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Задать вопрос экспертам

Консультация № 174646

28.11.2009, 18:01

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29.11.2009, 03:22

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Образование

Доброго времени суток уважаемые эксперты! Помогите пожалуйста в решении задачи.
Два параллельно соединенных элемента с одинаковыми ЭДС [size=3]ε[/size]1=[size=3]ε[/size]2=2В и внутренними сопротивлениями r1=1 Ом и r2=1,5 Ом замкнуты на внешнее сопротивление R=1,4 Ом (рисунок 1). Найти ток I в каждом из элементов и во всей цепи.
Заранее благодарю!
С уважением, Дмитрий.

Приложение:
Рисунок 1: http://s59.radikal.ru/i164/0911/5c/e35aca038f88.jpg

Обсуждение

давно

Мастер-Эксперт
27822
2370

29.11.2009, 01:48

общий

Веселов Дмитрий Валерьевич:
В уме подсчитал за полминуты: общий ток 1 А, 1-го элемента 0.6 А, 2-го 0.4 А. Подробности позже.

давно

Мастер-Эксперт
27822
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29.11.2009, 04:48

общий

это ответ

Здравствуйте, Веселов Дмитрий Валерьевич.
Поскольку ЭДС элементов одинаковы, их можно заменить одним "эквивалентным генератором" с ЭДС E_экв = 2 В и внутренним сопротивлением r_экв, эквивалентным параллельно соединённым сопротивлениям r₁ и r₂, т.е. r_экв = r₁*r₂/(r₁ + r₂) = 1*1.5/(1 + 1.5) = 0.6 Ом. Этот генератор замкнут на внешнее сопротивление R = 1.4 Ом, значит ток всей цепи I = E_экв/(r_экв + R) = 2/(0.6 + 1.4) = 1 А. Напряжение на внешнем сопротивлении U = I*R = 1*1.4 = 1.4 В. Ток 1-го элемента I₁ = (E_экв - U)/r₁ = (2 - 1.4)/1 = 0.6 А; ток 2-го элемента I₂ = (E_экв - U)/r₂ = (2 - 1.4)/1.5 = 0.4 А.

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