Different types of wire are rated according to their gauge. Each gauge correspon

Question

Different types of wire are rated according to their gauge. Each gauge corresponds to a different cross-sectional area bya complicated formula that is unimportant for our purposes. In the American Wire Gauge (AWG) system, the smaller thegauge, the larger the diameter of the wire. A #10 AWG wirehas a diameter of 0.100 in. The Underwriters Laboratories,Inc. (UL), which sets many safety standards for the United States,requires that this gauge of copper wire should carry no more than55.0 A in power transmission applications in order to prevent thepossibility of it becoming too hot and causing a fire.
a. What is the resistance of 1,000.0 ft of #10 AWG copperwire?
b. At what rate would heat energy be dissipated by this lengthof #10 AWG copper wire if it is required to carry the maximum ratedcurrent of 55.0 A?
a. What is the resistance of 1,000.0 ft of #10 AWG copperwire?
b. At what rate would heat energy be dissipated by this lengthof #10 AWG copper wire if it is required to carry the maximum ratedcurrent of 55.0 A?

Explanation / Answer

For this question, you would need to convert all the length valuesfrom customary to the metric in order to solve in theequations: 0.100 in = 0.00254 m 1,000 ft = 304.8 m a.) The question expects that you know what the resistivity forcopper is, which is 1.7x10^-8 m... So R = l/A = [(1.7x10^-8 m)(304.8m)] / (0.00254m)^2 = 0.25565 b.) Power = I^2R = (55.0A)^2(0.25565) = 773.341 W I hope this helps :)

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