Lesson 14 of 15
LC Resonant Frequency
LC Oscillator
An inductor (L) and capacitor (C) in series or parallel exchange energy back and forth at a natural resonant frequency:
f = rac{1}{2pisqrt{LC}}
- f — resonant frequency (Hz)
- L — inductance (H)
- C — capacitance (F)
The Energy Seesaw
The capacitor stores energy in its electric field (E = rac{1}{2}CV^2); the inductor stores energy in its magnetic field (E = rac{1}{2}LI^2). At resonance they alternate — like a pendulum swapping kinetic and potential energy — at frequency f.
Relation to the Pendulum
| LC Circuit | Pendulum |
|---|---|
| Charge q | Displacement x |
| Inductance L | Mass m |
| 1/C | Spring constant k |
| f = rac{1}{2pisqrt{LC}} | f = rac{1}{2pi}sqrt{ rac{k}{m}} |
Radio Tuning
Tuning a radio dial changes C in an LC circuit, selecting the resonant frequency that matches the desired station.
Examples
| L (H) | C (F) | f (Hz) |
|---|---|---|
| 1×10⁻³ | 1×10⁻⁶ | 5032.92 |
| 1×10⁻² | 1×10⁻⁴ | 159.15 |
| 0.1 | 1×10⁻³ | 15.92 |
| 1×10⁻³ | 1×10⁻⁷ | 15915.49 |
Your Task
Implement lc_resonance(L, C) returning the resonant frequency in Hz.
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