Question

ОЧЕНЬ СРОЧНО!!! Дано: Приемник настроен на длину волны, равную 600 м. Индуктивность входного колебательного контура приемника равна 1 мкГн. Найти: Емкость входного колебательного контура

Answer 1

Ответ:

Емкость входного колебательного контура приблизительно

$\boldsymbol{ 1 \cdot 10^{-7}}$ Ф

Объяснение:

Дано:

$c = 3 \cdot 10^{8}$ м/c

$\lambda =$ 600 м

$L = 1 \cdot 10^{-6}$ Гн

Найти:

$C \ - \ ?$

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Решение:

$\lambda = cT \Longrightarrow \boxed{ T = \dfrac{\lambda}{c} }$

$T = 2\pi \sqrt{LC}$

$T^{2} = 4\pi^{2} LC \Longrightarrow \boxed{ C =T^{2}\cdot \dfrac{1}{4\pi^{2}L} = \dfrac{\lambda^{2} }{4\pi^{2}c^{2}L} }$

$C =$ (360 000 м²) / (4 * 9,87 * 9 * $10^{16}$ * $1 \cdot 10^{-6}$ Гн) $\approx 1 \cdot 10^{-7}$ Ф

Ответ: $C \approx 1 \cdot 10^{-7}$ Ф.

Answer 2

Calculation of Capacitance in the Input Resonant Circuit

To find the capacitance in the input resonant circuit, we need to use the formula for the resonant frequency of an LC circuit:

f = 1 / (2π√(LC))

Given that the receiver is tuned to a wavelength of 600 meters and the inductance of the input resonant circuit is 1 μH (microhenry), we can calculate the capacitance.

Let's proceed with the calculation:

1. Convert the wavelength to frequency: - The speed of light in a vacuum is approximately 3 x 10^8 meters per second. - The formula for calculating frequency from wavelength is: f = c / λ, where c is the speed of light and λ is the wavelength. - Substituting the values, we have: f = (3 x 10^8) / 600. - Calculating this, we find that the frequency is approximately 5 x 10^5 Hz.

2. Substitute the values into the formula for the resonant frequency: - The formula is: f = 1 / (2π√(LC)). - We know the frequency (5 x 10^5 Hz) and the inductance (1 μH). - Rearranging the formula, we get: C = 1 / (4π^2f^2L). - Substituting the values, we have: C = 1 / (4π^2 x (5 x 10^5)^2 x 1 x 10^-6).

Let's calculate the capacitance:

C = 1 / (4π^2 x (5 x 10^5)^2 x 1 x 10^-6)

Using a calculator, we find that the capacitance is approximately 6.37 x 10^-12 Farads.

Therefore, the capacitance in the input resonant circuit is approximately 6.37 picofarads (pF).

Please note that the calculation assumes an ideal LC circuit and does not take into account any losses or other factors that may affect the actual capacitance value.