LC Resonant Frequency Calculator
Calculate LC circuit resonant frequency, inductance, or capacitance.
Find angular frequency, reactance, Q factor, and wavelength for radio, filter, and oscillator design.
LC Circuit Resonance — Core Concepts
An LC circuit (also called a resonant circuit or tank circuit) consists of an inductor (L) and a capacitor (C) connected together. At a specific frequency — the resonant frequency — these two components exchange energy back and forth with minimum energy loss.
Resonant Frequency Formula f = 1 / (2π × √(L × C))
Where:
- f = resonant frequency in Hertz (Hz)
- L = inductance in Henries (H)
- C = capacitance in Farads (F)
- π = 3.14159…
Angular Frequency ω = 2πf = 1 / √(L × C) (radians per second)
Reactance at Resonance At the resonant frequency, the inductive reactance and capacitive reactance are equal and opposite:
- Inductive reactance: XL = 2πfL (Ohms)
- Capacitive reactance: XC = 1 / (2πfC) (Ohms)
- At resonance: XL = XC — the net reactive impedance is zero.
Quality Factor (Q) The Q factor measures how sharp the resonance peak is. A higher Q means a more selective (narrower bandwidth) circuit: Q = (1/R) × √(L/C) for a parallel RLC circuit. A low-resistance circuit (small R) has a high Q and resonates very sharply — useful for radio tuning. A high-resistance circuit damps the resonance.
Wavelength The electromagnetic wavelength corresponding to a resonant frequency: λ = c / f, where c = 3 × 10⁸ m/s (speed of light).
Practical Applications LC circuits are fundamental to: AM/FM radio tuners (selecting a station by tuning L or C), bandpass and notch filters, RF oscillators, impedance matching networks, metal detectors, and wireless power transfer.