Complex Impedance Magnitude (RLC)

|Z| = √(R² + (ωL − 1/(ωC))²)

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Result
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Formula

|Z| = √(R² + (ωL − 1/(ωC))²)

Description

The magnitude of the impedance of a series RLC circuit combines resistance with the net reactance. Inductive reactance XL = ωL increases with frequency, while capacitive reactance XC = 1/(ωC) decreases. At resonance, XL = XC and the impedance equals R alone (minimum impedance). Below resonance the circuit is capacitive; above resonance it is inductive. This formula is essential for understanding filter behavior, resonant circuits, and the frequency-dependent impedance of any circuit containing R, L, and C elements.

Variables

  • |Z| — Impedance magnitude (Ω)
  • R — Resistance (Ω)
  • f — Frequency (Hz)
  • L — Inductance (H)
  • C — Capacitance (F)

Practical Notes

At resonance, f₀ = 1/(2π√(LC)), the impedance is purely resistive and equal to R. The quality factor Q = (1/R)√(L/C) determines the sharpness of the resonance. High-Q circuits (low R) have narrow bandwidth and high selectivity. For parallel RLC circuits, the impedance is maximum at resonance.

Related Concepts

All AC Circuits formulas →
Resonant Frequency Impedance (RLC Series) Quality Factor (Bandwidth) Quality Factor (RLC) Power Factor Apparent Power Reactive Power RLC Circuit Bandwidth

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