Question

Steel and aluminium wires have equal resistances and masses. Which of the wires is longer and how many times? (Given, densities of steel and aluminium arc $7.8\times {10}^{3}kg{m}^{-3}$ and $2.7\times {10}^{3}kg{m}^3$ and their resistivities are ($0.15\mu \Omega .mand0.028\mu \Omega .m$ respectively)

• A. The aluminium wire is 3.9 times longer
• B. The aluminium wire is 1.3 times longer
• C. The aluminium wire is 2.6 times longer
• D. The steel wire is 3.9 times longer

Answer 1

The correct option is A The aluminium wire is 3.9 times longer

let the lenght $L_s$ and $L_a$ and cross section are be $A_s$ and $A_a$

mass is same

${\rho }_s{L}_s{A}_s={\rho }_a{L}_a{A}_a$

$7.8\times L_s\times A_s=2.7\times L_a\times A_a$....1

$R={\rho }_{resistivity}\frac{l}{A}$

Since Resistance is same

$0.15\frac{L_s}{A_s}=.028\frac{L_a}{A_a}$.....2

from equation 1 and 2

$\frac{L_a}{L_s}=3.9$