Describe on Wheatstone’s Bridge

An important application of Kirchoff’s law is the Wheatstone’s bridge (Figure).

Wheatstone’s network consists of resistances P, Q, R and S connected to form a closed path. A cell of emf E is connected between points A and C. The current I from the cell is divided into I₁, I₂, I₃ and I₄ across the four branches. The current through the galvanometer is Ig. The resistance of galvanometer is G.

Fig: Wheatstone’s bridge

Applying Kirchoff’s current law to junction B,

I₁ – I_g – I₃ = 0 … (1)

Applying Kirchoff’s current law to junction D

I₂ + I_g – I₄ = 0 … (2)

Applying Kirchoff’s voltage law to closed path ABDA

I₁ P + I_g G – I₂ R = 0 … (3)

Applying Kirchoff’s voltage law to closed path ABCDA

I₁ P + I₃ Q – I₄ S – I₂ R = 0 … (4)

When the galvanometer shows zero deflection, the points B and D are at same potential and I_g = 0. Substituting I_g = 0 in equation (1), (2) and (3)

I₁ = I₃ … (5)

I₂ = I₄ … (6)

I₁ P = I₂ R … (7)

Substituting the values of (5) and (6) in equation (4)

I₁ P + I₁ Q – I₂ S – I₂ R = 0

I₁ (P + Q) = I₂ (R+S) … (8)

Dividing (8) by (7)

I₁ (P + Q) / I₁ P = I₂ (R+S) / I₂ R

(P + Q) / P = I (R+S) / R

1 + Q/P = 1 + S/R

so, Q/P = S/R or, P/Q = R/S

This is the condition for bridge balance. If P, Q and R are known, the resistance S can be calculated.