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Electricity, Magnetism, and Light PDF

789 Pages·2002·81.44 MB·English
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Sections R.2-R.4 discuss electricity at home and elsewhere, including automobiles and computers. Section R.5 poses two electrical questions, and Section R.6 presents the electric fluid model and R.7 applies it to answer them. Section R.8 discusses why the electric fluid model must be extended, and how to reconcile the collective nature of the electric fluid with the behavior of individual electrons. Section R.9 reviews vectors, primarily addition and subtraction, and Section R.10 discusses two rules for multiplying vectors, the scalar product and the vector product. Rol Introduction Without electricity, modern life would be impossible. Almost every item on your person~from your shoes to your sunglasses~owes its manufacture to electrical power. Indeed, since this is also true of your clothing, without electricity you might well be completely naked. This chapter discusses electricity in the home. Most importantly, it tries to make physical and perceptible that difficult-to-visualize stuff called electricity. The next chapter reports the struggles of early scientists~even as they were learning to ask the right questions~to grasp the elusive electricity. Together, both chapters provide a foundation of ideas and concepts, expressed mainly without equations. R.1.1 The Electric Fluid M o d e l Serves as a Conceptual Guide Once the rules to produce and detect static electricity were established, the major advances were (1) Stephen Gray's 1729 discovery of two classes of materials (conductors, which transport electricity, and insulators, which do not transport electricity); (2) Charles Dufay's 1733 discovery of two classes of electric charges and the rule that "opposites attract and likes repel"; and (3) Benjamin Franklin's 1750 development of the electric fluid model. This model implies the first quantitative law of electricity~the Law of Conservation of Review/Preview ~ Electricity: Its Uses and Its Visualization Electric Charge. Once this law was understood, it became easier to manipulate electricity, and to study other electrical phenomena in a quantitative fashion. The amount of electric fluid is known as electric charge Q; its unit is the coulomb, or C. The electric fluid model serves as a conceptual guide through Chapter 8, which deal with static electricity and electric currents. The mathematical the- ory of electricity in electrical conductors, although not strictly analogous to the mathematical theory of ordinary fluids, nevertheless describes a type of fluid. As for air and water, the amount of the electric fluid is conserved. However, compared to air and water, the electric fluid has some special properties. Thus, two blobs with an excess (or a deficit) of electric fluid repel each other (a conse- quence of Dufay's discovery), whereas two drops of water are indifferent to each other. Our modern view of ordinary matter is that it has relatively light and mo- bile negatively charged electrons, and relatively heavy and immobile positively charged nuclei. This view can be made consistent with the electric fluid model and can explain Gray's two classes of materials, conductors and insulators. R.2 Electricity at Home: A Presumed Common Experience R~2.1 Hot, Neutral, and Ground Modern buildings are equipped with three-hole electrical wall outlets (or re- ceptacles, or sockets), where the plugs of electrical devices must be inserted to obtain electrical power, as in Figure R. 1 (a). The holes of the outlet are called hot, neutral, and ground. In normal operation, electric current is carried only by the hot and neutral wires. Electric current is measured in amperes (A), or amps. If you stood on the ground in bare feet and accidentally touched the neu- tral or the ground wire of a properly wired electrical outlet, you would not be shocked. However, you would receive a shock if you touched the hot wire: your Lightbulb Neutral Hot Metallic sides of bulb holder (to neutral) Contact on base Ground (to hot) (a) (b) Figure R.1 (a) Grounded three-prong wall outlet. (b) Lightbulb with electrical contacts on its base and on sides. R.2 Electricity at Home: A Presumed Common Experience Internal "short" Motor inside case to metal case You Drill j Metal handle "Hot" "Neutral" "Ground" wire Feet on ground Figure R.2 How grounded wiring protects you when there is a snort. feet, touching the ground, would provide a path for the current to flow, thus completing an electric circuit. The size difference in Figure R.1 (a) between the neutral and hot holes~ the