When the bridge is balanced, what is the current flowing through the galvanometer?

Question

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Option A: 0

Explanation & Concepts:
In a Wheatstone bridge, the bridge is said to be balanced when the potential difference between the galvanometer terminals is zero. Since there is no potential difference, no current flows through the galvanometer, resulting in a null deflection.

Working Principle: The bridge operates on the null-detector principle. When the ratio of resistances in adjacent arms is equal ($R_1/R_2 = R_3/R_4$), the bridge nodes connected to the galvanometer are at the same electric potential. According to Ohm's law, $I = \frac{\Delta V}{R_g}$; when $\Delta V = 0$, the current $I_g$ through the galvanometer must be zero.

Key Formulas: $\frac{R_1}{R_2} = \frac{R_3}{R_4}$ — Balance condition for Wheatstone Bridge; $I_g = \frac{V_B - V_D}{R_g} = 0$ — Null deflection condition

Key Points: Balanced state indicates zero potential difference across the galvanometer nodes.; The sensitivity of the bridge is maximum when all four arms have equal resistance.; The galvanometer acts as a null detector in precision measurements.

Advantages: High accuracy for measuring unknown resistances.; Independent of supply voltage fluctuations when in null state.

Disadvantages: Not suitable for measuring extremely low or very high resistances directly.; Requires manual or automated balancing adjustments.

Applications: Measurement of unknown resistance.; Strain gauge measurement circuits.; Temperature sensing (RTD circuits).

Additional Info: The bridge is generally used for resistances in the range of $1 \Omega$ to $1 M\Omega$.. Option B is incorrect because, at balance, the ratio is fixed and $I_g$ is independent of the absolute values as long as the ratio holds.. Option C and D are irrelevant as the galvanometer current is dictated by the potential node balance.

Answer: A is correct — When a Wheatstone bridge is balanced, the potentials at the galvanometer terminals are identical, resulting in zero current flow.

Exam Tip: Always remember that in any bridge circuit (Wheatstone, Maxwell, Hay, etc.), the 'balance' condition is defined by the absence of current through the detector branch.

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Option B: Depends on the ratio arms $R_1$ and $R_2$

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Option C: Varies by a factor of 2

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Option D: Depends on the type of null detector used

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