Wheatstone Bridge

Question

The resistance of each arm of the Wheatstone bridge is 10 Ohm. A resistance of 10 Ohm is connected in series with galvanometer. The equivalent resistance across the battery is:

RankGuru · Accepted Answer

1. **Identify the bridge type**: The circuit is a balanced Wheatstone bridge because the product of opposite resistances is equal ($10 	imes 10 = 10 	imes 10$).
2. **Bridge property**: In a balanced Wheatstone bridge, the potential difference across the galvanometer (or any bridge resistor) is zero.
3. **Simplification**: Since no current flows through the galvanometer branch, it can be neglected.
4. **Equivalent Resistance Calculation**: The circuit simplifies to two parallel branches, each having two $10	ext{ \Omega}$ resistors in series.
   - Each branch resistance: $10 + 10 = 20	ext{ \Omega}$.
   - Equivalent resistance: $\frac{1}{R_{eq}} = \frac{1}{20} + \frac{1}{20} = \frac{2}{20} \implies R_{eq} = 10	ext{ \Omega}$.

Wheatstone Bridge

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