Physics - Current Electricity Question with Solution | TestHub

For no current through the galvanometer, the wheatstone bridge should be balanced. For this, we must have $$\frac{\mathrm{P}}{\mathrm{Q}}=\frac{\mathrm{S}}{\mathrm{R}}$$ This condition is satisfied with only option (a).
When a $5\Omega$ resistor is connected in series with $Q$, the equivalent resistance in the P-arm becomes $10\Omega$. $$\therefore \frac{\mathrm{P}}{\mathrm{Q}}=\frac{10}{10}=1$$ and $\frac{\mathrm{S}}{\mathrm{R}}=\frac{4}{4}=1$ $\Rightarrow \frac{\mathrm{P}}{\mathrm{Q}}=\frac{\mathrm{S}}{\mathrm{R}}$