Переходные процессы в электрических цепях (E=150 В, L=0,09 Гн, R1=300 Ом, R2=300 Ом, R3=600 Ом, C=5 мкФ, ключ размыкается), страница 3

                                                                                                                                               (47)

7. Анализ полученного уравнения

                                                                                                                                               (47)

                    

                   

а) Из полученного дифференциального уравнения:

                                                                                                                                                     (48)

                                                                                                                                                     (49)

б) При :

=const   и     ==>

 ==>                                                                                                                                                      (50)

     [A]

8. Решение дифференциального уравнения классическим методом

 - корни вещественные, различные

                                                                                                                                                     (51)

                                                                                                                                                     (52)

                                                                                                                                                     (53)

Рассмотрим уравнение (53) при t=0:                                                                                                                                                      (54)

   ==>                                                                                                                                                         (55)

Подставим A₁ в (53):

                                                                                                                                                     (56)

Продифференцируем (56):

                                                                                                                                                     (57)

Рассмотрим (57) при t=0:

                                                                                                                                                     (58)

Таким образом  и                                                                                                                                                      (59)

Подставим (59) в (56):

                                                                                                                                                     (60)

Таким образом:  [A]                                                                                                                                                     (61)

9. Определение остальных токов и напряжений

                                                                                                                                                     (62)

                                                                                                                                                     (63)

                                                                                                                                                     (64)

                                                                                                                                                     (65)

                                                                                                                                                     (66)

                                                                                                                                                     (67)

                                                                                                                                                     (68)

10. Проверочная таблица