Wheatstone Bridge Balance Condition

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.