RLC Impedance Calculator
Impedance, phase and the resonance a tuner exploits.
Work out RLC Impedance. Impedance, phase and the resonance a tuner exploits. Shows the working, not just the answer.
Scientific notation works. 10 µF is 1e-5.
Series impedance
10 Ω
Phase +0° · resonance at 159.15 Hz
Z = √(R² + (XL − XC)²). Inductive and capacitive reactance oppose each other, so at the resonant frequency they cancel exactly and the impedance collapses to nothing but the resistance. That collapse is the sharpest thing a passive circuit does, and it is how every radio tuner picks one station out of the whole band — the circuit is a near short at one frequency and a near open everywhere else. Above resonance the inductor dominates and current lags the voltage; below it the capacitor dominates and current leads.
How the RLC Impedance Calculator works
Enter resistance, inductance, capacitance and frequency for the impedance, phase angle and resonant frequency. At resonance the reactances cancel exactly and the circuit becomes purely resistive.
Also known as: series rlc calculator · resonant frequency calculator · ac impedance calculator · reactance calculator
Frequently asked questions
How do I calculate RLC impedance?
Z = √(R² + (XL − XC)²), with XL = 2πfL and XC = 1/(2πfC). The reactances subtract because they act in opposition.
What is resonance?
The frequency where XL and XC are equal and cancel completely, leaving only the resistance. It occurs at f = 1/(2π√(LC)) and is where the impedance is at its minimum.
How does a radio tune to one station?
By adjusting a variable capacitor so the circuit resonates at the wanted frequency. At resonance it passes signal freely; a few kilohertz away the impedance rises sharply and the signal is rejected.
What does the phase angle mean?
Whether current leads or lags the voltage. Above resonance the inductor dominates and current lags; below it the capacitor dominates and current leads. At resonance they are in phase.
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