Copper and aluminum are being considered for a high-voltage transmission line th

Question

Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 78.3 A. The resistance per unit length is to be 0.143 ?/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b)the mass per unit length ? for a copper cable and (c) J and (d) ? for an aluminum cable.

(a) Number Units Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 78.3 A. The resistance per unit length is to be 0.143 ?/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b)the mass per unit length ? for a copper cable and (c) J and (d) ? for an aluminum cable.

Explanation / Answer

R/L = ?/A so A = (? *L)/R = 1.72x10^-8*1000/0.143 = 1.203x10^-4m^2

a) J = I/A = 78.3/1.203x10^-4 = 6.51 x 10^5 A/m^2

b) mass/unit length = density*A = 8960kg/m^3 * 1.203 x 10^-4 m^2 = 1.08 kg/m

c) R/L = ?/A so A = (? *L)/R = 2.75x10^-8 * 1000/0.143 = 1.923 x 10^-4 m^2

J = I/A = 78.3/1.923 x 10^-4 = 4.072 x 10^5 A/m^2

d) mass/unit length = density*A = 2600kg/m^3 * 1.923 x 10^-4m^2 = 0.499 kg/m

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