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In a series L-C-R circuit, V is the instantaneous voltage of the source, V_R is the voltage across the resistor, V_L is the voltage across the inductor, and V_C is the voltage across the capacitor. Which relation is always correct at any instant?

1. V = sqrt(V_R² + (V_L - V_C)²)
2. V = sqrt(V_L² + (V_R - V_C)²)
3. V² = V_C² + (V_R - V_L)²
4. V + V_R + V_L + V_C = 0

Correct answer: V + V_R + V_L + V_C = 0

Solution

The relation V = sqrt(V_R² + (V_L-V_C)²) is a phasor/RMS relationship valid for steady-state AC but NOT for instantaneous values. At any instant, Kirchhoff's voltage law gives: source voltage = sum of instantaneous voltage drops across all elements.

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