LC Resonant Frequency
Resonance of an LC pair — the Thomson formula.
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The engineering
Energy sloshing between the magnetic and electric stores at exactly one frequency — the heart of every tuned circuit from crystal sets to VCO tanks.
The √(L/C) row sets the tank's impedance level; same f₀, very different loading behavior.
Where this math comes from
William Thomson (Kelvin) derived the oscillation of a discharging capacitor through an inductor in 1853 — before anyone could observe it. Berend Feddersen photographed the oscillatory spark a few years later, and Hertz's 1887 resonators used exactly this physics to prove Maxwell right.
Marconi and the wireless generation then spent two decades tuning transmitters and receivers with this one formula — 'syntony,' they called it, and it was the patent war of its day.
- 1853Lord KelvinPredicts LC oscillation mathematically.
- 1859Berend FeddersenPhotographs oscillatory spark discharge — theory confirmed.
- 1887Heinrich HertzResonant circuits generate and detect radio waves.
- 1897Oliver LodgePatents syntonic (tuned) wireless telegraphy.
See the full timeline of the math behind every calculator →
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