Series LC resonant frequency

At what frequency will this choke and this cell ring together?

f = \frac{1}{2\pi\sqrt{L \cdot C}}

Method

1. Convert the inductance to henries and the capacitance to farads. Everything below is in SI; mixing millihenries with farads is the commonest way to get an answer that is wrong by three decades and looks plausible.
2. Multiply them: L × C. The product has units of seconds squared, which is the first check that the inputs were what you meant.
3. Take the square root. That is the time constant of the loop — very nearly the quarter-period of the ring.
4. Multiply by 2π and take the reciprocal. That converts the time constant into a frequency in hertz.
5. For the characteristic impedance, take √(L ÷ C). At resonance the inductive and capacitive reactances are equal and opposite, and this is the size of each.

Assumptions

• The inductance and capacitance are constant with frequency. Neither is, in a real VIC: a choke has self-capacitance and a self-resonance of its own, and water’s permittivity falls with frequency (the Cole-Cole behaviour). This answer is the lossless ideal.
• Series connection. A parallel LC has the same resonant frequency but behaves oppositely around it — high impedance rather than low.
• Resistance is ignored. Real damping pulls the peak slightly below this frequency; the shift is negligible for Q above about 5 and is not for a cell full of tap water.
• The cell is treated as a plain capacitor. It is not — it conducts, and its ESR is a function of water conductivity and frequency. Use this to find the neighbourhood, not the setpoint.