Series LCR Circuit

A series LCR circuit driven by AC has resistor, inductor, and capacitor sharing the SAME current — but with different phase relationships to the source voltage.

Impedance: Z = √(R² + (X_L − X_C)²) — the AC analogue of total resistance.

Peak current: I₀ = V₀/Z. RMS current: I_rms = V_rms/Z.

Phase angle between V and I: φ = arctan((X_L − X_C)/R). Positive φ → V leads I (inductive). Negative → V lags I (capacitive).

Voltage across R is IN PHASE with current; across L leads I by 90°; across C lags I by 90°.

When X_L = X_C (resonance), Z = R (minimum), I is maximum, and circuit behaves purely resistive.

Phasor diagram: V_R along I, V_L at +90° from I, V_C at −90° from I. Net voltage = vector sum.

Average power = V_rms · I_rms · cos φ. The factor cos φ is the POWER FACTOR.