Principle of wheatstone-Bridge :

# Principle of wheatstone-Bridge :

The scientist wheatstone drives a method to determine the resistance of a conductor which is called wheatstone method. In this method by the help of three known resistance we can determine the fourth unknown resistance.

          According to the principal of this method - “Four resistance are joined in the form of four arms of a quadrilateral, a cell and the key is joined on its one diagonal and a galvanometer and key is joined on another diagonal. The known resistance is so adjust for which the galvanometer showing null deflection. This is the balancing state of the bridge, in this state the ratio of resistance of two adjacent sides of a quadrilateral is equal to the ratio of the resistance of remaining two adjacent side”.

Circuit - Diagram

In above figure shows the wheatstone bridge method in which four registance P,Q,R and S are joined in the form of four arms of quadrilateral ABCD.

In the balancing state of bridge --

P/Q = R/S

Derivation of principle : 

In closed circuit ABDA

By Kirchoff's voltage law

∑ I.R + ∑ E = 0

I1P + IgG - I2R = 0 

I1P + IgG = I2R  ---------(1)

 In closed circuit  BCDB

By Kirchoff's voltage law

∑ I.R + ∑ E = 0

( I1 - Ig )Q - ( I2 + Ig )S - Ig.G = 0

( I1 - Ig )Q - ( I2 + Ig )S = Ig.G ---------(2)

In the balancing state of the bridge, Ig = 0

Putting Ig = 0 in eqn(1)

I1P + 0×G = I2.R 

I1.P = I2.R ---------(3)

Again putting Ig = 0 in eqn(2)

( I1 - 0 )Q - ( I2 + 0 )S = 0×G

I1.Q = I2.S ---------(4)

Dividing eqn(3) by eqn(4)

I1.P / I1.Q  =  I2.R / I2.S

[ P/Q  =  R/S ]

This is the principle of wheatstone bridge