Will a copper wire or an aluminum wire give the larger current to weight ratio for...

Will a copper wire or an aluminum wire give the larger current to weight ratio for high voltage transmission lines if both wires are to have the same resistance between any two points?

Solutions

Expert Solution

Since the resistance is same for both copper and aluminum,
R = cL/Ac = aL/Aa ...(1)
Where c and a are the resistivities of the copper and aluminum, L is the length of both materials, which are the same. Ac and Aa are the cross-sectional areas of copper and aluminum respectively.
From (1),
c/a = Ac/Aa
Substituting the resistivities,
Ac/Aa = (1.7 x 10^-8)/(2.8 x 10^-8) = 0.61 ...(2)

Mass = volume x density.
Mc = Vc x Dc for copper and Ma = Va x Da for aluminum
Where Vc and Va are the volume of copper and aluminum and Dc and Da are the densities of copper and aluminum respectively.
Mc/Ma = (Vc/Va) x (Dc/Da)
Vc/Va = [Ac x L] / [Va x L] = Ac/Aa
From (2), Ac/Aa = 0.61

Mc/Ma = 0.61 x (Dc/Da)
= 0.61 x (8.96/2.7)
= 2.01
So, current per weight of copper is almost twice as that of aluminum

genius_generous answered 1 year ago

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