A wire of $1 \Omega$ has a length of $1 \mathrm{~m}$. It is stetched till its length increases by $25 \%$. The percentage change in resistance to the neartest integer is :-
Correct Option: 1
As volume of wire remains constant so
$\mathrm{A}_{0} \ell_{0}=\mathrm{A}_{1} \ell_{1} \Rightarrow \mathrm{A}_{1}=\frac{\ell_{0} \mathrm{~A}_{0}}{\ell_{1}}$
Now
$\operatorname{Resistance}(\mathrm{R})=\frac{\rho \ell}{\mathrm{A}}$
$\frac{\mathrm{R}_{0}}{\mathrm{R}_{1}}=\frac{\ell_{0} / \mathrm{A}_{0}}{\rho \ell_{1} / \mathrm{A}_{1}}$
$\frac{1}{\mathrm{R}_{1}}=\frac{\ell_{0}}{\mathrm{~A}_{0}}\left(\frac{\ell_{0} \mathrm{~A}_{0}}{\ell_{1} \times \ell_{1}}\right) \quad \mathrm{R}_{1}=\frac{\ell_{1}^{2}}{\ell_{0}^{2}}=1.5625 \Omega$
So $\%$ change in resistance
$=\frac{\mathrm{R}_{1}-\mathrm{R}_{0}}{\mathrm{R}_{0}} \times 100 \%$
$=\frac{1.5625-1}{1} \times 100 \%$
$=56.25 \%$