Question

В цепь переменного тока стандартной частоты (n=50 Гц) с напряжением U=220В последовательно включены активное сопротивление R=150 Ом и конденсатор С=16мкФ. Найти максимальное значение силы тока Im.

Answer 1

Ответ:

Объяснение:

Дано:

ν = 50 Гц

U = 220 В

R = 150 Ом

C = 16 мкФ = 16·10⁻⁶ Ф

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Imax - ?

1)

Находим емкостное сопротивление:

Xc = 1 / (2π·ν·C) = 1 / (2·3,14·50·16·10⁻⁶) ≈ 200 Ом

2)

Полное сопротивление цепи:

Z = √ (R² + Xc²) = √ (150² + 200²) ≈ 250 Ом

3)

Действующее значение силы тока:

I = U / Z = 220 / 250 = 0,88 А

4)

Максимальное значение силы тока:

Imax = √(2) · I ≈ 1,41·0,88 ≈  1,2 A

Answer 2

Calculation of Maximum Current (Im) in an AC Circuit

To find the maximum value of the current (Im) in a series circuit with a standard frequency (n = 50 Hz) and voltage (U = 220 V), where an active resistance (R = 150 Ω) and a capacitor (C = 16 μF) are connected in series, we can use the following steps:

1. Calculate the reactance of the capacitor (Xc): - The reactance of a capacitor in an AC circuit is given by the formula Xc = 1 / (2πfC), where f is the frequency and C is the capacitance. - Substituting the given values, we have Xc = 1 / (2π * 50 * 16 * 10^(-6)).

2. Calculate the impedance of the circuit (Z): - The impedance of a series circuit is given by the formula Z = √(R^2 + Xc^2), where R is the resistance and Xc is the reactance of the capacitor. - Substituting the calculated value of Xc and the given value of R, we have Z = √(150^2 + Xc^2).

3. Calculate the maximum current (Im): - The maximum current in an AC circuit is given by the formula Im = U / Z, where U is the voltage and Z is the impedance. - Substituting the given value of U and the calculated value of Z, we have Im = 220 / Z.

Let's calculate the maximum current (Im) using the above steps.

1. Calculate the reactance of the capacitor (Xc): - Xc = 1 / (2π * 50 * 16 * 10^(-6)) - Xc ≈ 198.94 Ω

2. Calculate the impedance of the circuit (Z): - Z = √(150^2 + Xc^2) - Z ≈ √(22500 + 198.94^2) - Z ≈ √(22500 + 39578.03) - Z ≈ √(62078.03) - Z ≈ 249.16 Ω

3. Calculate the maximum current (Im): - Im = 220 / Z - Im ≈ 220 / 249.16 - Im ≈ 0.883 A

Therefore, the maximum value of the current (Im) in the given AC circuit is approximately 0.883 A.