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Resistance and the Ohm 21
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resistance through an electric device for a constant voltage of 1 V.
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When 1 V is placed across 1 of resistance, assuming that the power supply can deliver an unlimited number of charge carriers, there is a current of 1 A. If the resistance is doubled to 2 , the current decreases to 0.5 A. If the resistance is cut by a factor of 5 to 0.2 , the current increases by the same factor, to 5 A. The current flow, for a constant voltage, is said to be inversely proportional to the resistance. Figure 2-3 is a graph that shows various currents, through various resistances, given a constant voltage of 1 V across the whole resistance. Resistance has another property. If there is a current flowing through a resistive material, there is always a potential difference across the resistive component (called a resistor). This is shown in Fig. 2-4. In general, this voltage is directly proportional to the current through the resistor. This behavior of resistors is useful in the design of electronic circuits, as you will learn later in this book. Electrical circuits always have some resistance. There is no such thing as a perfect conductor. When some metals are chilled to temperatures near absolute zero, they lose practically all of their resistance, but they never become absolutely perfect, resistance-free conductors. This phenomenon, about which you might have heard, is called superconductivity.
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through a component having resistance, a voltage exists across that component.
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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. In electronics, the resistance of a component often varies, depending on the conditions under which it is operated. A transistor, for example, might have high resistance some of the time, and low resistance at other times. High/low resistance variations can be made to take place thousands, millions, or billions of times each second. In this way, oscillators, amplifiers, and digital devices function in radio receivers and transmitters, telephone networks, digital computers, and satellite links (to name just a few applications).
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Electricians and electrical engineers sometimes talk 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 . 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 of a component or circuit in ohms, you can get the conductance in siemens: divide 1 by the resistance. If you know the conductance in siemens, you can get the resistance: divide 1 by the conductance. Resistance, as a variable quantity, is denoted by an italicized, uppercase letter R. Conductance, as a variable quantity, is denoted as an italicized, uppercase letter G. If we express R in ohms and G in siemens, then the following two equations describe their relationship: G = 1/R R = 1/G Units of conductance much smaller than the siemens are often used. A resistance of 1 k is equal to 1 millisiemens (1 mS). If the resistance is 1 M , the conductance is one microsiemens (1 S). You ll sometimes hear about kilosiemens (kS) or megasiemens (MS), representing resistances of 0.001 and 0.000001 (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 can have conductances in the megasiemens range. Suppose a component has a resistance of 50 . Then its conductance, in siemens, is 1/50 S, which is equal to 0.02 S. We can call this 20 mS. Or imagine a piece of wire with a conductance of 20 S. Its resistance is 1/20 , which is equal to 0.05 . You will not often hear the term milliohm. But you could say that this wire has a resistance of 50 m , and you would be technically right. Determining conductivity is tricky. If wire has a resistivity of 10 /km, you can t say that it has a conductivity of 1/10, or 0.1, S/km. It is true that a kilometer of such wire has a conductance of 0.1 S, but 2 km of the wire has a resistance of 20 (because there is twice as much wire). That 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. That would be a mistake! Conductance decreases with increasing wire length. Figure 2-5 illustrates the resistance and conductance values for various lengths of wire having a resistivity of 10 /km.
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