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A combination of two identical resistors connected in series has an equivalent resistance of 12. ohms. What is the equivalent resistance of the combination of these same two resistors when connected in parallel?

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Answer:

R1 + R2 = R = 12 for resistors in series - so R1 = R2 if they are identical

2 R1 = 12         and R1 = R2 = 6 ohms

1 / R = 1 / R1 + 1 / R2     for resistors in parallel

R = R1 * R2 / (R1 + R2) = 6 * 6 / (6 + 6) = 3

The equivalent resistance would be 3 ohms if connected in parallel

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