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A resistor and an ideal inductor are connected in series in an AC circuit. Three ideal hot-wire voltmeters V1, V2, and V3 are connected across the resistor, the inductor, and the AC source respectively. Which relation correctly describes the readings?

1. V3 = V1 + V2
2. V3 > (V1 + V2)
3. V3 < (V1 + V2)
4. None of these

Correct answer: V3 < (V1 + V2)

Solution

In a series RL AC circuit, V_R and V_L are perpendicular phasors. The source voltage V3 = sqrt(V1² + V2²). By the triangle inequality, sqrt(V1² + V2²) < V1 + V2 for any positive V1, V2. So V3 < V1 + V2.

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