Draw a circuit diagram of a meter bridge used to determine the unknown resistance R of a given wire. Hence derive the expression for R in terms of the known resistance S.

Explanation

In a meter bridge, the unknown resistance X is connected in one gap and a resistance R in other gap. A galvanometer is connected between point B and D throuth a jockey (J). A battery is connected between A and C. A suitable resistance is introduced in the circuit from the resistance box and the jockey is slided on the wire till a point D is located such that the deflection in the galvanometer is zero.

Let, the distance of the point D from A be `l_(X)` and from C be ` 'l_(R)' .`
`therefore ` By balancing condition of bridge,
`(X)/(R)=("Resistance of length "l_(X))/("Resistance of length "l_(R))`
We know, `R=(rho l)/(A)`
Where, `rho` is specific rsistance of the wire.
`therefore (X)/(R)=(rho^(l)X)/(A)xx(A)/(rho^(l)R)=(l_(X))/(l_(R))`
`therefore (X)/(R)=(l_(X))/(100-l_(X)) `
`" "[because l_(X)+l_(R)=100 cm therefore l_(R)=100-l_(X)]`
`X=((l_(X))/(100-l_(X)))R`