Copper and aluminium are being considered for a high-voltage transmission line that must carry a current of 62.3 A. The resistance per unit length is to be . We have to compute for each choice of material (a) the current density and (b) the mass of 1.00 m of cable. The densities of copper and aluminium are 8960 and , respectively.

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The mass densities of copper and aluminium are

and

.

And electrical resistivities of these materials are

and

(a)

We will first find the cross-sectional areas of the copper and aluminium wires, having resistance per unit length of

. We will use the result that resistance, R, of a wire of length, l, resistivity, , and cross-sectional area, A, is given by

Therefore, for copper wire

And, similarly for aluminium wire

The transmission line is to carry current of 62.3 A. Therefore, the current density in the copper cable will be

and the current density in the aluminium cable will be

(b)

Mass of 1-m of copper cable will be

and the mass of 1-m of aluminium cable will be