Explain with a neat circuit diagram how will you determine unknown resistance ‘X' by using meter bridge
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 T1 and T2 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 T3 fitted in between T1 and T2. 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
T1, T2, T3: Metal Strips
D: Null point
J: Sliding key (jockey)
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 lX 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.