Two resistors of 3 Ω and X Ω are connected in parallel such that the effective resistance is 2 Ω. What is the value of X (in Ω)?
6
For resistors in parallel, the reciprocal of the effective resistance is the sum of the reciprocals of the individual resistances: \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}\).
Substituting \(R = 2\,\Omega\), \(R_1 = 3\,\Omega\) and \(R_2 = X\): \(\frac{1}{2} = \frac{1}{3} + \frac{1}{X}\).
So \(\frac{1}{X} = \frac{1}{2} - \frac{1}{3} = \frac{3 - 2}{6} = \frac{1}{6}\), which gives \(X = 6\,\Omega\).
Check: \(R = \frac{R_1 R_2}{R_1 + R_2} = \frac{3 \times 6}{3 + 6} = \frac{18}{9} = 2\,\Omega\), which is the given effective resistance.
Hence, 6.
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