If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.
Answer (integer)
44
Solution
Let $\ell_{0}$ be its initial length and $A_{0}$ be initial area.
<br/><br/>
Considering volume to be conserved
<br/><br/>
$$
\begin{aligned}
& \text { Vol. }=\ell_{0} A_{0}=\left(1.2 \ell_{0}\right) \mathrm{A} \\\\
& A_{\text {final }}=\frac{A_{0}}{1.2} \\\\
& R_{\text {in }}=\frac{\rho \ell_{0}}{A_{0}} \\\\
& R_{\text {final }}=\frac{\rho 1.2 \ell_{0}}{\frac{A_{0}}{1.2}}=\frac{\rho \ell_{0}}{A_{0}}(1.2)^{2}
\end{aligned}
$$
<br/><br/>
$=\mathrm{R}_{\text {in }}(1.44)$
<br/><br/>
Hence increase $=44 \%$
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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