#### Question

Explain with a neat circuit diagram how will you determine unknown resistance ‘X' by using meter bridge

#### Solution

It consists of a 1-metre long wire of uniform cross-section area made of magnetism stretched on a wooden board.

There are two L-shaped strips T_{1} and T_{2} which are also fitted from the ends of the wire on the top side. These strips are made up of copper. There is another straight strip T_{3} fitted in between T_{1} and T_{2}. This gives rise to the formation of two gaps, a left gap and a right gap.

A metre scale is fitted along the wire which measures the length of the wire.

AC: One-metre long uniform wire

X: Unknown resistance

R: Resistance from resistance box

G: Galvanometer

T_{1}, T_{2}, T_{3}: Metal Strips

D: Null point

J: Sliding key (jockey)

R_{h}: Rheostat

Determination of unknown resistance:

Unknown resistance X is connected to the left gap and a resistance box R in the right gap. A galvanometer is connected between point B and D through 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 tapped on the wire till a point D is located such that the galvanometer deflection is zero. The distance of the point D from A is measured on the scale say l_{X} The distance of the point D from C is measured on the scale. R l By adjusting the value of R, the neutral point is obtained in the middle of the wire. In the balanced condition of the bridge.

`X/R = ("Resistance of length "l_X)/("Resistance of length" l_r)`

Since `R = rho 1/A`

where `rho` is a specific resistance of the material of a wire

`:. X/R = ((rhol_X)/A)/((rhol_R)/A) = l_X/l_R`

∵ `l_X +l_R = 100 `cm

`:. l_R = 100 - l_X`

`:. X= R((1_X)/(100-l_X))`

Hence the value of unknown resistance ‘X’ can be determined.