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A 6 V battery with negligible internal resistance drives a uniform wire of length 1 m (a potentiometer). The positive terminal of a second battery (emf 4 V, internal resistance 1 ohm) is connected to end A of the wire, and a galvanometer in that branch shows zero deflection when the jockey contacts the wire at point C. Find the length AC.

1. 2/3 m
2. 1/3 m
3. 3/5 m
4. 1/2 m

Correct answer: 2/3 m

Solution

The potentiometer gradient is 6 V/m; balancing 4 V gives AC = 4/6 = 2/3 m.

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