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The resistance of the series combination of two resistors is S . When they are joined in parallel the equivalent resistance becomes P . If S = nP , then the minimum possible value of n is

Correct answer

4

Step-by-step solution

In series combination, S = R 1 + R 2 In parallel combination, P = R 1 R 2 R 1 + R 2 ∵   S = nP ∴ R 1 + R 2     = n R 1 R 2 R 1 + R 2 ∴ R 1 + R 2 2 = n R 1 R 2 For minimum value, R 1 = R 2 = R R + R 2 = n R × R ⇒ 4 R 2 = nR 2 ⇒ n = 4

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