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Консультация № 200611

10.04.2021, 19:50

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Теле-радио-аппаратура

Здравствуйте! Прошу помощи в следующем вопросе: Неразветвленная электрическая цепь, у которой R = 4 Ом, L = 6,3 мГн, С = 160 мкФ питается от генератора синусоидального тока с f = 100 Гц и напряжением 120 В. Вычислить ток в цепи, косинус угла сдвига между током и напряжением, реактивную и полную мощность цепи. Вычертить электрическую схему и векторную диаграмму токов и напряжений.

Обсуждение

давно

Посетитель
226425
1567

10.04.2021, 23:52

общий

это ответ

Здравствуйте, k.kristina.88!
Дано:
R = 4 Ом
L = 6,3 мГн = 6,3*10^-3 Гн
С = 160 мкФ = 160*10^-6 Ф
f = 100 Гц
U = 120 В
Найти:
I; cos[$966$]; Q; S
Решение:
Последовательная неразветвленная R-L-C-цепь изображена на рис.1

Рис.1.

1. Индуктивное сопротивление цепи
X_L=2[$960$]*f*L = 3,97 Ом;
2. Ёмкостное сопротивление цепи
X_C=1/2[$960$]*f*C = 9,92 Ом;
3. Реактивное сопротивление
X=|X_L-X_C| = 5,95 Ом;
4. Полное сопротивление
Z=[$8730$](X²+R²) = 7,2 Ом;
5. Коэффициент мощности
cos[$966$]=R/Z = 0,555;
6. Сила тока в цепи (по закону Ома)
I=U/Z = 16,7 A;
7. Полная мощность
S=U*I = 2004 В*А;
8. Реактивная мощность
Q=S*sin[$966$] = 1666 ВАр,
где
[$966$]=arccos 0,555 = 56,25[$176$] - угол сдвига фаз между током и напряжением.
Векторная диаграмма токов и напряжений (не в масштабе) представлена ниже на рис.2.

Рис.2.

Удачи

5

Спасибо большое!

Об авторе:
С уважением
shvetski

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