The receiving oscillating circuit consists of a coil with inductance L = 1.0 μH. What is the capacitance of the capacitor

The receiving oscillating circuit consists of a coil with inductance L = 1.0 μH. What is the capacitance of the capacitor of this circuit, if the receiver is tuned to the wavelength “lambda = 100 m”? The speed of propagation of electromagnetic waves c = 3.0 * 10 ^ 8 m / s

Let the given receiving oscillatory circuit, tuned to a wavelength λ = 100 m, consist of a coil with inductance L = 1.0 μH = 10 ^ (- 6) H and a capacitor with capacitance C.

The capacitance and inductance of the circuit are related by Thomson’s formula for calculating the oscillation period in it: Т = 2 ∙ π ∙ √ (L ∙ С), where the constant value is π ≈ 3.14, then С = Т² / (4 ∙ π² ∙ L).

The period can be found through the wavelength: T = λ / s, where c = 3.0 ∙ 10 ^ 8 m / s is the speed of propagation of electromagnetic waves.

We get: С = λ² / (4 ∙ π² ∙ s² ∙ L). Substitute the values ​​of physical quantities in the calculation formula and find the capacitance of the capacitor of this circuit:

С = 10000 / (4 ∙ 9.86 ∙ 9 ∙ 10 ^ 16 ∙ 10 ^ (- 6));

C = 2.8 ∙ 10 ^ (- 9) F = 2.4 nF.

Answer: The capacitance of the loop capacitor is 2.4 nF