Question:
A wire of $1 \Omega$ has a length of $1 \mathrm{~m}$. It is stretched till its length increases by $25 \%$. The percentage change in a resistance to the nearest integer is:
Correct Option: , 4
Solution:
(4)
For stretched or compressed wire
$\mathrm{R} \propto \mathrm{I}^{2}$
$\frac{R_{1}}{R_{2}}=\frac{l_{1}^{2}}{l_{2}^{2}}$
$\Rightarrow \frac{\mathrm{R}}{\mathrm{R}_{2}}=\frac{\mathrm{R}^{2}}{(1.251)^{2}}$
$\Rightarrow \mathrm{R}_{2}=1.5625 \mathrm{R}$
$\%$ increase $\rightarrow 56.235 \%$