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The Wheatstone bridge is a circuit for precise resistance measurement, consisting of four resistors in a diamond configuration with a galvanometer across one diagonal and a battery across the other. Balance condition: $P/Q = R/S$, where $P, Q$ and $R, S$ are opposite arms. At balance, no current flows through the galvanometer, and the galvanometer branch can be removed for simplified analysis.

The meter bridge (slide-wire bridge) is a practical implementation: a uniform wire of length 100 cm serves as two adjacent arms. A known resistance $R$ and unknown $X$ form the other two arms. At balance: $X = R \times l/(100-l)$ where $l$ is the balance point. Minimum error occurs when $l \approx 50$ cm (all arms roughly equal).

Important properties: (1) Balance condition is independent of the battery EMF, internal resistance, and galvanometer resistance. (2) Interchanging battery and galvanometer does not change the balance condition. (3) Sensitivity is maximum when all four arms are equal. (4) End corrections account for the non-zero resistance of connecting strips.

The Kelvin double bridge extends this principle to measure very low resistances by eliminating lead resistance errors.