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Консультация № 201029
01.06.2021, 11:15
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
"N одинаковых источников ЭДС с одинаковым внутренним сопротивлением r=1 Ом соединяют в батарею и подключают к клеммам этой батареи нагрузку с сопротивлением R=5 Ом. Если все источники ЭДС соединены в батарею последовательно, то на нагрузке выделяется в 9 раз большая мощность, чем в том случае, когда батарея собрана из параллельно соединенных источников. Найти число N источников ЭДС."
"N одинаковых источников ЭДС с одинаковым внутренним сопротивлением r=1 Ом соединяют в батарею и подключают к клеммам этой батареи нагрузку с сопротивлением R=5 Ом. Если все источники ЭДС соединены в батарею последовательно, то на нагрузке выделяется в 9 раз большая мощность, чем в том случае, когда батарея собрана из параллельно соединенных источников. Найти число N источников ЭДС."
Обсуждение
01.06.2021, 13:35
общий
это ответ
В обоих случаях P=U*I, U=I*R. Значит, P=I2R, где P - мощность, выделяемая на нагрузке, а I - сила тока, проходящего через нагрузку.
Значит, нужно искать отношение квадратов силы тока.
1) В случае последовательного соединения
[$8496$]ЦЕПИ = N*[$8496$]
RЦЕПИ = R + N*r
IПОСЛЕД.=[$8496$]ЦЕПИ/RЦЕПИ=N*[$8496$]/(R + N*r)
2) В случае параллельного соединения
[$8496$]ЦЕПИ = [$8496$]
RЦЕПИ = R + r/N
IПАРАЛ.= [$8496$]ЦЕПИ/RЦЕПИ=[$8496$]/(R + r/N)=N*[$8496$]/(N*R + r)
IПОСЛЕД./IПАРАЛ.={ N*[$8496$]/(R + N*r) }/{ N*[$8496$]/(N*R + r)} = (N*R + r)/(R + N*r)
Поскольку PПОСЛЕД./PПАРАЛ.=( IПОСЛЕД./IПАРАЛ. )2 => IПОСЛЕД./IПАРАЛ. = sqrt( PПОСЛЕД./PПАРАЛ. )
Подставляем значения:
(5*N+1)/(5 + 1*N)=sqrt(9) =3
(5*N+1)/(5 + N)=3
(5*N+1) = 3*(5 + N)
2*N=14
N=7
ОТВЕТ: 7 источников ЭДС.
Значит, нужно искать отношение квадратов силы тока.
1) В случае последовательного соединения
[$8496$]ЦЕПИ = N*[$8496$]
RЦЕПИ = R + N*r
IПОСЛЕД.=[$8496$]ЦЕПИ/RЦЕПИ=N*[$8496$]/(R + N*r)
2) В случае параллельного соединения
[$8496$]ЦЕПИ = [$8496$]
RЦЕПИ = R + r/N
IПАРАЛ.= [$8496$]ЦЕПИ/RЦЕПИ=[$8496$]/(R + r/N)=N*[$8496$]/(N*R + r)
IПОСЛЕД./IПАРАЛ.={ N*[$8496$]/(R + N*r) }/{ N*[$8496$]/(N*R + r)} = (N*R + r)/(R + N*r)
Поскольку PПОСЛЕД./PПАРАЛ.=( IПОСЛЕД./IПАРАЛ. )2 => IПОСЛЕД./IПАРАЛ. = sqrt( PПОСЛЕД./PПАРАЛ. )
Подставляем значения:
(5*N+1)/(5 + 1*N)=sqrt(9) =3
(5*N+1)/(5 + N)=3
(5*N+1) = 3*(5 + N)
2*N=14
N=7
ОТВЕТ: 7 источников ЭДС.
5
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