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) → $r$
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 $R_{eq} = r$.