An oscillating circuit with an inductance of 1 mH is tuned to a wavelength of 300 m.

An oscillating circuit with an inductance of 1 mH is tuned to a wavelength of 300 m. What is the capacitance of the capacitor?

Data: L – inductance of the specified circuit (L = 1 mH = 10 ^ -3 H); λ is the working wavelength (λ = 300 m).

Const: C – the speed of propagation of light (C ≈ 3 * 10 ^ 8 m / s).

To find out the required capacity of the capacitor used, consider the equality: λ / Vv = λ / C = T (period) = 2 * Π * √ (L * Cx), whence we express: Cx = (λ / (C * 2 * Π)) 2 / L.

Let’s perform the calculation: Cx = (λ / (C * 2 * Π)) ^ 2 / L = (300 / (3 * 10 ^ 8 * 2 * 3.14)) ^ 2/10 ^ -3 ≈ 2.54 * 10 ^ -11 F.

Answer: The required capacitance of the capacitor used is 25.4 pF.