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Консультация № 196064
06.08.2019, 19:30
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Записать правила Кирхгофа для предложенной схемы.
Записать правила Кирхгофа для предложенной схемы.
Прикрепленные файлы:
Обсуждение
08.08.2019, 15:17
общий
это ответ
Здравствуйте, dar777!
Для облегчения решения задачи полезно на Вашей схеме обозначить предполагаемые направления токов и напряжений и задать для них позиционные обозначения (I1 , I2 … U3). Задаём зелёной стрелкой направление обхода контура.
В Вашей схеме 2 узла (точки B и E) и 3 ветви, образующие 2 контура. Значит, по первому закону Кирхгофа надо составить 2-1=1 уравнений (кол-во_узлов - 1) :
I1 = I2 + I3
Если цепь содержит P узлов и M ветвей, то она описывается M-(P-1) уравнениями напряжений. В нашем случае осталось добавить 2 уравнения по Второму закону Кирхгофа : алгебраич сумма ЭДС, действующая в замкнутом контуре, равна алгебраич сумме падений напряжения в этом контуре. Суммируем ЭДС и напряжения соответственно, беря со знаком плюс, если величина совпадает с направлением обхода и минус, если не совпадает :
E1 = I3·R2 + I1·R1
E2 = I2·R3 - I3·R2
Эта полная система 3х линейных уравнений позволяет найти все токи и напряжения.
Её решение (получено в Маткаде ru.wikipedia.org/wiki/Mathcad ) :
I1 = (E1·R2 + E1·R3 + E2·R2) / RR
I2 = (E1·R2 + E2·R1 + E2·R2) / RR
I3 = (E2·R1 - E1·R3) / RR
здесь RR = R1·R2 + R1·R3 + R2·R3
Упрощённая проверка : При E1 = E2 = 10 Вольт , R1 = R2 = R3 = 1 Ом получаем I1 = 10А , I2 = 10 А , I3 = 0.
Если R1 оборвать, тогда I1 = 0 , I2 = 5 А , I3 = -5 А . Проверка успешна.
см Законы Кирхгофа electroandi.ru/toe/dc/zakony-kirkhgofa.html
Для облегчения решения задачи полезно на Вашей схеме обозначить предполагаемые направления токов и напряжений и задать для них позиционные обозначения (I1 , I2 … U3). Задаём зелёной стрелкой направление обхода контура.
В Вашей схеме 2 узла (точки B и E) и 3 ветви, образующие 2 контура. Значит, по первому закону Кирхгофа надо составить 2-1=1 уравнений (кол-во_узлов - 1) :
I1 = I2 + I3
Если цепь содержит P узлов и M ветвей, то она описывается M-(P-1) уравнениями напряжений. В нашем случае осталось добавить 2 уравнения по Второму закону Кирхгофа : алгебраич сумма ЭДС, действующая в замкнутом контуре, равна алгебраич сумме падений напряжения в этом контуре. Суммируем ЭДС и напряжения соответственно, беря со знаком плюс, если величина совпадает с направлением обхода и минус, если не совпадает :
E1 = I3·R2 + I1·R1
E2 = I2·R3 - I3·R2
Эта полная система 3х линейных уравнений позволяет найти все токи и напряжения.
Её решение (получено в Маткаде ru.wikipedia.org/wiki/Mathcad ) :
I1 = (E1·R2 + E1·R3 + E2·R2) / RR
I2 = (E1·R2 + E2·R1 + E2·R2) / RR
I3 = (E2·R1 - E1·R3) / RR
здесь RR = R1·R2 + R1·R3 + R2·R3
Упрощённая проверка : При E1 = E2 = 10 Вольт , R1 = R2 = R3 = 1 Ом получаем I1 = 10А , I2 = 10 А , I3 = 0.
Если R1 оборвать, тогда I1 = 0 , I2 = 5 А , I3 = -5 А . Проверка успешна.
см Законы Кирхгофа electroandi.ru/toe/dc/zakony-kirkhgofa.html
5
Это самое лучшее решение!
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