A number 14 copper wire has a diameter of 1.63 mm. Calculate the resistance of a

Question

A number 14 copper wire has a diameter of 1.63 mm. Calculate the resistance of a 27 m long piece of that wire. Use rho = 1.72 times 10^-8 Ohm m for the resistivity of copper. For safety, the Canadian Electrical Code limits the allowable current that such a wire may carry. When used in indoor wiring, the limit is 15 A for rubber-insulated wire of that size. How much power would be dissipated in the piece of wire when carrying the maximum allowable current? What would be the potential difference between the ends of the piece of wire?

Explanation / Answer

here,

diameter , d = 1.63 mm = 1.63 * 10^-3 m

radius , r = d/2 = 8.15 * 10^-4 m

length , l = 27 m

p = 1.72 * 10^-8 ohm.m

the resistance , R = p * l/area

R = 1.72 * 10^-8 * 27 /( pi * (8.15 * 10^-4 )^2)

R = 0.22 ohm

the resistance of wire is 0.22 ohm

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