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 :

Solution

Physics sir · 3 steps

Find the unknown first, shunt it, then rebalance. The question wants the change, not the new length.

1. Find the unknown. At balance, R_(left)/R_(right) = l/(100 - l). With l = 40 cm, 2/X = 40/60, so X = 3 Ω.
2. Shunt it. A 2 Ω shunt sits in parallel with 3 Ω, so the right gap now holds (2 × 3)/(2 + 3) = 1.2 Ω. A smaller right-gap resistance pushes the balance point to the right.

   2/1.2 = l'/(100 - l') ⇒ 5(100 - l') = 3l' ⇒ l' = 62.5 cm

3. So. The balance length moves from 40 cm to 62.5 cm, a change of 62.5 - 40 = 22.5 cm, which is option (b).

The idea to keep. In a metre bridge, balance length divides the wire in the same ratio as the two resistances. A shunt lowers that gap's resistance, so recompute the ratio and read what the question asks: new length or change.

Answer from the NTA final answer key. Solution by PrepWiser.