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A potentiometer wire has length L. A cell of emf E gives a balance point at a distance L/3 from the positive end. If the wire's length is increased by L/2 (new length 3L/2) while the primary-circuit battery is ideal, at what distance from the positive end will the same cell now balance?

1. L/2
2. 2L/3
3. L/6
4. 4L/3

Correct answer: L/2

Solution

The balance condition fixes the potential at the balance point; lengthening the wire reduces the gradient proportionally, so the balancing length scales up by the ratio (3L/2)/L = 3/2, giving (L/3)*(3/2) = L/2.

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