formula backwards, plugging in the power rating for P and the resistance of the unit forR, and solve for I. Or you can find the square root of P/R. Remember to use amperes forcurrent, ohms for resistance, and watts for power.The power rating for a given resistor can, in effect, be increased by using a networkof 2 × 2, 3 × 3, 4× 4, etc., units in series-parallel. You’ve already learned about this. If youneed a 47-ohm, 45-W resistor, but all you have is a bagful of 47-ohm, 1-W resistors, youcan make a 7 × 7 network in series-parallel, and this will handle 49 W. It might look ter-rible, but it’ll do the job.Power ratings are specified with a margin for error. A good engineer never tries totake advantage of this and use, say, a 1/4-W unit in a situation where it will need to draw0.27 W. In fact, good engineers usually include their own safety margin. Allowing 10 per-cent, a 1/4-W resistor should not be called upon to handle more than about 0.225 W. Butit’s silly, and needlessly expensive, to use a 2-W resistor where a 1/4-W unit will do, un-less, of course, the 2-W resistor is all that’s available.Temperature compensationAll resistors change value somewhat when the temperature changes dramatically. Andbecause resistors dissipate power, they can get hot just because of the current theycarry. Often, this current is so tiny that it doesn’t appreciably heat the resistor. But insome cases it does, and the resistance might change. Then the circuit will behave dif-ferently than it did when the resistor was still cool.There are various ways to approach problems of resistors changing value whenthey get hot.One method is to use specially manufactured resistors that do not appreciablychange value when they get hot. Such units are called temperature-compensated. Butone 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 dis-sipated 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 iden-tical, 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 threetimes the intended resistance, and connect them all in parallel. Or you can take severalresistors, say four of them, each with about 1/4 the intended resistance, and connectthem in series.It is unwise to combine several resistors with greatly different values. This can re-sult in one of them taking most of the load while the others loaf, and the combinationwill 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 inseries (or in parallel). Then the one whose resistance decreases with heat (negative tem-perature 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 proba-bly won’t be able to find two such resistors without spending at least as much money as youTemperature compensation111