Physics - Magnetism Question with Solution | TestHub

We know that $\mathrm{R}=\rho \frac{l}{\mathrm{A}}$ $\therefore \text{ For }l=\mathrm{L}\text{ and }\mathrm{A}=\mathrm{A};{\mathrm{R}}_1=\rho \frac{\mathrm{L}}{\mathrm{A}}$ For $l=\frac{\mathrm{L}}{2}$ and $\mathrm{A}=2\mathrm{A}$; $R_2=\rho \frac{\left(\frac{L}{2}\right)}{2A}=\frac{1}{4}\left(\rho \frac{L}{A}\right)=\frac{1}{4}{R}_1$ For $l=2\mathrm{L}$ and $\mathrm{A}=\frac{\mathrm{A}}{2}$; ${\mathrm{R}}_3=\rho \frac{2\mathrm{L}}{\left(\frac{\mathrm{A}}{2}\right)}=4\left(\rho \frac{\mathrm{L}}{\mathrm{A}}\right)=4{\mathrm{R}}_1$ Thus $R_3>R_1>R_2$ Therefore, the wire having length $2\mathrm{L}$ and area $\frac{\text{ A }}{2}$ has the maximum resistance.