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Resistance and the ohm 27
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Table 2-1. Resistivity for copper wire, in terms of the size in American Wire Gauge (AWG).
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Wire size, AWG 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Resistivity, ohms/km 0.52 0.83 1.3 2.7 3.3 5.3 8.4 13 21 34 54 86 140 220 350
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deliver an unlimited number of charge carriers, there will be a current of 1A. If the resistance is doubled, the current is cut in half. If the resistance is cut in half, the current doubles. Therefore, the current flow, for a constant voltage, is inversely proportional to the resistance. Figure 2-3 is a graph that shows various currents, through various resistances, given a constant voltage of 1V across the whole resistance.
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2-3 Current versus resistance through an electric device when the voltage is constant at 1 V.
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28 Electrical units Resistance has another property in an electric circuit. If there is a current flowing through a resistive material, there will always be a potential difference across the resistive object. This is shown in Fig. 2-4. The larger the current through the resistor, the greater the EMF across the resistor. In general, this EMF is directly proportional to the current through the resistor. This behavior of resistors is extremely useful in the design of electronic circuits, as you will learn later in this book.
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2-4 Whenever a resistance carries a current, there is a voltage across it.
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Electrical circuits always have some resistance. There is no such thing as a perfect conductor. When some metals are chilled to extremely low temperatures, they lose practically all of their resistance, but they never become absolutely perfect, resistancefree conductors. This phenomenon, about which you might have heard, is called superconductivity. In recent years, special metals have been found that behave this way even at fairly moderate temperatures. Researchers are trying to concoct substances that will superconduct even at room temperature. Superconductivity is an active field in physics right now. Just as there is no such thing as a perfectly resistance-free substance, there isn t a truly infinite resistance, either. Even air conducts to some extent, although the effect is usually so small that it can be ignored. In some electronic applications, materials are selected on the basis of how nearly infinite their resistance is. These materials make good electric insulators, and good dielectrics for capacitors, devices that store electric charge. In electronics, the resistance of a component often varies, depending on the conditions under which it is operated. A transistor, for example, might have extremely high resistance some of the time, and very low resistance at other times. This high/low fluctuation can be made to take place thousands, millions or billions of times each second. In this way, oscillators, amplifiers and digital electronic devices function in radio receivers and transmitters, telephone networks, digital computers and satellite links (to name just a few applications).
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Conductance and the siemens
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The better a substance conducts, the less its resistance; the worse it conducts, the higher its resistance. Electricians and electrical engineers sometimes prefer to speak
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Power and the watt 29 about the conductance of a material, rather than about its resistance. The standard unit of conductance is the siemens, abbreviated S. When a component has a conductance of 1 S, its resistance is 1 ohm. If the resistance is doubled, the conductance is cut in half, and vice-versa. Therefore, conductance is the reciprocal of resistance. If you know the resistance in ohms, you can get the conductance in siemens by taking the quotient of 1 over the resistance. Also, if you know the conductance in siemens, you can get the resistance in ohms by taking 1 over the conductance. The relation can be written as: siemens ohms 1/ohms, or 1/siemens
Smaller units of conductance are often necessary. A resistance of one kilohm is equal to one millisiemens. If the resistance is a megohm, the conductance is one microsiemens. You ll also hear about kilosiemens or megasiemens, representing resistances of 0.001 ohm and 0.000001 ohm (a thousandth of an ohm and a millionth of an ohm) respectively. Short lengths of heavy wire have conductance values in the range of kilosiemens. Heavy metal rods might sometimes have conductances in the megasiemens range. As an example, suppose a component has a resistance of 50 ohms. Then its conductance, in siemens, is 1 50, or 0.02 S. You might say that this is 20 mS. Or imagine a piece of wire with a conductance of 20 S. Its resistance is 1/20, or 0.05, ohm. Not often will you hear the term milliohm ; engineers do not, for some reason, speak of subohmic units very much. But you could say that this wire has a resistance of 50 milliohms, and you would be technically right. Conductivity is a little trickier. If wire has a resistivity of, say, 10 ohms per kilometer, you can t just say that it has a conductivity of 1/10, or 0.1, siemens per kilometer. It is true that a kilometer of such wire will have a conductance of 0.1 S; but 2 km of the wire will have a resistance of 20 ohms (because there is twice as much wire), and this is not twice the conductance, but half. If you say that the conductivity of the wire is 0.1 S/km, then you might be tempted to say that 2 km of the wire has 0.2 S of conductance. Wrong! Conductance decreases, rather than increasing, with wire length. When dealing with wire conductivity for various lengths of wire, it s best to convert to resistivity values, and then convert back to the final conductance when you re all done calculating. Then there won t be any problems with mathematical semantics. Figure 2-5 illustrates the resistance and conductance values for various lengths of wire having a resistivity of 10 ohms per kilometer.
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