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RESISTANCE AND OHM S LAW
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When electric current ows through a metal wire or through other circuit elements, it encounters a certain amount of resistance, the magnitude of which depends on
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the electrical properties of the material Resistance to the ow of current may be undesired for example, in the case of lead wires and connection cable or it may be exploited in an electrical circuit in a useful way Nevertheless, practically all circuit elements exhibit some resistance; as a consequence, current owing through an element will cause energy to be dissipated in the form of heat An ideal resistor is a device that exhibits linear resistance properties according to Ohm s law, which states that V = IR Ohm s law (213)
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that is, that the voltage across an element is directly proportional to the current ow through it R is the value of the resistance in units of ohms ( ), where 1 = 1 V/A (214)
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The resistance of a material depends on a property called resistivity, denoted by the symbol ; the inverse of resistivity is called conductivity and is denoted by the symbol For a cylindrical resistance element (shown in Figure 220), the resistance is proportional to the length of the sample, l, and inversely proportional to its cross-sectional area, A, and conductivity, v= l i A
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+ l A v R= l A R v 1/R
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Physical resistors with resistance R Typical materials are carbon, metal film Circuit symbol i-v characteristic
Figure 220 The resistance element
It is often convenient to de ne the conductance of a circuit element as the inverse of its resistance The symbol used to denote the conductance of an element is G, where G= 1 siemens (S) R where 1 S = 1 A/V (216)
Thus, Ohm s law can be restated in terms of conductance as: I = GV (217)
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Fundamentals of Electric Circuits
i Linear range v
Light bulb i Linear range
Exponential i-v characteristic (semiconductor diode)
b4 b3 b2 b1
Ohm s law is an empirical relationship that nds widespread application in electrical engineering, because of its simplicity It is, however, only an approximation of the physics of electrically conducting materials Typically, the linear relationship between voltage and current in electrical conductors does not apply at very high voltages and currents Further, not all electrically conducting materials exhibit linear behavior even for small voltages and currents It is usually true, however, that for some range of voltages and currents, most elements display a linear i-v characteristic Figure 221 illustrates how the linear resistance concept may apply to elements with nonlinear i-v characteristics, by graphically de ning the linear portion of the i-v characteristic of two common electrical devices: the light bulb, which we have already encountered, and the semiconductor diode, which we study in greater detail in 8 The typical construction and the circuit symbol of the resistor are shown in Figure 220 Resistors made of cylindrical sections of carbon (with resistivity = 35 10 5 -m) are very common and are commercially available in a wide range of values for several power ratings (as will be explained shortly) Another common construction technique for resistors employs metal lm A common power rating for resistors used in electronic circuits (eg, in most consumer electronic appliances such as radios and television sets) is 1 W Table 21 lists the standard values for 4 commonly used resistors and the color code associated with these values (ie, the common combinations of the digits b1 b2 b3 as de ned in Figure 222) For example, if the rst three color bands on a resistor show the colors red (b1 = 2), violet (b2 = 7), and yellow (b3 = 4), the resistance value can be interpreted as follows: R = 27 104 = 270,000 = 270 k
Color bands black brown red orange yellow green 0 1 2 3 4 5 6 blue violet 7 8 gray white 9 silver 10% 5% gold
Table 21 Common resistor values values ( 1 -, 1 -, 1 -, 1-, 2-W rating) 8 4 2 Code 10 12 15 18 22 27 33 39 47 56 68 82 Brn-blk-blk Brn-red-blk Brn-grn-blk Brn-gry-blk Red-red-blk Red-vlt-blk Org-org-blk Org-wht-blk Ylw-vlt-blk Grn-blu-blk Blu-gry-blk Gry-red-blk 100 120 150 180 220 270 330 390 470 560 680 820 Multiplier k Multiplier k Multiplier k Multiplier Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown 10 12 15 18 22 27 33 39 47 56 68 82 Red Red Red Red Red Red Red Red Red Red Red Red 10 12 15 18 22 27 33 39 47 56 68 82 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 100 120 150 180 220 270 330 390 470 560 680 820 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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