Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).
Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).
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Solution and Explanation
In a parallel combination, the reciprocal of the total resistance \(R_{{total}}\) is the sum of the reciprocals of the individual resistances: \[ \frac{1}{R_{{total}}} = \frac{1}{R_X} + \frac{1}{R_Y} = \frac{1}{3 \, \Omega} + \frac{1}{6 \, \Omega} \] \[ \frac{1}{R_{{total}}} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} \] \[ R_{{total}} = \frac{6}{3} = 2 \, \Omega \] Thus, the equivalent resistance of the parallel combination of the two resistors is \(2 \, \Omega\).
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