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

Answer: (D)

125 : 15 : 1

Answer 2

$R = \rho\frac{l}{A} = \rho\frac{l^{2}}{V} = \rho\frac{l^{2}}{m}\sigma$ $\left( \because\sigma = \frac{m}{V} \right)$

$R_{1}:R_{2}:R_{3} = \frac{l_{1}^{2}}{m_{1}}:\frac{l_{2}^{2}}{m_{2}}:\frac{l_{3}^{2}}{m_{3}} = 25:\frac{9}{3}:\frac{1}{5} = 125:15:1$