Physics - Current Electricity Question with Solution | TestHub

Consider small volume element between $\mathrm{r}$ and $\mathrm{r}+\mathrm{d}\mathrm{r}$
Resistance of this volume along rational directions,
$\mathrm{d}\mathrm{R}=\frac{\mathrm{\rho }dr}{4\mathrm{\pi }{r}^2}$
As all element resistance are in series,
$\mathrm{R}=\underset{r=\mathrm{a}}{\overset{r=\mathrm{b}}{\int }}\frac{\mathrm{\rho }dr}{4\mathrm{\pi }{r}^2}=\frac{\mathrm{\rho }}{4\mathrm{\pi }}{\left(-\frac{1}{r}\right)}_{r=\mathrm{a}}^{r=\mathrm{b}}=\frac{\mathrm{\rho }}{4\mathrm{\pi }}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{b}}\right)$