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A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery used across the potentiometer wire has an emf of 2.0 V and a negligible internal resistance. The potentiometer wire itself is 4 m long. When the resistance R, connected across the given cell, has values of (i) infinity (ii) 9.5Ω, the balancing lengths, on the potentiometer wire are found to be 3 m and 2.85 m, respectively. The value of internal resistance of the cell is:

1. 0.25Ω
2. 0.95Ω
3. 0.5Ω
4. 0.75Ω

Correct answer: 0.75Ω

Solution

The internal resistance of the cell can be calculated using the formula: r = R * (l1 - l2) / l2, where l1 = 3 m, l2 = 2.85 m, and R = 9.5Ω. Substituting the values, r = 9.5 * (3 - 2.85) / 2.85 = 0.75Ω.

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