Question

Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).

Hint:

In a parallel circuit, the total resistance decreases as more resistors are added. The reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

Answer 1

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 \(2 \, \Omega\).