LC Resonant Frequency Calculator Formula
Understand the math behind the lc resonant frequency calculator. Each variable explained with a worked example.
Formulas Used
Resonant Frequency
resonant_freq = 1 / (2 * pi * sqrt(inductance * 1e-3 * capacitance * 1e-6))Angular Frequency
angular_freq = 1 / sqrt(inductance * 1e-3 * capacitance * 1e-6)Variables
| Variable | Description | Default |
|---|---|---|
inductance | Inductance(mH) | 10 |
capacitance | Capacitance(μF) | 100 |
How It Works
LC Resonant Frequency
An LC circuit oscillates at a natural frequency determined by the inductance and capacitance.
Formula
f = 1 / (2*pi*sqrt(L*C))
At resonance, the inductive and capacitive reactances are equal and cancel, leaving only resistance to limit current.
Worked Example
An LC circuit with L = 10 mH and C = 100 μF.
- 01f = 1 / (2*pi*sqrt(L*C))
- 02f = 1 / (2*pi*sqrt(10e-3 * 100e-6))
- 03f = 1 / (2*pi*sqrt(1e-6))
- 04f = 1 / (2*pi*0.001)
- 05f = 1 / 0.006283 = 159.15 Hz
Frequently Asked Questions
What is resonance in an LC circuit?
Resonance occurs when the inductor and capacitor exchange energy back and forth at a natural frequency, like a pendulum swinging.
Where are LC circuits used?
In radio tuners (selecting a station frequency), oscillators, filters, and impedance matching networks.
What limits the oscillation in a real LC circuit?
Resistance in the wire and components gradually converts the oscillating energy to heat, causing the oscillation to decay (damped oscillation).
Ready to run the numbers?
Open LC Resonant Frequency Calculator