Copper and aluminum are being considered for the cables in a high-voltage transm

Question

Copper and aluminum are being considered for the cables in a high-voltage transmission line where each must carry a current of 66.0 A.The resistance of each cable is to be 0.185 per kilometer. The electrical resistivities for copper and aluminum are Copper = 1.67 ×108-m, and Aluminum = 2.65 ×108·m; the mass density of copper is 8,920 kg/m3 and that of aluminum is 2,702 kg/m3.

(a) If this line carries power from Niagara Falls to New York City (approximately 500 km), how much power is lost along the way in the cable?

(b) Compute the necessary cable diameter for each choice of cable material.

Explanation / Answer

a)

L = length of the cable = 500 km

resistance per unit length = 0.185

R = total resistance = (0.185) (500)

i = current = 66 A

Power lost is given as

P = i2 R = (66)2 ((0.185) (500)) = 4.03 x 105 Watt

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