neutral hole is visibly longer than the hot one--is to ensure that only one of the two possible types of connection takes place in devices like a lamp. Figure R. 1 (b) illustrates the connections for a lightbulb inserted in a lamp with a modern, asymmetrical ("polarized") two-prong plug, which in turn is plugged into a correctly wired wall-socket. The wall-socket's hot wire is connected to the (relatively inaccessible) base of the bulb-holder. For an old-fashioned sym- metrical ("unpolarized") two-prong plug, the hot wire could just as likely be connected to the more accidentally touched threaded end of the bulb-holder; the first cartoon characters, of the prepolarized plug 1930s, regularly received shocks in this manner. To help ensure proper wiring, inside the lamp the screws for the two electrical connections typically have different colors, one like copper (the hot wire) and one that is silver-gray (the neutral wire). The round prong, or ground wire, is employed for safety purposes. Figure R.2 depicts a "short" between the hot wire and the electrically conducting case of an electric drill. (A "short" is a connection that shouldn't be there; shorts are undesirable.) Without the ground wire, the drill operator would provide the only path from the hot wire to ground: hot wire to short to case to person to ground. With the ground wire, there is an alternate "path of least resistance" through which most of the electric current can pass: hot wire to short to case to ground wire to ground. Ro2o2 Voltage and Frequency of Electrical Power in the House Voltage bears much the same relationship to electricity as pressure does to water. We write V as an abbreviation for the unit of voltage, the volt. The electrical Review/Preview ~ Electricity: Its Uses and Its Visualization power in a house in the United States is provided at 120 V. The voltage os- cillates from minimum to maximum and back again in 1/60 of a second. This corresponds to a frequency of 60 cps (cycles per second) or, more technically, 60 Hz (hertz). The power is provided by an electric company, which uses huge electrical generators to convert mechanical energy from turbines to electrical energy. The turbines are driven by water or by steam. The mechanical energy of the churning waters of the Columbia River (recall the quote at the beginning of the chapter) provides a large fraction of the power needs of the Pacific North- west. On the other hand, the chemical energy released by burning coal or oil, or the nuclear energy released in a nuclear reactor, vaporizes water into steam and drives the steam that turns a turbine. The electric light had an extraordinary influence on human society. American children learn that, in the 1830s, the young president-to-be Abraham Lincoln stayed up late reading by candlelight. However, by the 1890s, house lighting by electricity was becoming available in large cities. Nevertheless, not until the Rural Electrification Project of the 1930s did many parts of the United States finally become freed of the fire hazards of oil lamps and candles. In the year 2000, many people in the United States were still alive who could remember not having electrical lighting. R~2.3 Watts and Impedance Matching When you turn on a light switch, light is produced by bulbs that are rated in units of the watt, or W. (The watt is the SI, or SystOme lnternationale, unit of power, or energy per second; it is a joule per second, or J/s.) If there is an electrical power failure, for illumination you use a flashlight, with power provided by one or more voltaic cells; for a car the power is provided by six voltaic cells in series, which truly constitutes a battery. If you have ever tried to power a house lightbulb with a car battery, you noticed that it did not light. This is due to poor impedance matching. A mechanical example of poor impedance matching is the use of a regular tennis ball with (relatively small) table-tennis rackets. Impedance mismatch of another type occurs when a bulb intended for a low voltage application (flashlights, automobiles, some external house lighting) is used in a house application; the bulb then gets so much power that it burns up. A mechanical example is the use of a table-tennis ball with (relatively large) regular tennis rackets. Proper impedance matching is a fundamental design principle. We now preview a few simple but important equations in order to apply them to some real-life situations. R.2~4 Current Is the Rate of Charge Flow If a constant current I flows for a time t, then it transfers a charge Q given by Hence the unit of charge, the coulomb (C), has the same units as the ampere- second, so C = A-s. If 0.2 C of charge is transferred in 5 s, by (R. 1) this corre- sponds to a current I = 0.2/5 = 0.04 A. R.2 Electricity at Home: A Presumed Common Experience High voltage Resistance R Low voltage In ~ Out Current ! Current ! I _. . . . . .A V I Response ~ i = .