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Консультация № 194624
07.02.2019, 17:21
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1
Здравствуйте! Прошу помощи в следующем вопросе:
342. Определить электродвижущую силу аккумуляторной батареи, ток короткого замыкания которой 10 А, если при подключении к ней резистора 2 Ом сила тока в цепи равна 1 А.
342. Определить электродвижущую силу аккумуляторной батареи, ток короткого замыкания которой 10 А, если при подключении к ней резистора 2 Ом сила тока в цепи равна 1 А.
Обсуждение
08.02.2019, 13:27
общий
это ответ
Здравствуйте, dar777!
Ваша простая, НЕразветвлённая эл-цепь содержит всего 3 элемента : Источник ЭДС с искомым значением E , его внутреннее сопротивление Ri и сопротивление нагрузки Rн = 2 Ом.
По закону Ома ток нагрузки в такой цепи равен
Iн = E / (Ri + Rн) = 1 Ампер (1)
При коротком замыкании резистор нагрузки закорочен перемычкой, и тогда ток короткого замыкания ограничен малым внутренним сопротивлением самого источника ЭДС :
Iкз = E / Ri = 10 А (2)
Выражение Ri = E / Iкз , полученное из уравнения (2), подставляем в первое выражение :
Iн = E / (E / Iкз + Rн)
Решаем уравнение : E / Iкз + Rн = E / Iн
E / Iн - E / Iкз = Rн
E = Rн / (1/ Iн - 1 / Iкз) = Rн·Iн·Iкз / (Iкз - Iн) = 2·1·10 / (10-1) = 20/9 = 2,222 Вольт.
Проверяем : Ri = E / Iкз = (20/9) / 10 = 2/9 Ом
Iн = E / (Ri + Rн) = (20/9) / (2/9 + 2) = 20 / (2+18) = 1 Ампер - Проверка успешна.
Ваша простая, НЕразветвлённая эл-цепь содержит всего 3 элемента : Источник ЭДС с искомым значением E , его внутреннее сопротивление Ri и сопротивление нагрузки Rн = 2 Ом.
По закону Ома ток нагрузки в такой цепи равен
Iн = E / (Ri + Rн) = 1 Ампер (1)
При коротком замыкании резистор нагрузки закорочен перемычкой, и тогда ток короткого замыкания ограничен малым внутренним сопротивлением самого источника ЭДС :
Iкз = E / Ri = 10 А (2)
Выражение Ri = E / Iкз , полученное из уравнения (2), подставляем в первое выражение :
Iн = E / (E / Iкз + Rн)
Решаем уравнение : E / Iкз + Rн = E / Iн
E / Iн - E / Iкз = Rн
E = Rн / (1/ Iн - 1 / Iкз) = Rн·Iн·Iкз / (Iкз - Iн) = 2·1·10 / (10-1) = 20/9 = 2,222 Вольт.
Проверяем : Ri = E / Iкз = (20/9) / 10 = 2/9 Ом
Iн = E / (Ri + Rн) = (20/9) / (2/9 + 2) = 20 / (2+18) = 1 Ампер - Проверка успешна.
5
Это самое лучшее решение!
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