JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Current Electricity

The length of a metallic wire is increased by

20%

and its area of cross section is reduced by

4%

. The percentage change in resistance of the metallic wire is

Answer: 25

Solution

The resistance of a wire is

R = ρ \frac{ℓ}{A}

. Increasing the length by

20%

gives

ℓ^{'} = 1.2 ℓ

, and reducing the cross-section by

4%

gives

A^{'} = 0.96 A

. The new resistance is

R^{'} = ρ \frac{1.2 ℓ}{0.96 A} = \frac{1.2}{0.96} R = 1.25 R

, so the percentage change is

\frac{R ^{'} - R}{R} \times 100 = 25%

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Integer answer