Question

Using Kirchhoff’s laws, obtain the equation of the balanced state in Wheatstone Bridge.

Derive the condition for which a Wheatstone Bridge is balanced.

Answer 1

The Wheatstone Bridge is shown in the figure:

Applying Kirchhoff’s II law to mesh ABDA:

I₁P + I_gG – I₂R = 0    ...(1)

For the mesh BCDB:

(I₁ − I_g)Q + [−(I₂ + I_g)S] + [−I_gG] = 0    ...(2)

When the bridge is balanced, no current flows through the galvanometer.

i.e., I_g = 0    ...(3)

∴ From equations (1), (2), and (3):

I₁P = I₂R    ...(4)

I₁Q = I₂S    ...(5)

From equations (4) and (5):

`P/Q = R/S`