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Консультация № 200034
04.01.2021, 21:04
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Здравствуйте! Прошу помощи в следующем вопросе: Электрическая цепь, состоящая из двух последовательно соединенных сопротивлений, подключена к источнику постоянного напряжения. Одно из сопротивлений переменное. При изменении этого сопротивления на нем выделяется мощность 16 Вт при двух значениях сопротивления 1 Ом и 4 Ом.
Найдите наибольшую мощность, которая выделялась на переменном сопротивлении в этом эксперименте. Ответ приведите в [Вт].
Большое спасибо за помощь!
Найдите наибольшую мощность, которая выделялась на переменном сопротивлении в этом эксперименте. Ответ приведите в [Вт].
Большое спасибо за помощь!
Обсуждение
05.01.2021, 16:27
общий
это ответ
Здравствуйте, maks.zverkov.05!
Условие : R1 = 1 Ом ; R2 = 4 Ом ; P0 = 16 Вт.
Вычислить макси-мощность Pm .
Решение : Чертим электро-схему Вашей эл-цепи и видим, что эта цепь - простейшая, НЕразветвлённая и линейная (не содержит НЕлинейных элементов).
Значит ток можно вычислять по закону Ома I = E / (r + R)
Мощность на переменном резистрое R равна P = I2·R
Нам не известны ни ЭДС E источника, ни сопротивление r постоянного резистора.
Поэтому находим производную функции P(R) и приравниваем её нулю.
Составляем систему из 3х уравнений.
Решать эту систему Вы можете любым удобным Вам способом. Я решаю в приложении Маткад (ссылка) . Маткад работает быстро и избавляет меня от частых ошибок. Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : наибольшая мощность, которая выделялась на переменном сопротивлении в этом эксперименте, равна 18 Вт.
Электро-схему, формулы и проверочный график прилагаю.
Условие : R1 = 1 Ом ; R2 = 4 Ом ; P0 = 16 Вт.
Вычислить макси-мощность Pm .
Решение : Чертим электро-схему Вашей эл-цепи и видим, что эта цепь - простейшая, НЕразветвлённая и линейная (не содержит НЕлинейных элементов).
Значит ток можно вычислять по закону Ома I = E / (r + R)
Мощность на переменном резистрое R равна P = I2·R
Нам не известны ни ЭДС E источника, ни сопротивление r постоянного резистора.
Поэтому находим производную функции P(R) и приравниваем её нулю.
Составляем систему из 3х уравнений.
Решать эту систему Вы можете любым удобным Вам способом. Я решаю в приложении Маткад (ссылка) . Маткад работает быстро и избавляет меня от частых ошибок. Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : наибольшая мощность, которая выделялась на переменном сопротивлении в этом эксперименте, равна 18 Вт.
Электро-схему, формулы и проверочный график прилагаю.
5
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