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Консультация № 199771
04.12.2020, 12:32
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Уважаемые эксперты! Пожалуйста, помогите решить задачу! 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 на выводах цепи, падения напряжения на всех участках цепи, а также активную, реактивную и полную мощность цепи. Вычертить электрическую схему и векторную диаграмму токов и напряжений.
Обсуждение
08.12.2020, 13:50
общий
Адресаты:
Я долго старался в решении Вашей предыдущей задачи rfpro.ru/question/199621 (ссылка) , чертил красивые цветные график и схему, сделал проверку вычислений.
А Вы не постарались вникнуть в свою задачу и в моё решение, и снизили мне Оценку. Лучше я помогу благодарным просителям.
А Вы не постарались вникнуть в свою задачу и в моё решение, и снизили мне Оценку. Лучше я помогу благодарным просителям.
09.12.2020, 07:53
общий
это ответ
Здравствуйте, 9033332793!
Ток в цепи определяем по формуле для закона Ома в комплексной форме:
где U - входное напряжение, Z - полное комплексное сопротивление цепи. В данном случае, для цепи, состоящей из последовательно соединённых активного сопротивления R, индуктивности L и ёмкости С, оно равно
При заданных исходных данных [$969$] = 2[$960$]f = 2[$183$]3.1416[$183$]100 = 628.32 c[sup]-1[/sup], R = 4 Ом, [$969$]L = 628.32[$183$]0.0063 = 3.9584 Ом, 1/[$969$]C = 1/628.32[$183$]0.00016 = 9.9472 Ом. Подставляя эти значения, получаем
Фазовый сдвиг тока относительно напряжения определяется выражением
откуда [$966$] = arccos 0.5554 = 56[$186$]
Падение напряжения на отдельных элементах определяется по закону Ома как произведение силы тока на комплексное сопротивление элемента, равное R для сопротивления, j[$969$]L для индуктивности и -j/[$969$]C для ёмкости. В данном случае
Можно заметить, что U[sub]R[/sub]+U[sub]L[/sub]+U[sub]C[/sub] = U, что подтверждает правильность решения.
Для цепи с силой тока i и комплексным сопротивлением Z потребляемая мощность определяется как P = |i|[sup]2[/sup][$183$]Z. В данном случае
то есть суммарная активная мощность элементов равна 1110.566 Вт, а реактивная 1662.733 ВАр.
Ток в цепи определяем по формуле для закона Ома в комплексной форме:
где U - входное напряжение, Z - полное комплексное сопротивление цепи. В данном случае, для цепи, состоящей из последовательно соединённых активного сопротивления R, индуктивности L и ёмкости С, оно равно
При заданных исходных данных [$969$] = 2[$960$]f = 2[$183$]3.1416[$183$]100 = 628.32 c[sup]-1[/sup], R = 4 Ом, [$969$]L = 628.32[$183$]0.0063 = 3.9584 Ом, 1/[$969$]C = 1/628.32[$183$]0.00016 = 9.9472 Ом. Подставляя эти значения, получаем
Фазовый сдвиг тока относительно напряжения определяется выражением
откуда [$966$] = arccos 0.5554 = 56[$186$]
Падение напряжения на отдельных элементах определяется по закону Ома как произведение силы тока на комплексное сопротивление элемента, равное R для сопротивления, j[$969$]L для индуктивности и -j/[$969$]C для ёмкости. В данном случае
Можно заметить, что U[sub]R[/sub]+U[sub]L[/sub]+U[sub]C[/sub] = U, что подтверждает правильность решения.
Для цепи с силой тока i и комплексным сопротивлением Z потребляемая мощность определяется как P = |i|[sup]2[/sup][$183$]Z. В данном случае
то есть суммарная активная мощность элементов равна 1110.566 Вт, а реактивная 1662.733 ВАр.
5
Спасибо огромное!
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