Two resistors of 6 Ω and 3 Ω are connected in parallel. What is their equivalent resistance ?
2 Ω
When resistors are connected in parallel, the same voltage acts across each of them and the reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances: \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}\).
Step 1 — Substitute the values: \(\frac{1}{R} = \frac{1}{6} + \frac{1}{3} = \frac{1 + 2}{6} = \frac{3}{6} = \frac{1}{2}\).
Step 2 — Take the reciprocal: R = 2 Ω. As expected, the parallel combination is smaller than the smallest single resistor (3 Ω).
9 Ω is the series sum (6 + 3), 3 Ω is only the smaller resistor itself, and 1 Ω is too small; a parallel combination can never fall below the value given by the reciprocal formula.
2 Ω option is correct.
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