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Circuit and electromagnetism basics

What is the combined resistance of a 6 Ω and a 3 Ω resistor connected in parallel?

  1. A2 Ω
  2. B9 Ω
  3. C4.5 Ω
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Answer: A. 2 Ω

For two resistors in parallel, the combined resistance is R1R2/(R1 + R2) (product over sum): 6 × 3/(6 + 3) = 18/9 = 2 Ω. It is also the reciprocal of 1/6 + 1/3 = 1/2. A parallel combination is smaller than its smallest resistor (3 Ω). Both resistors see the same voltage and the current divides in inverse proportion to resistance, so the 3 Ω resistor carries twice the current of the 6 Ω one.

  • A. Correct. 6 × 3/(6 + 3) = 2 Ω.
  • B. 9 Ω is the combined resistance in series.
  • C. 4.5 Ω is the average of the two, not the parallel resistance.
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