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Задать вопрос экспертам

Консультация № 173370

17.10.2009, 23:37

0.00 руб.

0 1 1

Образование

Добрый день, нужно срочно решить следующую задачу:

При поочередном замыкании источника тока на резисторы с сопротивлением R1=20 Ом и R2=2.0 Ом во внешней цепи выделяется одинаковая мощность. определите внутреннее сопротивление r источника тока

Заранее огромное спасибо!

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

18.10.2009, 00:33

общий

это ответ

Здравствуйте, Zhukouski.
пусть внутреннее сопротивление r и ЭДС E
В первом случае ток I₁=E/(R₁+r)
мощность на резисторе P₁=I₁²*R₁=R₁*E²/(R₁+r)²
Во втором случае ток I₂=E/(R₂+r)
мощность на резисторе P₂=I₂²*R₂=R₂*E²/(R₂+r)²
R₁*E²/(R₁+r)²=R₂*E²/(R₂+r)²
R₁/(R₁+r)²=R₂/(R₂+r)²
R₁*(R₂+r)²=R₂*(R₁+r)²
R₁*R₂²+2R₁*R₂*r+R₁*r²=R₂*R₁²+2R₁*R₂*r+R₂*r²
R₁*R₂²+R₁*r²=R₂*R₁²+R₂*r²
(R₁-R₂)*r²=R₁*R₂*(R₁-R₂)
r²=R₁*R₂
r=[$8730$](R₁*R₂)=6,32 Ом

5

Спасибо огромное!

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