrogen atom, the simplest of all atoms, has one proton and one electron, while the copper atom has 29 electrons, 29 protons, and 35 neutrons. Silicon, which is important because of its use in transistors and other electronic devices, has 14 electrons, 14 protons, and 14 neutrons. Electrons orbit the nucleus in spherical orbits called shells, designated by letters K, L, M, N, and so on (Figure 2–3). Only certain numbers of elec- Nucleus trons can exist within any given shell. For example, there can be up to 2 electrons in the K shell, up to 8 in the L shell, up to 18 in the M shell, and up to 32 in the N shell. The number in any shell depends on the element. For instance, the copper atom, which has 29 electrons, has all three of its inner K L shells completely filled but its outer shell (shell N) has only 1 electron, Fig- M ure 2–4. This outermost shell is called its valence shell, and the electron in it N is called its valence electron. No element can have more than eight valence electrons; when a valence FIGURE 2–3 Simplified representa- shell has eight electrons, it is filled. As we shall see, the number of valence tion of the atom. Electrons travel in electrons that an element has directly affects its electrical properties. spherical orbits called “shells.” 32 Chapter 2 Voltage and Current Valence shell Shell K (2 electrons) Valence (1 electron) electron Nucleus 29 Shell L (8 electrons) Shell M (18 electrons) FIGURE 2–4 Copper atom. The valence electron is loosely bound. Electrical Charge In the previous paragraphs, we mentioned the word “charge”. However, we need to look at its meaning in more detail. First, we should note that electri- cal charge is an intrinsic property of matter that manifests itself in the form of forces—electrons repel other electrons but attract protons, while protons repel each other but attract electrons. It was through studying these forces that scientists determined that the charge on the electron is negative while that on the proton is positive. However, the way in which we use the term “charge” extends beyond this. To illustrate, consider again the basic atom of Figure 2–2. It has equal numbers of electrons and protons, and since their charges are equal and opposite, they cancel, leaving the atom as a whole uncharged. However, if the atom acquires additional electrons (leaving it with more electrons than protons), we say that it (the atom) is negatively charged; conversely, if it loses electrons and is left with fewer electrons than protons, we say that it is positively charged. The term “charge” in this sense denotes an imbalance between the number of electrons and protons present in the atom. Now move up to the macroscopic level. Here, substances in their normal state are also generally uncharged; that is, they have equal numbers of elec- trons and protons. However, this balance is easily disturbed—electrons can be stripped from their parent atoms by simple actions such as walking across a carpet, sliding off a chair, or spinning clothes in a dryer. (Recall “static cling”.) Consider two additional examples from physics. Suppose you rub an ebonite (hard rubber) rod with fur. This action causes a transfer of electrons from the fur to the rod. The rod therefore acquires an excess of electrons and is thus negatively charged. Similarly, when a glass rod is rubbed with silk, electrons are transferred from the glass rod to the silk, leaving the rod with a deficiency and, consequently, a positive charge. Here again, charge refers to an imbalance of electrons and protons. As the above examples illustrate, “charge” can refer to the charge on an individual electron or to the charge associated with a whole group of elec- trons. In either case, this charge is denoted by the letter Q, and its unit of mea- surement in the SI system is the coulomb. (The definition of the coulomb is considered shortly.) In general, the charge Q associated with a group of elec- trons is equal to the product of the number of electrons times the charge on each individual electron. Since charge manifests itself in the form of forces, charge is defined in terms of these forces. This is discussed next.  Section 2.1 Atomic Theory Review 33 Coulomb’s Law F r The force between charges was studied by the French scientist Charles Q1 ⫹ Coulomb (1736–1806). Coulomb determined experimentally that the force ⫹ between two charges Q1 and Q2 (Figure 2–5) is directly proportional to the Q2 F product of their charges and inversely proportional to the square of the dis- (a) Like charges tance between them. Mathematically, Coulomb’s law states repel Q Q2 F ⫽ kᎏ1ᎏ [newtons, N] (2–1) r2 ⫺ where Q1 and Q2 are the charges in coulombs, r is the center-to-center spac- ing between them in meters, and k ⫽ 9 ⫻ 109. Coulomb’s law applies to aggregates of charges as in Figure 2–5(a) and (b), as well as to individual ⫹ electrons within the atom as in (c). As Coulomb’s law indicates, force decreases inversely as the square of (b) Unlike