Question 416: Current Electricity

Question

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 __________.

Accepted Answer

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 $R'$ is then:
$ R' = \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%.

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 __________.

Choose the correct answer: