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Консультация № 186583
02.09.2012, 17:55
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Три батареи аккумуляторов с ЭДС ε1 = 2 В,
ε2 = 3 В и ε3 = 6 В и три резистора с сопротивлениями
R1 = 4 Ом, R2 = 6 Ом и R3 = 2 Ом соединены, как показано на рисунке. Определить силу тока в каждой ветви электрической цепи. Внутренними сопротивлениями r батарей аккумуляторов пренебречь.
Три батареи аккумуляторов с ЭДС ε1 = 2 В,
ε2 = 3 В и ε3 = 6 В и три резистора с сопротивлениями
R1 = 4 Ом, R2 = 6 Ом и R3 = 2 Ом соединены, как показано на рисунке. Определить силу тока в каждой ветви электрической цепи. Внутренними сопротивлениями r батарей аккумуляторов пренебречь.
Обсуждение
03.09.2012, 16:42
общий
это ответ
Здравствуйте, Massimo!
На рисунке ниже изображена схема замещения заданной электрической цепи.
Цепь содержит У = 2 узла (a и b) и В = 3 ветви. Количество независимых контуров цепи равно К = В - У + 1 = 3 - 2 + 1 = 2 (например, контуры 1 и 2).
Произвольно выбираем направления токов в ветвях: I1, I2, I3 (они показаны на рисунке стрелками с незаштрихованными концами). По первому закону Кирхгофа можно составить У - 1 = 2 - 1 = 1 независимое уравнение. Например, для узла a получим
По второму закону Кирхгофа можно составить К = 2 независимых уравнения. В частности, для контуров 1 и 2 получим
или, с учётом заданных числовых значений величин,
Решая систему уравнений (1) - (3), получим I1 [$8776$] -0,318 А, I2 [$8776$] 1,045 А, I3 [$8776$] 1,364 А. Знак "минус" свидетельствует о том, что ток в первой ветви имеет направление, противоположное показанному на рисунке.
С уважением.
На рисунке ниже изображена схема замещения заданной электрической цепи.
Цепь содержит У = 2 узла (a и b) и В = 3 ветви. Количество независимых контуров цепи равно К = В - У + 1 = 3 - 2 + 1 = 2 (например, контуры 1 и 2).
Произвольно выбираем направления токов в ветвях: I1, I2, I3 (они показаны на рисунке стрелками с незаштрихованными концами). По первому закону Кирхгофа можно составить У - 1 = 2 - 1 = 1 независимое уравнение. Например, для узла a получим
I1-I2+I3=0. (1)
По второму закону Кирхгофа можно составить К = 2 независимых уравнения. В частности, для контуров 1 и 2 получим
R1I1 + R2I2 = E1 + E2,
R2I2 + R3I3 = E2 + E3,
или, с учётом заданных числовых значений величин,
4I1 + 6I2 = 5, (2)
6I2 + 2I3 = 9. (3)
Решая систему уравнений (1) - (3), получим I1 [$8776$] -0,318 А, I2 [$8776$] 1,045 А, I3 [$8776$] 1,364 А. Знак "минус" свидетельствует о том, что ток в первой ветви имеет направление, противоположное показанному на рисунке.
С уважением.
5
Большое спасибо!!!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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