A Wheatstone bridge arrangement is shown as below:
Using Kirchoff's seconds law to the loop ABDA, we get
I1P - IgG - I2R = 0: G is the galvanometer resistance.
Applying Kirchoff's law to the loop ABDA, we get
(I1 - Ig)Q - (I2 - Ig)S - GIg = 0
When the bridge is balanced Ig = 0
Then, the equations can be written as,
I1 P - I2R = 0 or I1P = I2R .........(1)
I1Q - I2S = 0 or I1Q = I2S ..........(2)
On dividing equation (1) by (2), we get
P/Q = R/S, which is the balanced condition of a Wheatstone bridge.