Physics - Current Electricity Question with Solution | TestHub

We know $\mathrm{R}=\frac{\rho l}{\mathrm{A}},\mathrm{R}\propto \frac{l}{{\mathrm{r}}^2}$ As we starch the wire, its length will increase but its radius will decrease keeping the volume constant $\begin{array}{rl}& {\mathrm{V}}_{\mathrm{i}}={\mathrm{V}}_{\mathrm{f}}\\ & \pi {\mathrm{r}}^{2}l=\pi \frac{{\mathrm{r}}^2}{4}{l}_{\mathrm{f}}\\ & l_{\mathrm{f}}=4l\\ & \frac{{\mathrm{R}}_{\text{new }}}{{\mathrm{R}}_{\text{old }}}=\left(\frac{4l}{\frac{{\mathrm{r}}^2}{4}}\right)\frac{{\mathrm{r}}^2}{l}=16\\ & {\mathrm{R}}_{\text{new }}=16\mathrm{R}\\ \therefore & \mathrm{x}=16\end{array}$