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

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

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.