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Задать вопрос экспертам

Консультация № 160110

10.02.2009, 16:23

0.00 руб.

0 1 1

Образование

Уважаемые эксперты, не могу решить задачу: "При увеличении внешнего сопротивления в 5 раз напряжение на зажимах батареи увеличивается с U1= 10В до U2= 30В. Определить Э.Д.С. батареи?

Обсуждение

Неизвестный

10.02.2009, 21:30

общий

это ответ

Здравствуйте, Flyyer!
_________________________
При увеличении внешнего сопротивления в 5 раз
R2= 5*R1
напряжение на зажимах батареи увеличивается с
U1= 10В до
U2= 30В.
Определить Э.Д.С. батареи?
___
Обозначим внутреннее сопротивление батареи
R0

Ток в цепи
I= E/(R+R0)

Напряжение на зажимах батареи (на нагрузке)
U= I*R= E*R/(R+R0)
___________________
Решение
U1= E*R1/(R1+R0) (1)
U2= E*5*R1/(5*R1+R0) (2)

Выразим R0 через R1 и U1
R0+R1= E*R1/U1
R0= (E*R1/U1-R1)

и подставим его в уравнение (2)
U2= E*5*R1/(5*R1+(E*R1/U1-R1))= E*5*R1/(4*R1+E*R1/U1)= E*5/(4+E/U1)
5*E= U2*4+ E*(U2/U1)
E*(5-(U2/U1))= 4*U2

Получили 'E' выраженное через 'U1' и 'U2'
E= 4*U2/(5-(U2/U1))

Ответ
E= 4*30/(5-(30/10))= 60 (В)

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