Question

Конденсатор электроемкостью 10 пФ был подключен к источнику напряжением 100 В, а после зарядки переключен на катушку индуктивностью 100 мкГн. Определите период свободных колебаний, возникших в контуре, и максимальное значение силы тока.

Answer 1

Ответ:

........................................

Answer 2

Calculation of the Period of Free Oscillations

To determine the period of free oscillations in the circuit, we need to consider the values of the capacitance and inductance.

Given: - Capacitance (C) = 10 pF - Inductance (L) = 100 μH

The period of free oscillations (T) can be calculated using the formula:

T = 2π√(LC)

Substituting the given values into the formula, we get:

T = 2π√(10 pF * 100 μH)

Converting the units to farads (F) and henries (H):

T = 2π√(10 * 10^(-12) F * 100 * 10^(-6) H)

Simplifying the expression:

T = 2π√(10 * 10^(-18) F * 100 * 10^(-6) H)

T = 2π√(10 * 10^(-24) F * H)

T = 2π√(10 * 10^(-24)) * √(F * H)

T = 2π * 10^(-12) * √(F * H)

T ≈ 2π * 10^(-12) s

Therefore, the period of free oscillations in the circuit is approximately 2π * 10^(-12) seconds.

Calculation of the Maximum Current

To determine the maximum value of the current in the circuit, we need to consider the voltage and the reactance of the inductor.

Given: - Voltage (V) = 100 V - Inductance (L) = 100 μH

The reactance of an inductor (XL) can be calculated using the formula:

XL = 2πfL

Where: - XL is the reactance of the inductor - f is the frequency of the oscillations - L is the inductance

Since we are dealing with free oscillations, the frequency (f) can be calculated using the formula:

f = 1 / T

Substituting the given values into the formula, we get:

f = 1 / (2π * 10^(-12) s)

Simplifying the expression:

f ≈ 1 / (6.28 * 10^(-12) s)

f ≈ 1.59 * 10^(11) Hz

Now, substituting the frequency and inductance values into the reactance formula, we get:

XL = 2π * (1.59 * 10^(11) Hz) * (100 * 10^(-6) H)

Simplifying the expression:

XL = 2π * 1.59 * 10^(11) * 100 * 10^(-6) Ω

XL ≈ 1 Ω

The maximum current (Imax) can be calculated using Ohm's Law:

Imax = V / XL

Substituting the given voltage and reactance values, we get:

Imax = 100 V / 1 Ω

Simplifying the expression:

Imax = 100 A

Therefore, the maximum value of the current in the circuit is 100 Amperes.

Please note that the calculations provided are based on the given values and assumptions.