LC resonance and tank circuits explained
How an inductor and capacitor trade energy to ring at one frequency, why tank circuits tune radios, and how to read the result.
Energy bouncing between L and C
An LC circuit resonates because the inductor and capacitor store energy in different forms and hand it back and forth. The capacitor holds energy in an electric field between its plates, while the inductor holds it in a magnetic field around its coil. As the capacitor discharges it drives current through the inductor, which then recharges the capacitor with the opposite polarity, and the cycle repeats. Left alone in an ideal circuit this exchange would continue forever at one natural frequency, the resonant frequency this tool computes.
Where the square root comes from
The formula f = 1 / (2 pi sqrt(L C)) tells you that frequency falls as either component grows, and the square root is what makes the effect gentle. Quadrupling the capacitance only halves the frequency, so tuning across a wide band takes a large range of component values. This is why radio tuners pair a small variable capacitor with a fixed coil: even a modest change in capacitance sweeps the resonant point across a whole broadcast band.
Series versus parallel behaviour
The resonant frequency is the same whether the inductor and capacitor sit in series or in parallel, but what happens at that frequency is opposite. A series LC circuit drops to minimum impedance at resonance, so it behaves like a short and lets that frequency through, which suits notch and pass filters. A parallel LC tank instead rises to maximum impedance, so it blocks or selects that frequency, which is why oscillators and antenna tuners use the parallel form.
Why real circuits drift from the ideal
Real inductors have winding resistance and real capacitors leak, so the sharp ideal peak becomes a rounded hump described by a quality factor, or Q. Stray capacitance in the wiring and the input capacitance of whatever the tank drives add to C and pull the frequency down a little. Component tolerances of 5 to 20 percent mean two circuits built from the same design can resonate several percent apart. Use the calculated value as a starting point, then trim a component or add a small variable capacitor to land on the exact target.