With the help of neat labelled circuit diagram explain the use of metre bridge to determine unknown resistance.

Answer:

[Figure: a uniform wire AB, 1 m long, stretched on a metre scale between thick copper strips. The unknown resistance X is connected in the left gap (between A and C) and a resistance box R in the right gap (between C and B). The central point C of the strip is joined through a galvanometer G to a jockey J that slides along the wire. A cell, plug key K and rheostat are connected between A and B.]

Working: The metre bridge works on the principle of the Wheatstone bridge. A suitable resistance R is taken from the box and the key is closed. The jockey is slid along the wire to find the point D where the galvanometer shows no deflection (null point). Let AD = \(l_X\) and DB = \(l_R = 100 - l_X\) cm.

At balance, the four resistances X, R, \(R_{AD}\) and \(R_{DB}\) form a balanced Wheatstone bridge:

where \(\lambda\) is the resistance per unit length of the uniform wire. Therefore

The experiment is repeated for different values of R and with X and R interchanged, and the mean value of X is taken. The null point should be near the middle of the wire for best accuracy.