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Консультация № 196016
23.07.2019, 20:17
0.00 руб.
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1
1
Здравствуйте! Прошу помощи в следующем вопросе:
В RLC-контуре сопротивление 2 Ом, индуктивность 20 мГн, ёмкость 2 мФ. Определить период колебаний.
В RLC-контуре сопротивление 2 Ом, индуктивность 20 мГн, ёмкость 2 мФ. Определить период колебаний.
Обсуждение
24.07.2019, 15:40
общий
это ответ
Здравствуйте, dar777!
В условии задачи не уточнено, какой именно подразумевается RLC-контур : последовательный либо параллельный? Будем полагать, будто задан последовательный колебательный контур, как более популярный в учебных задачах (на практике чаще применяются параллельные колебат-контуры).
В учебной статье "Свободные затухающие электрические колебания" Ссылка1 выведены нужные нам формулы : Собственная частота контура, Частота затухающих колебаний…
Вычисления удобно делать в бесплатном приложении ru.wikipedia.org/wiki/Mathcad . Маткад вычисляет всё быстро и страхует от ошибок типа "человеческий фактор". Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : Период колебаний заданного последовательного контура равен 42 мСек .
Я также вычислил Волновое сопротивление контура Rвол = 3,2 Ом , оно больше, чем заданное R=2 Ом . Значит, предположение, будто для решения задан последовательный контур, верно. Ибо в параллельном контуре с такими же значениями Rвол и R вместо колебания произойдёт апериодический разряд. (В последовательном контуре чем меньше R , тем меньше затухание, а в параллельном контуре - наоборот: чем меньше R , тем больше затухание).
В условии задачи не уточнено, какой именно подразумевается RLC-контур : последовательный либо параллельный? Будем полагать, будто задан последовательный колебательный контур, как более популярный в учебных задачах (на практике чаще применяются параллельные колебат-контуры).
В учебной статье "Свободные затухающие электрические колебания" Ссылка1 выведены нужные нам формулы : Собственная частота контура, Частота затухающих колебаний…
Вычисления удобно делать в бесплатном приложении ru.wikipedia.org/wiki/Mathcad . Маткад вычисляет всё быстро и страхует от ошибок типа "человеческий фактор". Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : Период колебаний заданного последовательного контура равен 42 мСек .
Я также вычислил Волновое сопротивление контура Rвол = 3,2 Ом , оно больше, чем заданное R=2 Ом . Значит, предположение, будто для решения задан последовательный контур, верно. Ибо в параллельном контуре с такими же значениями Rвол и R вместо колебания произойдёт апериодический разряд. (В последовательном контуре чем меньше R , тем меньше затухание, а в параллельном контуре - наоборот: чем меньше R , тем больше затухание).
5
Это самое лучшее решение!
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