Question

Masses of three wires are in the ratio 1 : 3 : 5 and their lengths are in the ratio 5 : 3 : 1. The ratio of their electrical resistance is

• A. 1 : 3 : 5
• B. 5 : 3 : 1
• C. 1 : 15 : 125
• D. 125 : 15 : 1

Answer 1

The correct option is D 125 : 15 : 1

$R=\rho \frac{l}{A}=\rho \frac{l^2}{V}=\rho \frac{l^2}{m}\sigma (\because \sigma =\frac{m}{V})$
$R_1:R_2:R_3=\frac{l_1^2}{m_1}:\frac{l_2^2}{m_2}:\frac{l_3^2}{m_3}=25:\frac{9}{3}:\frac{1}{5}=125:15:1$