In a metre bridge experiment the balance point is obtained if the gaps are closed by 2 and 3 . A shunt of X is added to 3 resistor to shift the balancing point by 22.5 cm. The value of X is

Step-by-step solution

Let the initial balancing length be l₁ . Using the principle of the metre bridge: 2 3 = l₁ 100 - l₁ 3l₁ = 200 - 2l₁ 5l₁ = 200 l₁ = 40 cm When a shunt of X is connected across the 3 resistor, the equivalent resistance in the right gap becomes R_p = 3X 3 + X . Since the resistance in the right gap decreases, the balancing point shifts to the right. The new balancing length is: l₂ = 40 + 22.5 = 62.5 cm Applying the metre bridge principle again: 2 R_p = 62.5 100 - 62.5 2 R_p = 62.5 37.5 = 5 3 R_p = 6 5 = 1.2 Equating t