Electronics · Free Calculator
RLC Circuit Impedance Calculator
Find the impedance and phase of a series or parallel RLC circuit at a given frequency, and its resonant frequency.
Series RLCParallel RLCPhase angleResonance
Impedance |Z|138.8 Ω
Phase angle−43.93° (capacitive)
XL62.83 Ω
XC159.2 Ω
Resonant frequency f01.592 kHz
Q factor1
How this result was calculated
- XL = 2πfL = 62.83 Ω, XC = 1 ÷ (2πfC) = 159.2 Ω
- Z = √(R² + (XL − XC)²) = 138.8 Ω
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RLC Impedance Formulas
XL = 2πfL, XC = 1 ÷ (2πfC)
Series: Z = √(R² + (XL − XC)²), φ = atan((XL − XC) ÷ R)
Parallel: 1/Z = √((1/R)² + (1/XC − 1/XL)²)
f0 = 1 ÷ (2π√(LC))
Series: Z = √(R² + (XL − XC)²), φ = atan((XL − XC) ÷ R)
Parallel: 1/Z = √((1/R)² + (1/XC − 1/XL)²)
f0 = 1 ÷ (2π√(LC))
Worked example
Series R = 100 Ω, L = 10 mH, C = 1 µF at 1 kHz: XL = 62.8 Ω, XC = 159.2 Ω, so Z = √(100² + 96.3²) = 138.8 Ω at −43.9° (capacitive). Resonance is at 1.59 kHz.
Key insight: a series RLC circuit has minimum impedance (just R) at resonance, while a parallel one has maximum impedance there, which is why one makes a trap and the other a tank.
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Frequently Asked Questions
What is the impedance of a series RLC circuit at resonance?
Just R, because XL and XC cancel.
What does a negative phase angle mean?
The current leads the voltage, so the circuit behaves capacitively.
How is Q factor defined here?
Series Q = √(L/C) ÷ R; parallel Q = R ÷ √(L/C).
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