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

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

The frequency of free vibrations in the circuit is calculated by the formula:

ν = 1 / T = 1 / (2 x π x √ (L x C),

where L is the inductance of the circuit, measured in Henry, C is the capacitance of the capacitor, measured in Farads.

Let us express from this formula C:

L x C = (1 / (2 x π x ν)) ²;

C = 1 / (L x (2 x π x ν) ²).

Substitute the values and get the required capacitance of the capacitor:

C = 1 / (0.04 x (2 x 3.14 x 800) ²);

C ≈ 0.99 (μF).

Answer: the capacitance of the capacitor should be 0.99 μF.