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A 20 V AC is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is 12 V, the voltage across the coil is

1. 16 V
2. 10 V
3. 8 V
4. 6 V

Correct answer: 16 V

Solution

In a series RL circuit, \(V^2 = V_R^2 + V_L^2\) because the resistor and inductor voltages are 90° out of phase. With \(V = 20\) V and \(V_R = 12\) V, \(V_L = \sqrt{20^2 - 12^2} = \sqrt{256} = 16\) V.

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