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Two resistors are connected in series and their equivalent resistance is S. When the same two resistors are connected in parallel, their equivalent resistance becomes P. If S = nP, what is the smallest possible value of n?

1. 2
2. 3
3. 4
4. 1

Correct answer: 4

Solution

S/P = (R1+R2)^2/(R1*R2). By AM-GM this is minimum when R1 = R2, giving S/P = 4. So the smallest value of n is 4.

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