ELECTRICAL / CALCULATOR
AC / RLC Impedance
Calculate series RLC impedance, phase angle, power factor and resonant frequency.
Input Parameters
Edit the example values. Results update as you type.
Results
- Series Impedance Magnitude |Z|
- 10.009Ω
- Inductive Reactance XL
- 31.416Ω
- Capacitive Reactance XC
- 31.831Ω
- Net Reactance X
- -0.4151Ω
- Impedance Phase Angle φ
- -2.377°
- Power Factor cosφ
- 0.9991
- Circuit Type
- Capacitive
- Resonant Frequency f₀
- 50.329Hz
- Complex Impedance Z
- 10 − j0.4151Ω
Formula
ω = 2πf · XL = ωL · XC = 1/(ωC) · Z = R + j(XL − XC) · |Z| = √(R² + X²) · φ = atan2(X, R) · f₀ = 1/(2π√LC)Substitution
XL = 2π × 50 × 0.1 = 31.416 Ω；XC = 1/(2π × 50 × 0.0001) = 31.831 Ω；|Z| = √(10² + (-0.4151)²) = 10.009 ΩCalculation Steps
- Convert R, L, C and f to 10 Ω, 0.1 H, 0.0001 F and 50 Hz.
- Subtract capacitive from inductive reactance: X = -0.4151 Ω; impedance phase angle φ = atan2(X, R) = -2.377°.
- cosφ = R/|Z| = 0.9991; resonant frequency f₀ = 50.329 Hz.
Result Explanation
Uses an ideal series RLC circuit in sinusoidal steady state. A positive angle is inductive with lagging current; a negative angle is capacitive with leading current. Near-resonance detection uses a relative reactance tolerance of 10⁻⁹.
Formulas and FAQ
Z = R + j(2πfL − 1/(2πfC))Which RLC connection is supported?
The model is ideal series RLC. A positive impedance angle is inductive and a negative angle is capacitive. Parallel networks need their own equivalent impedance.