Question

Two wires of equal length, one of aluminium and the other of copperhave the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables.(rAl = 2.63 × 10–8 W m, rCu = 1.72 × 10–8 W m, Relative density ofAl = 2.7, of Cu = 8.9.)

Answer 1

Given: The resistivity of aluminium is ρ Al =2.63× 10 −8 Ωm, the relative density of aluminium is 2.7, the resistivity of copper is ρ Cu =1.72× 10 −8 Ωm and the relative density of copper is 8.9.

The resistance of a wire is given as,

R=ρ l A

Where, ρ is the resistivity, l is the length and A is the area of cross section.

For two wires of equal length and resistance, we can write,

ρ Al l A Al = ρ Cu l A Cu A Al A Cu = ρ Al ρ Cu

By substituting the values in the above equation, we get

A Al A Cu = 2.63× 10 −8 1.72× 10 −8 =1.529

The mass of a wire is given as,

m=V×d =Al×d

Where, d is the relative density of wire.

For two wires of equal length we can write,

m Al m Cu = A Al l× d Al A Cu l× d Cu = A Al × d Al A Cu × d Cu

By substituting the given values in the above equation, we get

m Al m Cu =1.529× 2.7 8.9 =0.46

It is clear that the mass of aluminium wire is less than the copper wire of same length.

Thus, the aluminium is lighter than copper.

Since aluminium is lighter than the copper therefore, aluminium is preferred for overhead power cables.