Resistance of a conducting wire is 15 ohm. If another wire of the same material and length but having one-third radius is taken, then the resistance of the second wire will be .

Question

Question

This question was previously asked in

RRB Group D 9 Sept 2022 Shift 3 Official Paper

Answer 1

Concept

Resistance of a conducting wire is given by: \(R = \frac{\rho l}{A}\)

where, R = resistance

\(\rho = resistivity \)

l = length

A = area

Calculation

Given, \(l_2 = l_1 \\d_2 = 3d_1\)

\(\rho = constant. \\ \frac{R_1}{R_2} = \frac {l_1}{A_1} \times \frac{A_2}{L_2} \\ as, A \propto d^2 \)

\( \frac{15}{R_2} = \frac{l_1}{d_1^2} \times \frac {3d_1^2}{l_1}\)

\(R_2 = 15 \times 9 \\ R_2 = 135 ohm\)

The correct answer is '135 ohm'.