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Консультация № 195053
24.03.2019, 19:26
0.00 руб.
24.03.2019, 21:09
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Совсем запутался я в схеме,помогите пожалуйста разобраться и решить задачу
Совсем запутался я в схеме,помогите пожалуйста разобраться и решить задачу
Прикрепленные файлы:
Обсуждение
24.03.2019, 22:25
общий
это ответ
Здравствуйте, qazxswedc!
Обозначим направление токов следующим образом
Для напряжения выберем такое положительное направление, чтобы ему соответствовало положительное направление I3
U=[$966$]1-[$966$]2
Подсчитаем напряжение в каждой ветви
[$8496$]1-I1(r1+R1)=U
[$8496$]2-I2(r2+R2+R4+R5)=-U
I3R3=U
С другой стороны, сумма токов (принимая входящие за положительные, а исходящие за отрицательные) в каждом узле равна нулю
I1-I2-I3=0
Итого 4 уравнения с 4 неизвестными. Можно решать любым удобным способом.
Например, выразим токи через напряжение
I1=([$8496$]1-U)/(r1+R1)
I2=([$8496$]2+U)/(r2+R2+R4+R5)
I3=U/R3
и подставим в четвёртое уравнение
([$8496$]1-U)/(r1+R1)-([$8496$]2+U)/(r2+R2+R4+R5)-U/R3=0
[$8496$]1/(r1+R1)-[$8496$]2/(r2+R2+R4+R5)=U(1/(r1+R1)+1/(r2+R2+R4+R5)+1/R3)
Находим напряжение
U=([$8496$]1/(r1+R1)-[$8496$]2/(r2+R2+R4+R5))/(1/(r1+R1)+1/(r2+R2+R4+R5)+1/R3)=(12/(2+4)-12/(2+16+1+6))/(1/(2+4)+1/(2+16+1+6)+1/2,8)=2,7 В
Находим ток в каждой ветви
I1=(12-2,7)/(2+4)=1,55 А
I2=(12+2,7)/(2+16+1+6)=0,59 А
I3=2,7/2,8=0,96 А
Обозначим направление токов следующим образом
Для напряжения выберем такое положительное направление, чтобы ему соответствовало положительное направление I3
U=[$966$]1-[$966$]2
Подсчитаем напряжение в каждой ветви
[$8496$]1-I1(r1+R1)=U
[$8496$]2-I2(r2+R2+R4+R5)=-U
I3R3=U
С другой стороны, сумма токов (принимая входящие за положительные, а исходящие за отрицательные) в каждом узле равна нулю
I1-I2-I3=0
Итого 4 уравнения с 4 неизвестными. Можно решать любым удобным способом.
Например, выразим токи через напряжение
I1=([$8496$]1-U)/(r1+R1)
I2=([$8496$]2+U)/(r2+R2+R4+R5)
I3=U/R3
и подставим в четвёртое уравнение
([$8496$]1-U)/(r1+R1)-([$8496$]2+U)/(r2+R2+R4+R5)-U/R3=0
[$8496$]1/(r1+R1)-[$8496$]2/(r2+R2+R4+R5)=U(1/(r1+R1)+1/(r2+R2+R4+R5)+1/R3)
Находим напряжение
U=([$8496$]1/(r1+R1)-[$8496$]2/(r2+R2+R4+R5))/(1/(r1+R1)+1/(r2+R2+R4+R5)+1/R3)=(12/(2+4)-12/(2+16+1+6))/(1/(2+4)+1/(2+16+1+6)+1/2,8)=2,7 В
Находим ток в каждой ветви
I1=(12-2,7)/(2+4)=1,55 А
I2=(12+2,7)/(2+16+1+6)=0,59 А
I3=2,7/2,8=0,96 А
5
Спасибо огромное Вам за Ваш труд и помощь!
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