Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter ? Hence explain why aluminium wires are preferred for overhead power cables. `(rho_(Al) = 2.63 xx 10^(-8) Omega m , rho_(Cu) = 1.72 xx 10^(-8) Omega` m, Relative density of Al = 2.7 , of Cu = 8.9 )

Explanation

Light weight cables are chosen for overhead power cables.
If volume density of mass for given wire is d then,
`d = (m)/(V) = (m)/(Al) = (m)/(((rho l)/(R))l) " " (because R = (rho l)/(A) rArr A = (rho l)/(R) )`
`therefore d = (mR)/(rho l^(2)) `
` therefore m = (rho l^(2) d)/(R)`
Here for given wires I and R are same and so,
m `prop rho`d
`therefore (m_(1) )/(m_(2)) = (rho_(1) d_(1))/(rho_(2) d_(2))`
Taking aluminium and copper wires as first and second wire respectively,
`(m_(1))/(m_(2)) = ((2.63 xx 10^(-8))( 2.7 xx 10^(3)))/((1.72 xx 10^(-8) ) (8.9 xx 10^(3)))`
` therefore (m_(1))/(m_(2))` = 0.4638
`therefore m_(1) lt m_(2)`
Aluminium wire is lighter than copper wire. Hence, aluminium wires are chosen as overhead power cables.