In a metre-bridge when a resistance in the left gap is 2 Ω and unknown resistance in the right gap, the balance length is found to be 40 cm . On shunting the unknown resistance with 2 Ω , the balance length changes by:

Step-by-step solution

In first circuit: For balanced condition, we get 2 40 = X 60 ⇒ X = 3 Ω In second case: Net resistance of the right side due to shunting becomes, X ' = 2 × 3 2 + 3 = 1 . 2 Ω Again for balanced condition, 2 ℓ = 1 . 2 100 - ℓ ⇒ 200 - 2 ℓ = 1 . 2 ℓ ⇒ ℓ = 200 3 . 2 = 62 . 5 cm Clearly, balance length changes by 22 . 5 cm .