AC foundations
LC resonant frequency
- where
- resonant frequency (Hz)
- inductance (H)
- capacitance (F)
Explain this equation
Gives the frequency at which an inductor and a capacitor naturally swap energy back and forth. Use it when checking tuned or filter circuits, or the risk of resonance between power-factor capacitors and supply inductance.
L is the inductance in henries and C the capacitance in farads. The inductor stores energy in its magnetic field and the capacitor in its electric field. f₀ is the frequency where the inductor's reactance, which rises with frequency, exactly equals the capacitor's reactance, which falls with frequency.
Setting 2πfL equal to 1/(2πfC) and solving for f gives this shape. The 2π converts angular frequency (radians per second) into ordinary hertz. The square root covers L and C together, because it is their product that matters.
100 mH with 100 µF gives about 50 Hz. Quadrupling either L or C halves the frequency; doubling one only divides it by about 1.41.
Watch out: enter base units, so convert mH and µF to H and F first. Real circuits have resistance and stray effects, so the true resonant point and the size of the peak will differ.
At ideal resonance the inductive and capacitive reactance magnitudes match. Convert both quantities to base units before taking their product and square root.
Series resonance leaves only the series resistance in the ideal model. Practical resonance may create large currents or component voltages.
Enter your values to see the result.
Common mistake
Forgetting the square root covers LC together.
Limits
Ideal LC resonance; real losses and parasitics alter behaviour.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.