& V ~ Driving force R Figure R.3 A resistor, a voltage difference, and an electric current: Ohm's law. R~2o5 Ohm's Law: When Current Is Proportional to the Driving Voltage Ohm's law is an experimentally determined relation that holds for most mate- rials (e.g., sea water or copper wire), but not all materials (e.g., the important semiconductors silicon and germanium). When the two ends of a wire are con- nected, respectively, to the high- and low-voltage terminals of a voltaic cell or of an electrical outlet, there is a voltage difference A V across the wire. Associated with A V is the electric current I passing through the wire. See Figure R.3, where the wire is represented by a jagged line. Ohm's law says that (1) current I flows in the direction from high voltage to low voltage; (2) I is proportional to the voltage difference A V across the object: iiiiii ii iiiiiiiiiiii iiiii iiiiiiiiiiiiiiii iiiii!i iiiii i!i i iiiiiii i ii iiiiiiiiiii iiiiiiiiiiiE!ii!iiiiiili ! i In (2), proportional means that R, called the electrical resistance, is inde- pendent of the value of A V. Ohm's law holds for copper, but not for silicon. Equation (R.2) can be made to apply to silicon if we let R depend on A V. Here's how to "read" (R.2). Knowing how to "read" an equation is an impor- tant skill. Equation (R.2) implies that if we measure both the "input" A V and the "output" l, and then we employ R = A V/I , then we can obtain the elec- trical resistance R. The unit of electrical resistance, the ohm, or f2 (the Greek letter Omega), is the same as a volt/amp = V/A. Thus S2 = V/A. Equation (R.2) does not apply to objects that store appreciable amounts of electrical energy (capacitors) or magnetic energy (inductors). Equation (R.2) also implies that if you increase the "input" A V, then you also increase the "output" l; and at fixed A V if you increase the resistance R, then you decrease "output" I. See Figure R.3. An equation like (R.2) holds for the water current through a pipe with a fluid resistance, driven by the pressure difference between one end of the pipe and the other. Of course, the units of voltage and pressure are different, as are the units of electric current and water current, and as are the units of electrical resistance and fluid resistance. Note that it is pressure difference that drives a water current; water will not flow through a pipe whose ends are connected to two reservoirs at the same pressure. Similarly, it is voltage difference that drives electric current through a wire; electric charge !2 will not flow through a wire whose ends are connected to two charge reservoirs at the same voltage. For water, we also can drive water current with water pumps. For electricity, we also can drive an electric current with voltaic cells, thermoelectric Review/Preview ~ Electricity: Its Uses and Its Visualization devices, electromagnetic induction, and by a variety of other means. Any source of energy that drives an electric current (even voltage difference) is called an electromotive force, or emf. Such a source of energy does work on the electric charge, so it also provides a force that causes an electric current to flow. R.2~.6 Power Is the Product of Current and Voltage Difference The power 72 (in watts, or W) going into a resistor (in the form of heat) is given by - I A V. (R.3) When (R.2) and (R.3) are combined, they yield another equation, .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . first obtained by Joule, and for that reason sometimes called Joule's law. From (R.3), the greater the current I at fixed A V, the greater the power 72; and the greater the voltage difference A V at fixed current I, the greater the power ~P: 4 A at 120 V provides 480 W; 8 A at 120 V provides 960 W; and 8 A at 240 V provides 1920 W. We will now employ equations (R.1-R.4) to answer some basic questions about power, voltage, current, electrical resistance, and electrical safety. R~2~7 Applications: Toasters and Power Cords Consider a toaster, one of the simplest of electrical devices. Its working element is a heat-resistant wire. Assuming that it produces 7~ - 720 W, and using A V = 120 V, (R.3) yields a current of I - 6 A. Putting this into (R.2) yields a value of R - 20 s2 for the electrical resistance of the toaster. Hence, from the current rating or power rating of a household appliance, we can deduce its electrical resistance. Similarly, a 50-foot-long, 16-gauge extension cord that is rated at 13 A for 125 V must also be rated at 13. 