In a Wheatstone Bridge, all the four arms have equal resistance \( r \). If the resistance of the galvanometer arm is also equal to \( r \), the equivalent resistance of the combination will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( r \)
A Wheatstone bridge is balanced when the ratio of the resistances on one side equals the ratio on the other side. With all four arms equal,
\( \displaystyle \frac{P}{Q} = \frac{R}{S} = \frac{r}{r} = 1 \)
so the two ends of the galvanometer arm are at the same potential and no current flows through it. The galvanometer arm can be removed, whatever its resistance.
What remains is two branches in parallel, each with two resistances \( r \) in series.
\( R_{\mathrm{branch}} = r + r = 2r \)
\( \displaystyle R_{\mathrm{eq}} = \frac{2r \times 2r}{2r + 2r} = r \)