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  4. Two non-ideal batteries are connected in parallel. Consider the following statements. (i) The equivalent emf is smaller than either of the two emfs. (ii) The equivalent internal resistance is smaller than either of the two internal resistances.

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Q. Two non-ideal batteries are connected in parallel. Consider the following statements. (i) The equivalent emf is smaller than either of the two emfs. (ii) The equivalent internal resistance is smaller than either of the two internal resistances.

Rajasthan PMTRajasthan PMT 2008Current Electricity

Solution:

Let emf of both cells are $ {{E}_{1}} $ and $ {{E}_{2}} $ and internal resistances are $ {{r}_{1}} $ and $ {{r}_{2}} $ . In parallel order, we have $ E={{E}_{1}}={{E}_{2}} $ Effective internal resistance of both cells $ \frac{1}{R}=\frac{1}{r}+\frac{1}{r} $ So, emf is equal to the emf of any of the cell and internal resistance is less than the resistance of any of cell. Hence, (ii) is right and (i) is wrong.