Question

Помогите решитьНайдите период и частоту собственных электромагнитных колебаний в контуре,содержащем катушку индуктивностью 3 мГн и конденсатор емкостью 2 мкФ.

Answer 1

T=2*pi*sqrt(L*C)=6,28*sqrt(3*10^-3*2*10^-6)=48,7*10^-5 c
v=1/T=1/48,7*10^-5=2000 Гц

Answer 2

Calculating the Period and Frequency of the Circuit's Eigen Electromagnetic Oscillations

To calculate the period and frequency of the circuit's eigen electromagnetic oscillations, we can use the following formulas:

Period (T) can be calculated using the formula: \[ T = 2\pi\sqrt{LC} \]

Frequency (f) can be calculated using the formula: \[ f = \frac{1}{T} \]

Where: - L = inductance of the coil (3 mH = 3 x 10^-3 H) - C = capacitance of the capacitor (2 µF = 2 x 10^-6 F)

Let's calculate the period and frequency using the given values.

Calculations

Using the given values: - L = 3 x 10^-3 H - C = 2 x 10^-6 F

We can calculate the period (T) and frequency (f) as follows:

Period (T): \[ T = 2\pi\sqrt{LC} \] \[ T = 2\pi\sqrt{(3 \times 10^{-3})(2 \times 10^{-6})} \]

Frequency (f): \[ f = \frac{1}{T} \]

Results

After performing the calculations, the period (T) and frequency (f) of the circuit's eigen electromagnetic oscillations are as follows:

Period (T): \[ T \approx 0.024 \, \text{s} \]

Frequency (f): \[ f \approx 41.7 \, \text{Hz} \]

Therefore, the period of the circuit's eigen electromagnetic oscillations is approximately 0.024 seconds, and the frequency is approximately 41.7 Hz.