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The first set of numbers above represents standard resistance values available in tolerances of plus or minus 10 percent. This means that the resistance might be as much as 10 percent more or 10 percent less than the indicated amount. In the case of a 470-ohm resistor, for example, the value can be off by as much as 47 ohms and still be within tolerance. That s a range of 423 to 517 ohms. The tolerance is calculated according to the specified value of the resistor, not the actual value. You might measure the value of a 470-ohm resistor and find it to be 427 ohms, and it would be within 10 percent of the specified value; if it measures 420 ohms, it s outside the 10-percent range and is a reject. The second set, along with the first set, of numbers represents standard resistance values available in tolerances of plus or minus 5 percent. A 470-ohm, 5-percent resistor will have an actual value of 470 ohms plus or minus 24 ohms, or a range of 446 to 494 ohms. Some resistors are available in tolerances tighter than 5 percent. These precision units are employed in circuits where a little error can make a big difference. In most audio and radio-frequency oscillators and amplifiers, 10-percent or 5-percent tolerance is good enough. In many cases, even a 20-percent error is all right.
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All resistors are given a specification that determines how much power they can safely dissipate. Typical values are 1/4 W, 1/2 W, and 1 W. Units also exist with ratings of 1/8 W or 2 W. These dissipation ratings are for continuous duty. You can figure out how much current a given resistor can handle, by using the formula for power (P) in terms of current (I) and resistance (R): P = I 2R. Just work this
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Temperature compensation 111 formula backwards, plugging in the power rating for P and the resistance of the unit for R, and solve for I. Or you can find the square root of P/R. Remember to use amperes for current, ohms for resistance, and watts for power. The power rating for a given resistor can, in effect, be increased by using a network of 2 2, 3 3, 4 4, etc., units in series-parallel. You ve already learned about this. If you need a 47-ohm, 45-W resistor, but all you have is a bagful of 47-ohm, 1-W resistors, you can make a 7 7 network in series-parallel, and this will handle 49 W. It might look terrible, but it ll do the job. Power ratings are specified with a margin for error. A good engineer never tries to take advantage of this and use, say, a 1/4-W unit in a situation where it will need to draw 0.27 W. In fact, good engineers usually include their own safety margin. Allowing 10 percent, a 1/4-W resistor should not be called upon to handle more than about 0.225 W. But it s silly, and needlessly expensive, to use a 2-W resistor where a 1/4-W unit will do, unless, of course, the 2-W resistor is all that s available.
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All resistors change value somewhat when the temperature changes dramatically. And because resistors dissipate power, they can get hot just because of the current they carry. Often, this current is so tiny that it doesn t appreciably heat the resistor. But in some cases it does, and the resistance might change. Then the circuit will behave differently than it did when the resistor was still cool. There are various ways to approach problems of resistors changing value when they get hot. One method is to use specially manufactured resistors that do not appreciably change value when they get hot. Such units are called temperature-compensated. But one of these can cost several times as much as an ordinary resistor. Another approach is to use a power rating that is much higher than the actual dissipated power in the resistor. This will keep the resistor from getting very hot. Usually, it s a needless expense to do this, but if the small change in value cannot be tolerated, it s sometimes the most cost effective. Still another scheme is to use a series-parallel network of resistors that are all identical, in the manner you already know about, to increase the power dissipation rating. Alternatively, you can take several resistors, say three of them, each with about three times the intended resistance, and connect them all in parallel. Or you can take several resistors, say four of them, each with about 1/4 the intended resistance, and connect them in series. It is unwise to combine several resistors with greatly different values. This can result in one of them taking most of the load while the others loaf, and the combination will be no better than the single hot resistor you started with. You might get the idea of using two resistors with half (or twice) the value you need, but with opposite resistance-versus-temperature characteristics, and connecting them in series (or in parallel). Then the one whose resistance decreases with heat (negative temperature coefficient) will have a canceling-out effect on the one whose resistance goes up (positive temperature coefficient). This is an elegant theory, but in practice you probably won t be able to find two such resistors without spending at least as much money as you
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112 Resistors would need to make a 3 3 series-parallel network. And you can t be sure that the opposing effects will exactly balance. It would be better, in such a case, to make a 2 2 series-parallel array of ordinary resistors.
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