Physics - Current Electricity Question with Solution | TestHub

Resistance between $\mathrm{P}$ and $\mathrm{Q}$ $$r_{\mathrm{PQ}}=r_{11}\left(\frac{r}{3}+\frac{r}{2}\right)=\frac{r\times \frac{5}{6}r}{r+\frac{5}{6}r}=\frac{5}{11}r$$ Resistance between Q and R $${\mathrm{r}}_{\mathrm{QR}}=\frac{\mathrm{r}}{2}11\left(\mathrm{r}+\frac{\mathrm{r}}{3}\right)=\frac{\frac{\mathrm{r}}{2}\times \frac{4}{3}\mathrm{r}}{\frac{\mathrm{r}}{2}+\frac{4}{3}\mathrm{r}}=\frac{4}{11}\mathrm{r}$$ Resistance between $\mathrm{P}$ and $\mathrm{R}$ $${\mathrm{r}}_{\mathrm{PR}}=\frac{\mathrm{r}}{3}\mathrm{l}\left(\frac{\mathrm{r}}{2}+\mathrm{r}\right)=\frac{\frac{\mathrm{r}}{3}\times \frac{3}{2}\mathrm{r}}{\frac{\mathrm{r}}{3}+\frac{3}{2}\mathrm{r}}=\frac{3}{11}\mathrm{r}$$ Hence, it is clear that ${\mathrm{r}}_{\mathrm{PQ}}$ is maximum