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 2

(12)

(13)

                                                                                                                                               (14)

(15)

                                                                                                                                               (16)

                                                                                                                                               (17)

                                                                                                                                               (18)

4. Определение начальных условий

А) Независимые начальные условия

                                                                                                                                               (19)

                                                                                                                                               (20)

Б) Зависимые начальные условия

Составим систему по законам Кирхгофа:

            (21)

Подставим в систему (21) t=0, учитывая ННУ из пункта 4.А)

            (22)                                                                                                                                  

Преобразуя систему (22), получим:

      (23)

Таким образом, получим систему зависимых начальных условий (24):

                                                                                                                                         (24)
5. Составление дифференциального уравнения по законам Кирхгофа

R3

R2

E

R1

 Определяем i₁:

Из (27):                                                                                                                                                (28)
Дифференцируем (26):                                                                                                                                                (29)
Дифференцируем (28):                                                                                                                                                (30)
Подставим (30) в (29):
     ==>                                                                                                                                               (31)
                                                                                                                                               (32)
Подставим (32) и (28) в (25):
                                                                                                                                               (33)


                                                                                                                                               (34)

		i2

6. Получение дифференциального уравнения методом

Д-алгебраизации

Запишем исходную систему уравнений (25)…(27) с помощью Д-алгебраизации:

Из системы (35)…(37) получим i₁;

                                                                                                                                               (42)

                                                                                                                                               (43)

                                                                                                                                               (44)

==>                                                                                                                                                (45)

==>                                                                                                                                                (46)