LC Resonant Frequency Calculator

At a glance:The resonant frequency of an LC circuit (composed of an inductor L and a capacitor C) is the frequency at which it naturally oscillates or responds most strongly to an external AC signal. Energy swings back and forth between the inductor's magnetic field and the capacitor's electric field (like a pendulum trading kinetic and potential energy); the natural frequency is f = 1/(2π√(LC)), where 2π converts angular frequency (ω=2πf). Frequency is inversely proportional to √(LC): larger L or C lowers the resonance, smaller raises it. Example: L=1 mH=1e-3 H, C=1 µF=1e-6 F → f=1/(2π√(1e-9))≈5033 Hz. At resonance the inductive reactance X_L=2πfL equals the capacitive reactance X_C=1/(2πfC) and they cancel. In a series LC circuit the total impedance is then minimal (only the resistance remains) and current is maximal; in a parallel (tank) LC circuit impedance is maximal and current minimal. This frequency selectivity makes LC circuits the heart of radio and communications. Applications: (1) radio/TV tuning — vary C or L to resonate with one station's carrier; (2) filters — band-pass/band-stop; (3) oscillators — LC tanks generate clock and transmitter signals; (4) wireless charging, induction heating, RFID rely on LC matching; (5) impedance matching and power filtering. Notes: the formula assumes an ideal lossless LC; real resistance broadens the peak (lower Q). Always use SI units (H, F); mind mH=1e-3 H, µH=1e-6 H, µF=1e-6 F, nF=1e-9 F, pF=1e-12 F. L and C must be > 0.