Determine the range of frequencies and wavelengths received by the radio receiver, if the inductance of the coil is 24 μH

Determine the range of frequencies and wavelengths received by the radio receiver, if the inductance of the coil is 24 μH, and the capacitance of the capacitor can be changed from 0.75 μF to 84 pF.

L = 24 μH = 24 * 10-6 H.

C1 = 0.75 μF = 0.75 * 10-6 F.

C2 = 84 pF = 85 * 10-12 F.

s = 3 * 108 m / s.

v1 -?

v2 -?

λ1 -?

λ2 -?

In order for the receiver to receive the radio frequency, it is necessary that the external oscillation frequency coincides with the frequency of the natural oscillations of the receiver circuit and the resonance phenomenon occurs.

The frequency of natural oscillations of the oscillating circuit of the receiver v is determined by the Thomson formula: v = 1/2 * P * √ (L * C), where L is the inductance of the coil of the oscillating circuit of the receiver, C is the capacitance of the capacitor of the receiver circuit.

v1 = 1/2 * P * √ (L * C1).

v1 = 1/2 * 3.14 * √ (24 * 10-6 H * 0.75 * 10-6 F) = 27936 Hz = 27.936 kHz.

v2 = 1/2 * P * √ (L * C2).

v2 = 1/2 * 3.14 * √ (24 * 10-6 H * 85 * 10-12 F) = 3538570 Hz = 3.54 MHz.

We express the wavelength λ by the formula: λ = c / v, where c is the speed of propagation of an electromagnetic wave, the speed of light.

λ1 = s / v1.

λ1 = 3 * 10 ^ 8 m / s / 27936 Hz = 10738.8 m.

λ2 = s / v2.

λ2 = 3 * 10 ^ 8 m / s / 3538570 Hz = 84.8 m.

Answer: v1 = 27.936 kHz, v2 = 3.54 MHz, λ1 = 10738.8 m, λ2 = 84.8 m.