Question

Explain the use of Wheatstone's metre bridge to determine an unknown resistance.

Answer 1

Construction: Three thick copper strips are positioned along each of the three edges of a rectangular wooden board. One meter of uniform resistance wire is stretched over a meter scale between the two end copper strips and soldered to them. In the two spaces that exist between the end strips and the centre strip, an unknown resistance (X) and a variable resistance (R) are coupled. A pencil jockey is connected to the common point of X and R, connection B, via a centre-zero galvanometer G. As seen in the image, an emf E cell is linked across AC in series with a rheostat Rh and a plug key K.

Wheatstone’s metre bridge

Working: To allow a current to flow through the circuit, key K is closed while maintaining an appropriate resistance (R) in the resistance box. When the galvanometer registers zero deflection, the jockey is tapped along the wire to determine the equipotential point D. Following bridge balancing, point D is referred to as the null point, and the technique is known as the null deflection method. The measurements are LX and LR of the null point's distances from the wire's two ends. In line with Wheatstone's network theory,

`X/R = ("resistance of the wire of length"  L_X (R_(AD)))/("resistance of the wire of length"  L_R (R_(DB)))`

∴ `X/R = (R_(AD))/(R_(DB))`

For a wire of length l, cross-sectional area A and resistivity ρ, its resistance R = `ρl/A`

∴ `R_(AD) = ρ(L_X)/A` and `R_(DB) = ρ(L_R)/A`

∴ `X/R = (R_(AD))/(R_(DB))`

= ` (ρ(L_X)/A)/(ρ(L_R)/A)`

= `L_X/L_R`

∴ X = `L_X/L_R xx R`

As R, L_X and L_R are known, the unknown resistance X can be calculated.