$\therefore $  $\frac{1}{\mathrm{R}_{\mathrm{PQ}}}=\frac{1}{4 \mathrm{R}}+\frac{1}{4 \mathrm{R}}+\frac{1}{2 \mathrm{r}}$ $=\frac{1}{2 \mathrm{R}}+\frac{1}{2 \mathrm{r}}$ $=\frac{\mathrm{R}+\mathrm{r}}{2 \mathrm{Rr}}$

$\Rightarrow \mathrm{R}_{\mathrm{PQ}}=\frac{2 \mathrm{Rr}}{\mathrm{R}+\mathrm{r}}$

If a potential difference is applied across $P$ and $Q,$ there will be no currents in arms $AO$ and $OB$. So these resistance will be ineffective.