Question

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. (rAl = 2.63 × 10–8 W m, rCu = 1.72 × 10–8 W m, Relative density of Al = 2.7, of Cu = 8.9.)

Answer 1

Two wires have same length and the resistance . as the specific resistance or resistivity of resistance are unequal , the areas are different.

we know formula, $R=\rho\frac{l}{A}$

for copper wire, $R_{Cu}=\rho_{Cu}\frac{l}{A_{Cu}}$

for aluminum wire, $R_{Al}=\rho_{Al}\frac{l}{A_{Al}}$

because $R_{Cu}=R_{Al}$

$so,\rho_{cu}\frac{l}{A_{cu}}=\rho_{Al}\frac{l}{A_{Al}}$

$\implies\frac{A_{Al}}{A_{cu}}=\frac{\rho_{Al}}{\rho_{cu}}\\\\=\frac{2.63\times10^{-8}}{1.72\times10^{-8}}=\frac{263}{172}$

we also know, density = mass/volume

mass = density × volume

mass = density × base area × length

$so,\frac{M_{Al}}{M_{cu}}=\frac{d_{Al}.v_{Al}.l}{d_{cu}.A_{cu}.l}\\\\=\frac{2.7\times263}{8.9\times172}=0.46$

thus, the Aluminium with for the same resistance is very light than copper and that is why Aluminium wire are preferred for overhead power cable.