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Консультация № 201547
25.10.2021, 09:59
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Здравствуйте, уважаемые эксперты! Прошу вас решить следующую задачу:
Какой физический процесс происходит в последовательной замкнутой цепи, состоящей из источника переменного напряжения с круговой частотой W = 500 и величиной 12 V, резистора R = 12 Ом, конденсатора C= 80 мкФ и катушки индуктивности = 50mГн. Определить величину тока в цепи и величину напряжения на конденсаторе и величину напряжения на катушке индуктивности.
Какой физический процесс происходит в последовательной замкнутой цепи, состоящей из источника переменного напряжения с круговой частотой W = 500 и величиной 12 V, резистора R = 12 Ом, конденсатора C= 80 мкФ и катушки индуктивности = 50mГн. Определить величину тока в цепи и величину напряжения на конденсаторе и величину напряжения на катушке индуктивности.
Обсуждение
27.10.2021, 03:00
общий
27.10.2021, 04:23
это ответ
Условие : Напряжение источника U = 12 В, круговая частота [$969$] = 500 рад/с, сопротивление R = 12 Ом, ёмкость C= 80·10-6 Ф, индуктивность L = 0,05 Гн.
Вычислить величину тока в цепи, величину напряжения на конденсаторе и величину напряжения на катушке индуктивности;
Классифицировать физический процесс, происходящий в заданной цепи.
Решение : В заданном последовательном колебательном контуре происходят так называемые Вынужденные колебания (навязанные от Источника напряжения, см "методичку" "Вынужденные электрические колебания" Ссылка от томского политех-университета).
Реактивное сопротивление конденсатора XC = 1 / ([$969$]·C) = 25 Ом;
Реактивное сопротивление катушки индуктивности XL = [$969$]·L = 25 Ом;
Общее комплексное сопротивление цепи : Z = R + j·(XL - XC) = 12 + j·(25 - 25) = 12 Ом - чисто активное. Значит, Контур находится в Резонансе напряжений.
Ток в цепи : i = U / Z = 12 / 12 = 1 А по закону Ома.
Ответ : Величина тока в цепи 1 Ампер;
Величина напряжения на конденсаторе UC = i·XC = 25 В;
Величина напряжения на катушке индуктивности UL = i·XL = 25 В;
Проверка : Комплексная сумма напряжений на всех элементах цепи должна равняться напряжению Источника напряжения:
Us = i·R + j·(i·XL - i·XC) = 1·12 + j·(1·25 - 1·25) = 12 + j·0 = 12 В = U , в чём и требовалось убедиться.
Вычислить величину тока в цепи, величину напряжения на конденсаторе и величину напряжения на катушке индуктивности;
Классифицировать физический процесс, происходящий в заданной цепи.
Решение : В заданном последовательном колебательном контуре происходят так называемые Вынужденные колебания (навязанные от Источника напряжения, см "методичку" "Вынужденные электрические колебания" Ссылка от томского политех-университета).
Реактивное сопротивление конденсатора XC = 1 / ([$969$]·C) = 25 Ом;
Реактивное сопротивление катушки индуктивности XL = [$969$]·L = 25 Ом;
Общее комплексное сопротивление цепи : Z = R + j·(XL - XC) = 12 + j·(25 - 25) = 12 Ом - чисто активное. Значит, Контур находится в Резонансе напряжений.
Ток в цепи : i = U / Z = 12 / 12 = 1 А по закону Ома.
Ответ : Величина тока в цепи 1 Ампер;
Величина напряжения на конденсаторе UC = i·XC = 25 В;
Величина напряжения на катушке индуктивности UL = i·XL = 25 В;
Проверка : Комплексная сумма напряжений на всех элементах цепи должна равняться напряжению Источника напряжения:
Us = i·R + j·(i·XL - i·XC) = 1·12 + j·(1·25 - 1·25) = 12 + j·0 = 12 В = U , в чём и требовалось убедиться.
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