Question

Four resistances 10 Ω, 10 Ω, 10 Ω and 15 Ω form a Wheatstone’s network. What shunt is required across 15 Ω resistor to balance the bridge

Answer 1

Given:

Four resistances 10 Ω, 10 Ω, 10 Ω and 15 Ω form a Wheatstone’s network.

To Find:

What shunt is required across 15 Ω resistor to balance the bridge

Solution:

The Wheatstone bridge works on the principle of null deflection, i.e. the ratio of their resistances are equal, and no current flows through the galvanometer.

The bridge has four arms which consist two unknown resistance, one variable resistance and the one unknown resistance along with the emf source and galvanometer.

he bridge is in balance condition when no current flows through the coil or the potential difference across the galvanometer is zero. This condition occurs when the potential difference across the a to b and a to d are equal, and the potential differences across the b to c and c to d remain same.

The current enters into the galvanometer divides into I1 and I2, and their magnitude remains same. The following condition exists when the current through the galvanometer is zero.

The Wheatstone bridge is more sensitive when all their resistances are equal, or their ratio is unity. Their sensitivity decreases when their ratio is less than unity. The reduction in sensitivity reduces the accuracy of the bridge.

P = 10      Q = 10      R = 10       S = 15 + R

$\frac{P}{Q} = \frac{R}{S} \\\\\frac{10}{10} = \frac{10}{R+ 15} \\R = -5$

Value of resistance cannot be negative.

Hence we have to attach a stunt parallel to S.

$\frac{10}{10}= \frac{(15 + R)10}{15R} \\15 R = (15+R)10\\R = 30 ohms$

The resistor of resistance 30 ohms must be connected in parallel to resistor S to balance the circuit.