In a metre bridge experiment the balance point is obtained if the gaps are closed by 2   Ω and 3   Ω . A shunt of X   Ω is added to 3   Ω resistor to shift the balancing point by 22 . 5   cm . The value of X is ______.

Step-by-step solution

Case 1 : No shunt is added The initial balancing length l of the bridge is, 2 3 = l 100 - l ⇒ 200 - 2 l = 3 l ⇒ l = 40   cm Case 2 : When shunt is added The new balancing length is, l 1 = 22 . 5 + 40 = 62 . 5   cm So, 62 . 5 37 . 5 = 2 3 X 3 + X ⇒ X = 2 .