Электрические цепи однофазного синусоидального тока. Трубникова В.Н - 12 стр.

     Комплекс полного электрического сопротивления схемы (входное
сопротивление):
                                                                       0                   0
                 Z2 ⋅Z3              10 ,009 ⋅ e j 53,168 ⋅ 7 ,075 ⋅ e − j 45 ,028
        Z = Z1 +         = j 4,006 +                                               =
                 Z2 + Z3                  (6 + j8,011) + (5 − j5,005)
                                                           0
          = 6 ,161 + j 3,233 = 6 ,958 ⋅ е j 27 ,689 Ом.
      Общий комплексный ток в цепи:
            U&      120                           − j 27 ,6890
       I&1 = =                      = 17 ,246 ⋅ e              = 15,271 − j8,014 А.
            Z 6 ,958 ⋅ e j 27 ,6890
      Комплексное напряжение U& 23 . Комплекс полного напряжения U&
есть сумма комплексных напряжений на элементах схемы U& 1 + U& 23 , тогда:
                                                                                   0
       U& 23 = U& − U& 1 = U& − I&1 ⋅ Z 1 = 120 − 17 ,246 ⋅ 4 ,006 ⋅ e j 90 =
                                                                   0
            = 87,9 − j 61,17 = 107,089 ⋅ e − j 34,834 В.
      Комплексные токи в параллельных ветвях:
              U& 23 107 ,089 ⋅ e − j 34 ,8340 107 ,089 j (−34 ,8340 −53,1680 )
        I&2 =      =                         =          ⋅e                     =
              Z2                  j 53,1680     10 ,009
                      10 ,009 ⋅ e
                                       0
              = 10 ,699 ⋅ e − j 88 ,002 = 0 ,373 − j10 ,693 А.
                U& 23 107 ,089 ⋅ e − j 34 ,8340 107 ,089 j (−34 ,8340 + 45 ,0280 )
          I&3 =      =                         =        ⋅e                         =
                Z3                − j 45 ,0280   7 ,075
                       7 ,075 ⋅ e
                                   0
              = 15,137 ⋅ e j10 ,194 = 14 ,898 + j 2 ,679 А.
      Комплексные напряжения на отдельных участках
                                               0                           0
         U& L1 = jX L1 ⋅ I&1 = 4 ,006 ⋅ e j 90 ⋅ 17 ,246 ⋅ e − j 27 ,689 =
                                           0
               = 69,081 ⋅ e j 62,311 = 32,1 + j 61,17 В;
                                                               0                       0
         U& R 2 = R2 ⋅ I&2 = 6 ⋅ 10 ,699 ⋅ e − j 88 ,002 = 64 ,197 ⋅ e − j 88 ,002 =
                = 2 ,238 − j 64 ,158 В;
                                               0                           0
         U& L 2 = jX L 2 ⋅ I&2 = 8,011 ⋅ e j 90 ⋅ 10 ,699 ⋅ e − j 88 ,002 =
                                       0
               = 85,714 ⋅ e j1,998 = 85,662 + j 2,988 В;
                                                   0                       0
         U& С 3 = jX С 3 ⋅ I&3 = 5,005 ⋅ e − j 90 ⋅ 15,137 ⋅ e j10 ,194 =
                                           0
               = 75,76 ⋅ e − j 79,806 = 13,408 − j 74,565 В;
                                                       0                       0
         U& R 3 = R3 ⋅ I&3 = 5 ⋅ 15,137 ⋅ e j10 ,194 = 75,687 ⋅ e j10 ,194 =
                = 74 ,492 + j13,395 В.