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Консультация № 197932
06.03.2020, 16:51
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Зависимость силы тока от времени в колебательном контуре определяется следующим образом: I(t) = Imcosωt, где ω = 10^3 рад/c. Найти индуктивность L контура, если его электроемкость С = 10^-5 Ф.
Сделать схематический рисунок.
Зависимость силы тока от времени в колебательном контуре определяется следующим образом: I(t) = Imcosωt, где ω = 10^3 рад/c. Найти индуктивность L контура, если его электроемкость С = 10^-5 Ф.
Сделать схематический рисунок.
Обсуждение
07.03.2020, 09:31
общий
это ответ
Здравствуйте, dar777!
Дано: Ток I(t) = Im·cos([$969$]·t) , Круговая частота [$969$] = 103 рад/c, электро-ёмкость С = 10-5 Ф .
Вычислить индуктивность L контура.
Решение : Амплитуда Im гармонических колебаний в контуре постоянна (не затухает от времени). Упоминание об источнике принудительных колебаний отсутствует в Условии задачи. Это значит, в контуре происходят свободные электро-магнитные колебания (см учебную статью "Электромагнитные колебания. ЕГЭ" Ссылка1 )
Циклическая частота этих колебаний равна: [$969$] = 1 / [$8730$](L·C)
Из этой формулы легко найти L·C = 1 / [$969$]2
Искомая L = 1 / (C·[$969$]2) = 1 / (10-5·10002)= 0,1 Гн
Ответ : индуктивность контура равна 0,1 Генри.
Схематический рисунок Вы можете скопировать из выше-указанной мною учебной статьи.
Дано: Ток I(t) = Im·cos([$969$]·t) , Круговая частота [$969$] = 103 рад/c, электро-ёмкость С = 10-5 Ф .
Вычислить индуктивность L контура.
Решение : Амплитуда Im гармонических колебаний в контуре постоянна (не затухает от времени). Упоминание об источнике принудительных колебаний отсутствует в Условии задачи. Это значит, в контуре происходят свободные электро-магнитные колебания (см учебную статью "Электромагнитные колебания. ЕГЭ" Ссылка1 )
Циклическая частота этих колебаний равна: [$969$] = 1 / [$8730$](L·C)
Из этой формулы легко найти L·C = 1 / [$969$]2
Искомая L = 1 / (C·[$969$]2) = 1 / (10-5·10002)= 0,1 Гн
Ответ : индуктивность контура равна 0,1 Генри.
Схематический рисунок Вы можете скопировать из выше-указанной мною учебной статьи.
5
Это самое лучшее решение!
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