JEE Main 2023 — Current Electricity Question with Solution

The resistance ($R$) of a wire can be calculated by the formula:

$R=\rho \frac{L}{A},$

where

• $\rho$ is the resistivity (a property of the material),
• $L$ is the length of the wire, and
• $A$ is the cross-sectional area of the wire.

If the length ($L$) is increased by 20%, $L$ becomes $1.2L$.

If the cross-sectional area ($A$) is reduced by 4%, $A$ becomes $0.96A$.

The new resistance $R^{\prime }$ is then:

$R^{\prime }=\rho \frac{1.2L}{0.96A}=1.25R,$

so the resistance has increased by 25%.

Therefore, the percentage change in the resistance of the metallic wire is 25%.