Question

Изменение силы тока в колебательном контуре происходит по закону i=1,2sin15,7t. Определите амплитудное значение силы тока, действующее значение тока, период и частоту собственных колебаний контура. Буду крайне благодарна за помощь.

Answer 1

Imax =1,2A - амплитуда силы тока
I=Imax/√2 =1,2/√2 ≈ 0,85A - действующее значение силы тока
ω=15,7 1/c -циклическая (круговая) частота
ν =ω/2π =15,7/2*3,14 =2,5 Гц  -частота
T=1/ν =1/2,5=0,4 c период

Answer 2

Amplitude of Current:

The amplitude of the current in the oscillating circuit can be determined from the given equation i = 1.2sin(15.7t). In this equation, the coefficient of the sine function represents the amplitude of the current. Therefore, the amplitude of the current is 1.2.

Effective Value of Current:

The effective value of the current, also known as the root mean square (RMS) value, can be calculated using the formula I_eff = (I_max)/sqrt(2), where I_max is the amplitude of the current. Substituting the value of I_max as 1.2, we can calculate the effective value of the current as follows:

I_eff = (1.2)/sqrt(2) = 0.848 A (rounded to three decimal places).

Period and Frequency of Self-Oscillations:

To determine the period and frequency of the self-oscillations of the circuit, we need to analyze the given equation i = 1.2sin(15.7t). In this equation, the coefficient of 't' inside the sine function represents the angular frequency (ω) of the oscillations.

The angular frequency (ω) can be calculated using the formula ω = 2πf, where f is the frequency of the oscillations. Comparing this formula with the given equation, we can determine that 15.7 = 2πf.

Solving for f, we get:

f = 15.7/(2π) ≈ 2.5 Hz (rounded to one decimal place).

The period (T) of the oscillations can be calculated using the formula T = 1/f. Substituting the value of f as 2.5 Hz, we can calculate the period as follows:

T = 1/2.5 ≈ 0.4 s (rounded to one decimal place).

Therefore, the period of the self-oscillations of the circuit is approximately 0.4 seconds, and the frequency is approximately 2.5 Hertz.