# qr code vb.net library Or, using eq. (13), eq. (15) becomes P RI I, so that P I 2R 17 in .NET Generate Code128 in .NET Or, using eq. (13), eq. (15) becomes P RI I, so that P I 2R 17

Or, using eq. (13), eq. (15) becomes P RI I, so that P I 2R 17
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Equations (11) through (17) should all be committed to memory, because they are of such fundamental importance. For our convenience, they are summarized below, where V is potential di erence in volts, I is current in amperes, R is resistance in ohms, and power is in watts. OHM S LAW: POWER: V RI P VI I V=R P I R
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R V=I P V 2 =R
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Problem 8 In Fig. 22, if V 48 volts and R 6 ohms, what current will ow Problem 9 In Problem 8, nd the power output of the battery using eqs. (15), (16), and (17). Problem 10 If the power input to a 75-ohm resistance is known to be 18 watts, what current is owing
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CHAPTER 2 Electric Current. Ohm s Law
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In devices such as electric heaters, irons, and toasters, the basic purpose is simply to develop a required amount of heat in the resistance wire used in such devices. In most applications, however, especially in electronics, resistance is not used in a circuit to develop heat, but is used for other purposes. The heat developed in resistance is, therefore, in most applications an undesired e ect. The principal reasons why this is true are as follows. 1. The resistance of a given length of a given type of wire depends, to some extent, upon the temperature of the wire. Thus, as the temperature of a wire increases, due to increased heat input, its resistance also tends to increase, and this is generally an undesirable e ect. Excessive heat generation adversely a ects the operation of other components in a circuit, and tends to cause physical deterioration of the resistor* itself.
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Let us discuss items (1) and (2) in more detail. To begin, it should be pointed out that the four principal factors that determine the resistance of a wire conductor are (a) the length L of the wire, (b) the cross-sectional area A of the wire, (c) the material of which the wire is made, (d) the temperature T of the wire.
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Let us deal with the rst three items rst. Experiment proves that the resistance R of a wire conductor is directly proportional to the length L and inversely proportional to the cross-sectional area A, a fact we show mathematically by writing R  L A 18
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where R is the resistance in ohms, L is the length in meters, A is the cross-sectional area in square meters, and where the proportional constant  (the Greek letter rho ) is called the resistivity ( ree sis TIV ity ), whose value depends upon the material the wire is made of and the temperature T of the wire. Note that, from eq. (18), we have  RA ohms meters 2 ohms meters L meters
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thus showing that resistivity  has the dimensions ohms times meters, or ohm m, as it is usually written. As mentioned above, the value of  depends on the kind of metal the wire is made of, and the temperature T of the wire. It is found that the resistivity of metals increases linearly with temperature over a wide range of temperature, and this fact is expressed in the form  0 1 0 T T0 19
* A device made solely to introduce resistance into a circuit is called a resistor ( ree SIS tor ). Thus, a 100 ohm, wire-wound resistor is a device constructed of wire having 100 ohms of resistance.
where
CHAPTER 2 Electric Current. Ohm s Law
 resistivity of the given metal at any temperature T8C, 0 resistivity of the given metal at the standard reference temperature of T0 208C, 0 the temperature coe cient of resistance of the metal at 208C. The values of 0 and 0 ( alpha sub zero ) have been found experimentally, a short table of values being given below.
0 (ohm m) Silver Copper Aluminum Tungsten Constantan (1.59)10 (1.75)10 8 (2.83)10 8 (5.50)10 8 (49.0)10 8
0 (per 8C) (3.75)10 3 (3.80)10 3 (4.03)10 3 (4.70)10 3 (0.01)10 3
Note 1: Constantan is an alloy of 45% nickel and 55% copper having, as the table shows, a high value of resistivity and a very low value of temperature coe cient. Note 2: In some wire tables a unit of length called the mil is used, where 1 mil 0.001 inch. A circular mil is de ned as the area of a circle 1 mil in diameter.
Let us next consider the power rating of a resistor, using, as a convenient example, a 100-ohm resistor. Suppose, for example, that we are dealing with an application in which the resistor must carry a current of, say, 0.8 amperes. Then, by eq. (17), the power input to the resistor will be P I 2 R 64 watts, which is 64 joules of work per second. Since 1 calorie 4.186 joules,* we have 64=4:186 15:289 calories of heat will be developed in the resistor each second. We thus have a problem in heat transfer, because if the heat generated in the resistor is not transferred away fast enough the temperature of the resistor will continue to rise until it is destroyed. The ability of a resistor to dissipate heat depends greatly upon the amount of exposed surface area the resistor has. Thus, resistors that must dissipate relatively large amounts of heat must be made physically larger than resistors that must dissipate only a relatively small amount of heat. The amount of heat that a given resistor can safely dissipate also depends, of course, on the temperature of the surrounding (ambient) air, and whether the ow of air is by natural convection or is driven by a fan or blower. Resistors can be purchased in values of resistance from less than 1 ohm to several megohms ( 1 megohm being 1 million ohms), and in power rating from 1 watt to several 4 hundred watts. When specifying the power rating of a resistor, the manufacturer will also state the maximum temperature of ambient air for which the rating is valid. For example, a manufacturer might state that the power rating of a certain resistor is 5 watts at 308C ambient, and an equipment designer must keep this in mind. Resistors that must dissipate more than 2 or 3 watts are generally of the wire-wound type, consisting of resistance wire, of low temperature coe cient, wound on a ceramic tube.
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