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Консультация № 197602
18.01.2020, 02:32
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Три конденсатора емкостями С1= 5мкФ, С2 =8 мкФ и С3 = 2мкФ соединены последовательно и присоединены к батарее с э.д.с. е=80 В. Определить заряды q1,q2,q3 конденсаторов и разности потенциалов U1,U2,U3 между их обкладками.
Три конденсатора емкостями С1= 5мкФ, С2 =8 мкФ и С3 = 2мкФ соединены последовательно и присоединены к батарее с э.д.с. е=80 В. Определить заряды q1,q2,q3 конденсаторов и разности потенциалов U1,U2,U3 между их обкладками.
Обсуждение
19.01.2020, 15:59
общий
это ответ
Здравствуйте, ssrazumov!
Дано : Ёмкости С1= 5мкФ, С2 =8 мкФ и С3 = 2мкФ, ЭДС= E = 80 Вольт.
Вычислить заряды и напряжения на конденсаторах.
Решение : Если бы источник ЭДС подсоединили к параллельно-соединённым конденсаторам, то на каждом конденсаторе стало бы одинаковое напряжение E = 80 Вольт. Но поскольку конденсаторы соединены последовательно, то через каждый конденсатор прошёл одинаковый зарядный электро-ток за одинаковое время. Ток, спадающий по экспоненциальному закону, зарядит все 3 конденсатора практически мгновенно (за несколько микро-секунд). Поэтому не отвлекаемся на изучение переходного процесса, а примем к сведению, что все конденсаторы получили одинаковый заряд. Какой именно заряд?
Ёмкость батареи из 3х последовательно-соединённых конденсаторов вычисляется по формуле :
C = 1 / (1/C1 + 1/C2 + 1/C3) = 1 / (1/5 + 1/8 + 1/2) = 40/33 = 1,212 мкФ (см учебную статью "Электроёмкость. Конденсаторы" Ссылка1 )
Заряд батареи конденсаторов (он же - заряд на каждом из 3х конденсаторов)
q = C·E = 97,0 мкКл
Напряжения на конденсаторах : U1 = q / C1 = 97,0 / 5 = 19,4 В,
U2 = q / C2 = 97,0 / 8 = 12,1 В,
U3 = q / C3 = 97,0 / 2 = 48,5 В.
Ответ : разности потенциалов между обкладками конденсаторов C1, C2, C3 равны U1 = 19,4 В, U2 = 12,1 В, U3 = 48,5 В.
Заряды всех конденсаторов одинаковы и равны q = 97 мкКл.
Проверяем : сумма напряжений на всех конденсаторах должна равняться ЭДС источника:
U1 + U2 + U3 = 19,4 + 12,1 + 48,5 = 80 Вольт. Проверка успешна!
Дано : Ёмкости С1= 5мкФ, С2 =8 мкФ и С3 = 2мкФ, ЭДС= E = 80 Вольт.
Вычислить заряды и напряжения на конденсаторах.
Решение : Если бы источник ЭДС подсоединили к параллельно-соединённым конденсаторам, то на каждом конденсаторе стало бы одинаковое напряжение E = 80 Вольт. Но поскольку конденсаторы соединены последовательно, то через каждый конденсатор прошёл одинаковый зарядный электро-ток за одинаковое время. Ток, спадающий по экспоненциальному закону, зарядит все 3 конденсатора практически мгновенно (за несколько микро-секунд). Поэтому не отвлекаемся на изучение переходного процесса, а примем к сведению, что все конденсаторы получили одинаковый заряд. Какой именно заряд?
Ёмкость батареи из 3х последовательно-соединённых конденсаторов вычисляется по формуле :
C = 1 / (1/C1 + 1/C2 + 1/C3) = 1 / (1/5 + 1/8 + 1/2) = 40/33 = 1,212 мкФ (см учебную статью "Электроёмкость. Конденсаторы" Ссылка1 )
Заряд батареи конденсаторов (он же - заряд на каждом из 3х конденсаторов)
q = C·E = 97,0 мкКл
Напряжения на конденсаторах : U1 = q / C1 = 97,0 / 5 = 19,4 В,
U2 = q / C2 = 97,0 / 8 = 12,1 В,
U3 = q / C3 = 97,0 / 2 = 48,5 В.
Ответ : разности потенциалов между обкладками конденсаторов C1, C2, C3 равны U1 = 19,4 В, U2 = 12,1 В, U3 = 48,5 В.
Заряды всех конденсаторов одинаковы и равны q = 97 мкКл.
Проверяем : сумма напряжений на всех конденсаторах должна равняться ЭДС источника:
U1 + U2 + U3 = 19,4 + 12,1 + 48,5 = 80 Вольт. Проверка успешна!
5
Спасибо!!!
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