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

$r$

The correct answer is Option (3) → $r$

Given:

All four arms of Wheatstone bridge have equal resistance $r$.

Resistance of galvanometer arm $= r$.

Analysis:

Since all arms have equal resistance, the bridge is balanced. Hence, no current flows through the galvanometer branch.

The galvanometer branch (resistance $r$) can therefore be ignored in equivalent resistance calculation.

The circuit then reduces to two series branches of resistance $2r$ each connected in parallel.

Equivalent resistance:

$ R_{eq} = \frac{(2r)(2r)}{2r + 2r} = \frac{4r^2}{4r} = r $

Therefore, the equivalent resistance of the combination is $R_{eq} = r$.