An important application of Kirchhoff’s rules is the Wheatstone’s bridge.

**Wheatstone’s
bridge**

An important application
of Kirchhoff’s rules is the Wheatstone’s bridge. It is used to compare
resistances and also helps in determining the unknown resistance in electrical
network. The bridge consists of four resistances P, Q, R and S connected as
shown in Figure 2.25. A galvanometer G is connected between the points B and D.
The battery is connected between the points A and C. The current through the
galvanometer is I_{G} and its resistance is G.

Applying Kirchhoff’s
current rule to junction B

Applying
Kirchhoff’s current rule
to junction D,

Applying Kirchhoff’s
voltage rule to loop ABDA,

Applying Kirchhoff’s
voltage rule to loop ABCDA,

When the points B and D
are at the same potential, the bridge is said to be balanced. As there is no
potential difference between B and D, no current flows through galvanometer (I_{G}
= 0). Substituting I_{G} = 0 in equation (2.45), (2.46) and (2.47), we
get

Substituting
the equation (2.49) and (2.50) in equation (2.48)

Dividing equation (2.52)
by equation (2.51), we get

This is the bridge
balance condition. Only under this condition, galvanometer shows null
deflection. Suppose we know the values of two adjacent resistances, the other
two resistances can be compared. If three of the resistances are known, the
value of unknown resistance (fourth one) can be determined.

**EXAMPLE 2.23**

In a Wheatstone’s bridge P = 100 Ω, Q = 1000 Ω and R = 40 Ω. If the galvanometer shows zero deflection, determine the value of S.

*Solution*

**EXAMPLE 2.24**

What is
the value of *x* when the Wheatstone’s
network is balanced?

P = 500
Ω, Q = 800 Ω, R = *x* + 400, S = 1000 Ω

*Solution*

P/Q = R/S

x + 400 =
0.625 × 1000

x + 400 =
625

x = 625 –
400

x = 225 Ω

Tags : Explanation, Formulas, Solved Example Problems | Kirchhoff’s rule , 12th Physics : Current Electricity

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12th Physics : Current Electricity : Wheatstone’s bridge | Explanation, Formulas, Solved Example Problems | Kirchhoff’s rule

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