Calculate Impedance Magnitude and Phase Angle for RLC Circuits
Configuration
R (Ω)
L (H)
C (F)
f (Hz)
Result
|Z|
Phase φ
PF = cos φ
Step-by-Step Calculation
RLC Impedance Formulas
XL = 2πfL, Xc = 1/(2πfC), X = XL - Xc
Series: Z = √(R² + X²), φ = arctan(X/R)
Parallel: 1/Z = √((1/R)² + (1/XL - 1/Xc)²)
Z = R (pure) at resonance where XL = Xc
Impedance is the AC equivalent of resistance. It includes both magnitude and phase. In RLC circuits, the interplay between inductive and capacitive reactance creates frequency-dependent behavior. At resonance, reactances cancel, giving minimum (series) or maximum (parallel) impedance.
⚠At resonance: series RLC has minimum impedance (=R). Parallel RLC has maximum impedance. Below resonance: Xc dominates (capacitive). Above: XL dominates (inductive).
Understanding RLC Impedance
Impedance is the total opposition a circuit offers to alternating current. It extends resistance to include frequency-dependent effects from inductors and capacitors. The real part (R) dissipates power, while the imaginary part (X = XL-Xc) stores and releases energy, causing phase shift between voltage and current.
Series RLC
Z = R + j(XL-Xc). |Z| = √(R²+X²). Current through all elements. Z min at resonance.
Parallel RLC
1/Z = 1/R + 1/jXL + 1/(-jXc). Voltage across all elements. Z max at resonance.
Phase Angle
φ>0: inductive (XL>Xc), current lags. φ<0: capacitive (Xc>XL), current leads. φ=0: resistive (XL=Xc, resonance).
Power Factor
PF = cos(φ) = P/S (real/apparent power). PF=1: all power used. PF=0: no real power. Utilities charge penalties for low PF.
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