• Tags: metre-bridge, Wheatstone, null-point
• Difficulty: Moderate

The metre bridge is a practical Wheatstone bridge. A uniform wire (100 cm, resistance ~1-2 ohm) forms two arms; a known resistance R and unknown X form the other two arms. At balance: R/X = $\frac{l}{100-l}$, so X = R*$\frac{100-l}{l}$. The galvanometer shows zero deflection at the null point l. For best sensitivity, the null point should be near 50 cm (when R ≈ X). Choose R to achieve this. End corrections account for the resistance of thick copper strips at the ends of the wire. If end corrections are alpha and beta at the two ends: R/X = $\frac{l+alpha}{(100-l+beta)}$. To minimize end corrections, use interchanging: measure with R on left, then on right, and average. Percentage error: $Delta_X$/X = $\frac{Delta_R}{R}$ + ($Delta_l$/l + $\frac{Delta_l}{100-l}$) — error is minimum when l = 50 cm (confirming the sensitivity argument).