What capacitance should a capacitor be included in an oscillatory circuit with an inductor of 0.76 H

What capacitance should a capacitor be included in an oscillatory circuit with an inductor of 0.76 H in order to obtain electrical oscillations of an audio frequency of 400 Hz in it?

The period of electromagnetic oscillations T in an oscillatory circuit, including a capacitor with a capacity C and a coil with inductance L, is calculated by the Thomson formula: T = 2 * π * √ (L * C), where π ≈ 3.14. The period is related to the vibration frequency ν by the formula: T = 1 / ν. Then: ν = 1 / T or ν = 1 / (2 * π * √ (L * C)). This means that the capacitance of the capacitor will be:

С = 1 / (4 * π ^ 2 * ν ^ 2 * L).

From the condition of the problem it is known that in an oscillatory circuit with an inductor L = 0.76 H, electrical oscillations of an audio frequency ν = 400 Hz were obtained. We get:

С = 1 / (4 * 3.14 ^ 2 * (400 Hz) ^ 2 * 0.76 H) = 0.2 ∙ * 10 ^ (- 9);

Ф ≈ 0.2 nF.

Answer: you need to include a capacitor with a capacity of ≈ 0.2 nF