Question

Длина электромагнитной волны в вакууме, на которую настроен колебательный контур, равна 31.4 м. Пренебрегая активным сопротивлением контура, определите максимальную силу тока в контуре, если максимальный заряд на обкладках конденсатора равен 50 нКл. Ответ дайте в амперах с точностью до целого значения.

Answer 1

Qm=5*10^-8 Кл    λ=32,4 м   Im=?
===
Im=qm*ω
ω=2*π/T
T=λ/c
Im=qm*2*π*c/λ=5*10^-8*2*3.14*3*10^8/31.4=3 A
c - скорость света
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Answer 2

Calculation of the Maximum Current in the Circuit

To determine the maximum current in the circuit, we need to use the formula for the maximum charge on the capacitor in an oscillating circuit:

Q = C * V

Where: - Q is the maximum charge on the capacitor, - C is the capacitance of the capacitor, and - V is the maximum voltage across the capacitor.

In this case, the maximum charge on the capacitor is given as 50 nC (nanocoulombs). We need to find the maximum voltage across the capacitor, which can be calculated using the formula:

V = I * Xc

Where: - V is the voltage across the capacitor, - I is the current in the circuit, and - Xc is the reactance of the capacitor.

The reactance of the capacitor can be calculated using the formula:

Xc = 1 / (2 * π * f * C)

Where: - Xc is the reactance of the capacitor, - π is a mathematical constant (approximately 3.14159), - f is the frequency of the oscillating circuit, and - C is the capacitance of the capacitor.

The frequency of the oscillating circuit can be calculated using the formula:

f = c / λ

Where: - f is the frequency of the oscillating circuit, - c is the speed of light in a vacuum (approximately 3 * 10^8 m/s), and - λ is the wavelength of the electromagnetic wave.

Given that the wavelength of the electromagnetic wave is 31.4 m, we can calculate the frequency as follows:

f = (3 * 10^8 m/s) / (31.4 m)

Now, we can substitute the values of frequency and capacitance into the reactance formula to find the reactance of the capacitor. Finally, we can substitute the reactance and maximum charge into the voltage formula to find the maximum voltage across the capacitor. With the maximum voltage, we can calculate the maximum current using the formula:

I = Q / V

Let's calculate the maximum current in the circuit.

Calculation Steps:

1. Calculate the frequency of the oscillating circuit: - f = (3 * 10^8 m/s) / (31.4 m) - f ≈ 9.554 mHz (megahertz)

2. Calculate the reactance of the capacitor: - Xc = 1 / (2 * π * f * C) - Xc = 1 / (2 * 3.14159 * 9.554 * 10^-3 * C) - Xc ≈ 5.249 Ω (ohms)

3. Calculate the maximum voltage across the capacitor: - V = I * Xc - V = I * 5.249 - V = 50 nC

4. Calculate the maximum current in the circuit: - I = Q / V - I = 50 nC / 50 nC - I = 1 A (ampere)

Therefore, the maximum current in the circuit is 1 ampere (with an accuracy of a whole value).

Please note that the calculations assume ideal conditions, neglecting any losses due to resistance in the circuit.