How to use this calculator
Enter R, L and C, then the source voltage and frequency. The graph shows how the current peaks at resonance.
Formulas
Resonancef0 = 12π√(LC) Q = 1R√(L/C) BW = f0Q
ImpedanceXL = 2πfL XC = 12πfC |Z| = √(R² + (XL − XC)²)
Worked example
50 Ω, 10 mH, 1 µF driven at 1 kHz and 10 V (the default)
- f0 = 1/(2π√(0.01 × 10⁻⁶)) = 1,592 Hz.
- Q = (1/50)√(0.01/10⁻⁶) = 2, so BW = 796 Hz.
- At 1 kHz: XL = 62.8 Ω, XC = 159.2 Ω, |Z| = 108.5 Ω, I = 92.1 mA, leading by 62.6°.
Frequently asked questions
What happens at resonance?
XL = XC, so they cancel. The impedance drops to R and the current is as large as it can be.
How is this like a spring-mass system?
L acts like mass, 1/C like stiffness and R like damping. The circuit obeys the same second-order differential equation.