Wheatstone Bridge Balance Condition

Question

In a balanced Wheatstone bridge the galvanometer shows no deflection, so which relation among the four arm resistances P, Q, R and S must hold?

RankGuru · Accepted Answer

A Wheatstone bridge is balanced when no current flows through the galvanometer, meaning the bridge points across it are at equal potential, a condition derived in NCERT Class 12, Chapter 3 (Current Electricity). Under this balance the ratio of resistances in one pair of adjacent arms equals the ratio in the other pair, giving $\frac{P}{Q} = \frac{R}{S}$. This follows because with zero galvanometer current the same current flows through P and Q, and another current flows through R and S, and equal potential drops force the ratio equality. The option $P + Q = R + S$ is wrong because bridge balance depends on the ratios of resistances, not their sums, so equal sums do not guarantee equal potentials. The option $PQ = RS$ mistakenly equates products of the arms rather than ratios, which does not follow from the equal-potential condition. The option $P/R = S/Q$ pairs the arms incorrectly and does not correspond to the actual diamond topology of the bridge. A consistency check confirms the result: rearranging $\frac{P}{Q} = \frac{R}{S}$ gives the equivalent cross-multiplied form $PS = QR$, which is precisely the standard balance condition used in the laboratory to measure an unknown resistance from three accurately known ones.

Wheatstone Bridge Balance Condition

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