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To obtain the greatest current through an external resistance of 3 Ω, a battery is formed by connecting n parallel branches, each branch containing m cells in series. If the battery uses 24 cells in all and each cell has an internal resistance of 0.5 Ω, which arrangement should be chosen?

1. m = 12, n = 2
2. m = 8, n = 3
3. m = 2, n = 12
4. m = 6, n = 4

Correct answer: m = 12, n = 2

Solution

Max current needs external R = internal resistance m*r/n: 3 = 0.5m/n -> m = 6n. With m*n = 24, n = 2 and m = 12.

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