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 60 A. the resistance per unit length is to be 0.155 ohm/km. the densities of copper and aluminum are 8960 and 2700 kg/m^3, respectively. Compute the magnitude J of the current density for a copper cable. Compute the magnitude J of the current density for an aluminum cable. And compute the mass per unit length lambda for a copper cable. And compute the mass per unit length lambda for an aluminum cable.

Explanation / Answer

R/L = /A so,

A = ( *L)/R

A = 1.72 x 10^-8 x 1000 / 0.155

A = 1.11 x 10^-4 m^2

a)

J = I/A

J = 60 / 1.11 x 10^-4

J = 5.41 x 10^5 A/m^2

b)

mass / unit length = density*A = 8960 kg/m^3 x 1.11 x 10^-4 m^2 = 0.9946 kg/m

c)

R/L = /A so,

A = ( *L)/R = 2.75 x 10^-8 x 1000 / 0.155

A = 1.774 x 10^-4 m^2

J = I/A = 60 / 1.774 x 10^-4 = 3.382 x 10^5 A/m^2

d)

mass/unit length = density*A = 2700kg/m^3 x 3.382 x 10^-4 m^2 = 0.9131 kg/m

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