Question

Какой должна быть емкость конденсатора чтобы обеспечить настройку колебательного контура в резонанс на длину волны 180 метров, если индуктивность катушки 25 мкгн? подробно

Answer 1

Λ=180 м                            найдем период колебаний из формулы:
с=3 10⁸ м/с                         с=λ/T  ⇒  T=λ/c;  T=180/3 10⁸=60 10⁻⁸=6 10⁻⁷ c;
L=25 мкГн=25 10⁻⁶ Гн       емкость конденсатора найдем из формулы
___________________     Томсона: 
C-?                                      T=2π√LC  ⇒  T²=4π²LC  ⇒  C=T²/4π²L;
                                            C=36 10⁻¹⁴/4*10*25 10⁻⁶=36 10⁻¹⁴/1000*10⁻⁶=
                                               =36 10⁻¹⁴/10³*10⁻⁶=36 10⁻¹¹ Ф=3,6 10⁻¹² Ф;
                         Ответ: С=3,6 10⁻¹² Ф.

Answer 2

Calculating the Capacitance for Resonance in an LC Circuit

To calculate the capacitance required to achieve resonance in an LC circuit at a wavelength of 180 meters, we need to use the formula for the resonant frequency of an LC circuit:

Resonant frequency (f) = 1 / (2π√(LC))

In this formula, L represents the inductance of the coil and C represents the capacitance.

Given that the inductance of the coil is 25 μH (microhenries), we can substitute the values into the formula and solve for the capacitance.

25 μH = 25 x 10^-6 H

Wavelength (λ) = 180 meters

Let's calculate the capacitance:

Step 1: Convert the wavelength to frequency using the formula:

Frequency (f) = Speed of light (c) / Wavelength (λ)

The speed of light is approximately 3 x 10^8 meters per second.

Frequency (f) = (3 x 10^8 m/s) / (180 m)

Step 2: Substitute the frequency and inductance values into the resonant frequency formula:

f = 1 / (2π√(LC))

1 / (2π√(LC)) = (3 x 10^8 m/s) / (180 m)

Step 3: Solve for the capacitance (C):

C = (1 / (2π√(LC))) / f

Now, let's calculate the capacitance using the given values:

C = (1 / (2π√((25 x 10^-6 H) * C))) / ((3 x 10^8 m/s) / (180 m))

Unfortunately, the provided search snippets do not contain the necessary information to calculate the capacitance. To provide a more accurate answer, I would need additional information or a specific value for the resonant frequency or the desired impedance of the circuit.

Please provide more details or specify the desired resonant frequency or impedance so that I can assist you further.