Question

Залежність сили струму від часу в коливальному контурі визначається рівнянням t=0,04sin800Πt. Індуктивність котушки в контурі 0,4 Гн. Знайдіть період коливань та максимальне значення енергії електричного поля

Answer 1

Відповідь:

16000

Пояснення:

Answer 2

Calculation of the Period of Oscillations

To find the period of oscillations in the given circuit, we can use the formula:

Period (T) = 2π / angular frequency (ω)

The angular frequency (ω) can be determined from the equation provided:

t = 0.04sin(800πt)

Comparing this equation with the standard form of a sinusoidal function, we can see that the angular frequency (ω) is equal to 800π.

Substituting this value into the formula for the period, we get:

T = 2π / (800π) = 1 / 400 ≈ 0.0025 seconds

Therefore, the period of oscillations in the given circuit is approximately 0.0025 seconds.

Calculation of the Maximum Value of Electric Field Energy

To calculate the maximum value of the electric field energy, we need to consider the energy stored in the inductor (coil) of the circuit. The energy stored in an inductor can be calculated using the formula:

Energy (E) = (1/2) * inductance (L) * current^2

In the given circuit, the inductance (L) is given as 0.4 H (henries). The current (I) can be determined from the equation provided:

I = 0.04sin(800πt)

To find the maximum value of the current, we can consider the maximum value of the sine function, which is 1. Therefore, the maximum value of the current is:

I_max = 0.04 * 1 = 0.04 A (amperes)

Substituting the values of inductance (L) and current (I_max) into the formula for energy, we get:

E_max = (1/2) * 0.4 * (0.04)^2 = 0.00016 J (joules)

Therefore, the maximum value of the electric field energy in the given circuit is approximately 0.00016 joules.

Please note that the calculations provided are based on the information given in the question.

Answer 3

Calculation of the Period of Oscillations

The equation given, t = 0.04sin(800πt), represents the time dependence of the current in the oscillating circuit. To find the period of oscillations, we need to determine the time it takes for the current to complete one full cycle.

The general form of a sinusoidal function is given by y = Asin(Bx + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift. In this case, the equation can be rewritten as t = 0.04sin(800πt) = 0.04sin(2πft), where f is the frequency.

Comparing this equation with the general form, we can see that B = 2πf. Therefore, the frequency of oscillations is f = 800 Hz.

The period of oscillations (T) is the reciprocal of the frequency, so T = 1/f. Substituting the value of f, we get T = 1/800 s = 0.00125 s.

The period of oscillations in the given circuit is 0.00125 seconds.

Calculation of the Maximum Value of Electric Field Energy

To find the maximum value of the electric field energy, we need to consider the energy stored in the inductor of the circuit. The energy stored in an inductor is given by the formula:

E = (1/2) * L * I^2,

where E is the energy, L is the inductance, and I is the current.

In this case, the inductance of the coil is given as 0.4 H (Henry) and the current is given by the equation t = 0.04sin(800πt).

To find the maximum value of the current, we can take the derivative of the equation with respect to time and set it equal to zero. However, since the equation is already in the form of a sinusoidal function, we can directly determine the maximum value of the current.

The maximum value of the current is equal to the amplitude of the sinusoidal function, which is 0.04 A.

Substituting the values of L and I into the formula for energy, we get:

E = (1/2) * 0.4 * (0.04)^2 = 0.000032 J.

The maximum value of the energy of the electric field in the given circuit is 0.000032 Joules.