Wheat stone Bridge: it is an arrangement of four resistances used to determine one of these resistances quickly and accurately in terms of remaining three resistances.

A wheat stone bridge consists of four resistance P,Q,R and S, connected to form the arms of a quadrilateral ABCD. A battery of emf ɛ is connected between points A and C and a sensitive galvanometer between B and D as shown in fig.

The resistance are so adjusted that no current flows through the galvanometer.

The bridge is then said to balanced condition P/Q = R/S

This is the wheat stone bridge principle.

Derivation: applying Kirchhoff’s law to the loop ABDA, we get

I₁ P + I_g G – I₂ R = 0

Where G is the resistance of the galvanometer

Similarly, applying KVL to loop BCDB, we get

(I₁ - I_g)Q – (I₂ + I_g)S – G I_g = 0

In the balanced condition of the bridge, I_g = 0, then above equations becomes

I₁P – I₂ R = 0

I₁Q – I₂ S = 0

Divide the above equations, we get

P/Q = R/S

This proves the condition for the balanced wheat stone bridge.