Question 123: Current Electricity

Question

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

Accepted Answer

Let $\ell_{0}$ be its initial length and $A_{0}$ be initial area.
Considering volume to be conserved
$$
\begin{aligned}
& 	ext { Vol. }=\ell_{0} A_{0}=\left(1.2 \ell_{0}ight) \mathrm{A} \\
& A_{	ext {final }}=\frac{A_{0}}{1.2} \\
& R_{	ext {in }}=\frac{ho \ell_{0}}{A_{0}} \\
& R_{	ext {final }}=\frac{ho 1.2 \ell_{0}}{\frac{A_{0}}{1.2}}=\frac{ho \ell_{0}}{A_{0}}(1.2)^{2}
\end{aligned}
$$
$=\mathrm{R}_{	ext {in }}(1.44)$
Hence increase $=44 \%$

Current Electricity

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

Integer / Numeric Answer Type