# Two thin metallic spherical shells of radii

Question:

Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $\left(r_{1} 1.$\frac{4 \pi \mathrm{Kr}_{1} \mathrm{r}_{2}\left(\theta_{2}-\theta_{1}\right)}{\mathrm{r}_{2}-\mathrm{r}_{1}}$2.$\frac{\pi r_{1} r_{2}\left(\theta_{2}-\theta_{1}\right)}{r_{2}-r_{1}}$3.$\frac{K\left(\theta_{2}-\theta_{1}\right)}{r_{2}-r_{1}}$4.$\frac{K\left(\theta_{2}-\theta_{1}\right)\left(r_{2}-r_{1}\right)}{4 \pi r_{1} r_{2}}$Correct Option: 1 Solution: Thermal resistance of spherical sheet of thickness$\mathrm{dr}$and radius$r$is$\mathrm{dR}=\frac{\mathrm{dr}}{\mathrm{K}\left(4 \pi \mathrm{r}^{2}\right)}R=\int_{r_{1}}^{r_{2}} \frac{d r}{K\left(4 \pi r^{2}\right)}\mathrm{R}=\frac{1}{4 \pi \mathrm{K}}\left(\frac{1}{\mathrm{r}_{1}}-\frac{1}{\mathrm{r}_{2}}\right)=\frac{1}{4 \pi \mathrm{K}}\left(\frac{\mathrm{r}_{2}-\mathrm{r}_{1}}{\mathrm{r}_{1} \mathrm{r}_{2}}\right)$Thermal current (i)$=\frac{\theta_{2}-\theta_{1}}{R}\mathrm{i}=\frac{4 \pi \mathrm{Kr}_{1} \mathrm{r}_{2}}{\mathrm{r}_{2}-\mathrm{r}_{1}}\left(\theta_{2}-\theta_{1}\right)\$