charges distance; thus, if the distance between two charges is doubled, the force attract decreases to (1⁄ 2)2 ⫽ 1⁄ 4 (i.e., one quarter) of its original value. Because of this relationship, electrons in outer orbits are less strongly attracted to the Electron nucleus than those in inner orbits; that is, they are less tightly bound to the nucleus than those close by. Valence electrons are the least tightly bound and Orbit will, if they acquire sufficient energy, escape from their parent atoms. ⫹ Free Electrons The amount of energy required to escape depends on the number of electrons (c) The force of attraction keeps electrons in orbit in the valence shell. If an atom has only a few valence electrons, only a small amount of additional energy is needed. For example, for a metal like copper, FIGURE 2–5 Coulomb law forces. valence electrons can gain sufficient energy from heat alone (thermal energy), even at room temperature, to escape from their parent atoms and wander from atom to atom throughout the material as depicted in Figure 2–6. (Note that these electrons do not leave the substance, they simply wander from the valence shell of one atom to the valence shell of another. The material there- fore remains electrically neutral.) Such electrons are called free electrons. In copper, there are of the order of 1023 free electrons per cubic centimeter at room temperature. As we shall see, it is the presence of this large number of free electrons that makes copper such a good conductor of electric current. On the other hand, if the valence shell is full (or nearly full), valence electrons are FIGURE 2–6 Random motion of free much more tightly bound. Such materials have few (if any) free electrons. electrons in a conductor. Ions As noted earlier, when a previously neutral atom gains or loses an electron, it acquires a net electrical charge. The charged atom is referred to as an ion. If the atom loses an electron, it is called a positive ion; if it gains an electron, it is called a negative ion. Conductors, Insulators, and Semiconductors The atomic structure of matter affects how easily charges, i.e., electrons, move through a substance and hence how it is used electrically. Electrically, materials are classified as conductors, insulators, or semiconductors. 34 Chapter 2 Voltage and Current Conductors Materials through which charges move easily are termed conductors. The most familiar examples are metals. Good metal conductors have large num- bers of free electrons that are able to move about easily. In particular, silver, copper, gold, and aluminum are excellent conductors. Of these, copper is the most widely used. Not only is it an excellent conductor, it is inexpensive and easily formed into wire, making it suitable for a broad spectrum of applica- tions ranging from common house wiring to sophisticated electronic equip- ment. Aluminum, although it is only about 60% as good a conductor as cop- per, is also used, mainly in applications where light weight is important, such as in overhead power transmission lines. Silver and gold are too expen- sive for general use. However, gold, because it oxidizes less than other mate- rials, is used in specialized applications; for example, some critical electrical connectors use it because it makes a more reliable connection than other materials. Insulators Materials that do not conduct (e.g., glass, porcelain, plastic, rubber, and so on) are termed insulators. The covering on electric lamp cords, for example, is an insulator. It is used to prevent the wires from touching and to protect us from electric shock. Insulators do not conduct because they have full or nearly full valence shells and thus their electrons are tightly bound. However, when high enough voltage is applied, the force is so great that electrons are literally torn from their parent atoms, causing the insulation to break down and conduc- tion to occur. In air, you see this as an arc or flashover. In solids, charred insulation usually results. Semiconductors Silicon and germanium (plus a few other materials) have half-filled valence shells and are thus neither good conductors nor good insulators. Known as semiconductors, they have unique electrical properties that make them important to the electronics industry. The most important material is silicon. It is used to make transistors, diodes, integrated circuits, and other electronic devices. Semiconductors have made possible personal computers, VCRs, portable CD players, calculators, and a host of other electronic products. You will study them in great detail in your electronics courses. IN-PROCESS 1. Describe the basic structure of the atom in terms of its constituent particles: LEARNING electrons, protons, and neutrons. Why is the nucleus positively charged? Why CHECK 1 is the atom as a whole electrically neutral? 2. What are valence shells? What does the valence shell contain? 3. Describe Coulomb’s law and use it to help explain why electrons far from the