Question

Question 3.16: 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. (ρAl = 2.63 × 10 −8 Ω m, ρCu = 1.72 × 10 −8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)

Class 12 - Physics - Current Electricity Current Electricity Page-129

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

Here it is clear that $M_{Al} < M_{cu}$ ,
thus, the aluminum with for the same resistance is very light than copper and that is why aluminum wire are preferred for overhead power cable.