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Two identical batteries each of e.m.f 2V and internal resistance 1Ω are available to produce heat in an external resistance by passing a current through it. The maximum power that can be developed across R using these batteries is

1. 3.2 W
2. 2.0 W
3. 1.28 W
4. 8/9 W

Correct answer: 3.2 W

Solution

To maximize power across the external resistance R, the batteries should be connected in parallel. The equivalent e.m.f is 2V, and the equivalent internal resistance is 0.5Ω. Using the maximum power transfer theorem, R = r = 0.5Ω. The maximum power is P = (E²) / (4r) = (2²) / (4 × 0.5) = 3.2 W.

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