Metre Bridge

The metre bridge is simply a practical, laboratory-scale realisation of the Wheatstone's bridge, built around a single one-metre length of uniform manganin wire, AB, stretched along a metre scale on a wooden board between two copper strips, C and D (Figure 2.26). A third copper strip, E, mounted between C and D, splits the bridge wire's two gaps: an unknown resistance P is connected in gap $G_1$, and a known, standard resistance Q is connected in gap $G_2$. A jockey (a sliding contact) connected to strip E through a galvanometer G and a high resistance HR can be moved along the wire, its exact position read off directly against the metre scale; a Lechlanche cell and a key K complete the primary circuit across the two ends of the bridge wire.

The jockey's position is adjusted until the galvanometer shows exactly zero deflection, at position J on the wire. At this balance point, the portions of bridge wire AJ (length $l_1$) and JB (length $l_2$) act as the bridge's R and S arms (since resistance is proportional to length for a uniform wire of resistance-per-length r), so the balance condition $P/Q=R/S$ from equation (2.53) becomes

$\dfrac{P}{Q} = \dfrac{r\cdot l_1}{r\cdot l_2} = \dfrac{l_1}{l_2} \qquad (2.54,\ 2.55,\ 2.56)$ …