Question

In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf’s of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be _____ cm.

Answer 1

Correct Answer: 25

To solve the problem, we must understand the relationship between the electromotive force (emf) of a cell and the balancing point in a potentiometer. The potential difference across a wire in a potentiometer is directly proportional to the length of the wire, provided the wire is uniform.

Given the initial condition where the original cell balances at 75 cm of the wire and the ratio of the emf's of the two cells is 3:2, we need to find the difference in the balancing lengths when the first cell is replaced by another cell:

1. Let E₁ be the emf of the first cell and E₂ be the emf of the second cell. We know that E₁/E₂ = 3/2.
2. If L₁ is the balancing length for the first cell and L₂ for the second cell, then by the property of the potentiometer: E₁/E₂ = L₁/L₂.
3. Substituting the given ratio: 3/2 = 75/L₂.
4. Solving for L₂, we have L₂ = (2/3) × 75 = 50 cm.
5. Thus, the difference in balancing lengths, ΔL = L₁ - L₂ = 75 cm - 50 cm = 25 cm.

Therefore, the difference in the balancing length of the potentiometer wire in the two cases is 25 cm, which falls within the given range (25,25).