The radio receiver was set to receive transmissions of the radio station "Osvita" at a wavelength of 165 m. What is the inductance of the input oscillating circuit of the radio receiver, if the capacitance of the circuit is 200 pF?
Question
The radio receiver was set to receive transmissions of the radio station "Osvita" at a wavelength of 165 m. What is the inductance of the input oscillating circuit of the radio receiver, if the capacitance of the circuit is 200 pF?
Solution
To find the inductance (L) of the input oscillating circuit of the radio receiver, we can use the formula for the resonant frequency of an LC circuit:
f = 1 / (2π√(LC))
Where: f is the frequency, L is the inductance, C is the capacitance.
First, we need to convert the given wavelength to frequency. The relationship between frequency (f) and wavelength (λ) is given by the speed of light (c):
f = c / λ
Given that the speed of light is approximately 3 x 10^8 m/s and the wavelength is 165 m, we can find the frequency:
f = (3 x 10^8 m/s) / 165 m = 1.81818 x 10^6 Hz
Next, we can rearrange the formula for the resonant frequency to solve for L:
L = 1 / (4π^2f^2C)
Substituting the given capacitance (C = 200 pF = 200 x 10^-12 F) and the calculated frequency:
L = 1 / (4π^2(1.81818 x 10^6 Hz)^2 * 200 x 10^-12 F)
Solving this gives:
L ≈ 1.22 x 10^-6 H
So, the inductance of the input oscillating circuit of the radio receiver is approximately 1.22 µH.
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