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Консультация № 195519
05.05.2019, 21:44
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
При подключении к батарее гальванических элементов сопротивления 16 Ом сила тока в цепи была 1 А, а при подключении сопротивления 8 Ом сила тока стала 1.8 А. Найти ЭДС и внутреннее сопротивление батареи.
При подключении к батарее гальванических элементов сопротивления 16 Ом сила тока в цепи была 1 А, а при подключении сопротивления 8 Ом сила тока стала 1.8 А. Найти ЭДС и внутреннее сопротивление батареи.
Обсуждение
06.05.2019, 15:37
общий
это ответ
Здравствуйте, mustang289!
В Вашей простейшей, неразветвлённой эл-цепи 3 элемента соединены последовательно : Батарея с ЭДС E, её внутреннее сопротивление Ri (обе величины неизвестны) и сопротивление нагрузки R1 = 16 Ом, при котором ток в цепи был I1 = 1 Ампер.
Все элементы - линейны, значит, и вся эта линейная цепь связана законом Ома :
I1·(Ri + R1) = E
Во 2м случае, при сопротивление нагрузки R2 = 8 Ом, ток в цепи стал I2 = 1,8 Ампер.
I2·(Ri + R2) = E
Для решения этой системы уравнений подставляем левую часть первого уравнения вместо правой части второго :
I2·(Ri + R2) = I1·(Ri + R1)
Группируем неизвестные сомножители в левую часть : I2·Ri - I1·Ri = I1·R1 - I2·R2
Вычисляем Ri = (I1·R1 - I2·R2) / (I2 - I1) = (1·16 - 1,8·8) / (1,8 - 1) = (16 - 14,4) / 0,8 = 2 Ома
Подставляем значение Ri в первое уравнение, получим E = I1·(Ri + R1) = 1·(2+16) = 18 Вольт.
Искомые величины найдены. Проверяем решение подстановкой найденных значений в Уравнение2 :
I2·(Ri + R2) = 1,8·(2+8) = 18 Вольт - полное совпадение! Проверка успешна!
В Вашей простейшей, неразветвлённой эл-цепи 3 элемента соединены последовательно : Батарея с ЭДС E, её внутреннее сопротивление Ri (обе величины неизвестны) и сопротивление нагрузки R1 = 16 Ом, при котором ток в цепи был I1 = 1 Ампер.
Все элементы - линейны, значит, и вся эта линейная цепь связана законом Ома :
I1·(Ri + R1) = E
Во 2м случае, при сопротивление нагрузки R2 = 8 Ом, ток в цепи стал I2 = 1,8 Ампер.
I2·(Ri + R2) = E
Для решения этой системы уравнений подставляем левую часть первого уравнения вместо правой части второго :
I2·(Ri + R2) = I1·(Ri + R1)
Группируем неизвестные сомножители в левую часть : I2·Ri - I1·Ri = I1·R1 - I2·R2
Вычисляем Ri = (I1·R1 - I2·R2) / (I2 - I1) = (1·16 - 1,8·8) / (1,8 - 1) = (16 - 14,4) / 0,8 = 2 Ома
Подставляем значение Ri в первое уравнение, получим E = I1·(Ri + R1) = 1·(2+16) = 18 Вольт.
Искомые величины найдены. Проверяем решение подстановкой найденных значений в Уравнение2 :
I2·(Ri + R2) = 1,8·(2+8) = 18 Вольт - полное совпадение! Проверка успешна!
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