The frequency of free oscillations of an oscillatory circuit containing a coil with inductance L = 0.04H is equal

The frequency of free oscillations of an oscillatory circuit containing a coil with inductance L = 0.04H is equal to v = 800Hz. What is the capacitance of the capacitor of this circuit?

These tasks: L – coil inductance (L = 0.04 H); ν is the known oscillation frequency of the circuit used (ν = 800 Hz).
To find out the required capacitance of the capacitor in the circuit used, we use the equality: 2 * Π * √ (L * Cx) = T (period) = 1 / ν, whence we express: L * Cx = 1 / (ν * 2 * Π) 2 and Cx = (1 / (ν * 2 * Π) 2) / L.
Let’s calculate: Cx = (1 / (ν * 2 * Π) 2) / L = (1 / (800 * 2 * 3.14) 2) / 0.04 ≈ 9.9 * 10-7 F.
Answer: The capacitance of the capacitor in the circuit used should be 9.9 * 10-7 F.