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 80.0 A. The resistance per unit length is to be 0.125 ohm/km. The densities of copper and aluminum are 8960 and 2700 kg/m3, respectively. A/m2 Compute: the magnitude J of the average current density for a copper cable the mass per unit length A for a copper cable. Kg/m the magnitude J of the average current density for an aluminum cable A/m2 the mass per unit length A for an aluminum cable. kg/m

Explanation / Answer

a) Resistance per unit length,r = 0.125ohm/km = 1.25*10^-4ohm/m resistivity of copper = 1.69*10^-8 ohm.m so, cross section area, a = 1.69*10^-8/1.25*10^-4 = 1.352*10^-4 m2 J = current/a = 80/1.352*10^-4 = 5.92*10^5 A/m2 b)mass/length = density*cross-section = 8960*1.352*10^-4 kg/m = 1.21kg/m c)similar to a)part cross-section, a = 2.75*10^-8/1.25*10^-4 = 2.2*10^-4 m2 J = current/a = 80/2.2*10^-4 = 3.64*10^5 A/m2 d) mass/length = density*cross-section = 2700*2.2*10^-4 kg/m = 0.594kg/m

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