Question

Соленоид идеального колебательного контура имеет индуктивность 100 мГн, а ток в нем измеряется по закону i=0,05*cos10^5 . Найти максимальное значение энергии поля кондесатора

Answer 1

W=L*I²/2        W=100*10⁻³*0,05*0,05/2=0,000125 Дж

Answer 2

Solving for the Maximum Energy of the Capacitor in an Ideal Oscillatory Circuit

To find the maximum value of the energy stored in the capacitor in an ideal oscillatory circuit, we need to determine the maximum value of the current and the maximum value of the voltage across the capacitor.

Given: - Inductance (L) = 100 mH = 0.1 H - Current (i) = 0.05 * cos(10^5 t)

To find the maximum value of the current, we can use the amplitude of the cosine function, which is 0.05.

To find the maximum value of the voltage across the capacitor, we can use the relationship between voltage and current in an ideal oscillatory circuit. In an ideal oscillatory circuit, the voltage across the capacitor (Vc) is given by the equation:

Vc = -L * di/dt

Where: - Vc is the voltage across the capacitor - L is the inductance of the circuit - di/dt is the derivative of the current with respect to time

Taking the derivative of the current equation, we get:

di/dt = -0.05 * 10^5 * sin(10^5 t)

Substituting the values into the equation for the voltage across the capacitor, we get:

Vc = -0.1 * (-0.05 * 10^5 * sin(10^5 t))

Simplifying the equation, we have:

Vc = 0.5 * 10^5 * sin(10^5 t)

Now, we can find the maximum value of the voltage across the capacitor by taking the absolute value of the amplitude of the sine function, which is 0.5 * 10^5.

Finally, to find the maximum energy stored in the capacitor, we can use the equation:

E = 0.5 * C * Vc^2

Where: - E is the energy stored in the capacitor - C is the capacitance of the circuit - Vc is the voltage across the capacitor

Since the circuit is ideal, the energy stored in the capacitor is equal to the energy stored in the inductor. Therefore, we can use the same equation to find the maximum energy stored in the inductor.

Please note that the value of the capacitance (C) is not provided in the given information. If you have the value of the capacitance, please provide it so that we can calculate the maximum energy stored in the capacitor.

Let me know if you have any further questions!