1 2 5 - 1625 W for 125 V. Excess power will start to melt the wire's insulation. R~2,8 Overload: Fuses and Circuit Breakers Most modern house wiring is rated to carry safely a current of either 15 A or 20 A. Circuit breakers (found in a fuse or breaker box, often located in some obscure part of the house) protect the house wiring from carrying too large an electric current; they "trip" if the current exceeds the rated value. Overload can occur by using too many appliances on the same outlet; if a 1000 W hairdryer, a 600 W toaster, and a 1200 W microwave oven were all to use the same outlet, the total power consumption would be 2800 W, corresponding to 23.3 A, an overload even on a 20 A circuit. Extension cords provide a way to exceed a rated value, even for a house that is properly wired. In the summer of 1992, a fraternity house in Bryan, Texas, burned down; someone had operated an air conditioner using an extension cord with too low a current rating. The extension cord, under the overload of current, began heating up like toaster wire, ultimately setting on fire the insulation or a R.3 Some Uses of Electrical Power 7 nearby object. For an air conditioner rated at 72 - 2 4 0 0 W, and A V = 120 V, (R.3) yields I = 20 A. Circuit breakers can safely carry such a current, but a 10 A or 12 A extension cord cannot. Note that, by (R.2), the air conditioner, when running, has an effective electrical resistance of R = 120/20 = 6 S2. Electrical motors, such as those employed in air conditioners, have different electrical properties when they are turning than when they have not yet started to turn. When turning, electrical motors produce a back emf that opposes the driving emf, and this causes the current to be less when it is running than when it is starting up. When an electrical motor is prevented from turning, no back emf is produced, so a larger current goes to the motor, which can cause it to burn out. Fuses are intended to burn out if excessively large currents flow through them, thus protecting electrical devices and electrical wiring from too large a current flow. Circuit breakers, on the other hand, do not burn out, and can be reset, and for that reason they have supplanted fuses in modern buildings. In the 1940s and earlier, when fuses were used instead of circuit breakers, many a house burned down because, on overloaded circuits, people "cleverly" replaced fuses by pennies, which permitted a much higher current flow than the fuses they replaced. (Those who knew that pennies would serve to pass current, like a fuse, but didn't know that they wouldn't protect the house wiring, unlike a fuse, illustrate the maxim that "a little knowledge is a dangerous thing.") Fuses (which typically are used in automobiles) must be replaced, once the cause of the electrical problem has been fixed. R~3 Some Uses of Electrical Power Fans, blenders, and many other appliances employ electric motors to convert electrical energy to mechanical energy. Electric motors use the magnetism of electric currents to provide the torque needed to turn the fan or blender blade. Automobiles use the chemical energy of a car battery to provide electrical energy to start the starting motor, which in turn provides the mechanical energy to start the gasoline engine. (The earliest automobiles employed no starting mo- tors and no batteries; cars were started by the driver turning a crank to provide the mechanical energy to start the engine. That is the origin of the term crank over used to describe how the starting motor gets the gasoline engine turning.) The chemical energy in gasoline (released as explosions within the cylinders of the engine) is converted to mechanical energy (the pistons move, and this causes the crankshaft to turn). Some of this mechanical energy gets converted into electrical energy by an electrical generator~also called an alternator. This goes into recharging the chemical energy of the battery, which then has enough chemical energy to start the car later. Motors and generators are discussed in Chapter 13. Radios and TVs receive, tune, demodulate (i.e., extract the useful signal), filter, and amplify weak and scrambled electromagnetic signals (Chapter 15), making them intelligible and clear. Stereo systems do much the same for unin- telligible signals embedded in plastic on a record or compact disk. We discuss many aspects of the operation of these devices in Chapter 14. A "walkman" employed to play compact disks (CDs) or cassette tapes uses up the chemical energy in its voltaic cells much more rapidly than one used only

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