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A potentiometer wire AB of length L has total resistance 12r and is connected to a driver cell D of emf e and internal resistance r. A second cell C of emf e/2 and internal resistance 3r is connected for balancing. At what length AJ does the galvanometer read zero?

1. 5/12 L
2. 11/24 L
3. 11/12 L
4. 13/24 L

Correct answer: 13/24 L

Solution

The driver current is e/(12r+r)=e/13r, giving a drop of 12e/13 across the full wire. Setting (12e/13)(AJ/L)=e/2 yields AJ=13L/24.

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