![[дано.png]]
###### Комплексные аналоги элементов схемы:
$J_{3}=\frac{7.1}{\sqrt{2}}(\cos(2.498) + j\sin(2.498))= -4+3j$
$E_{1} = \frac{894.4}{\sqrt{2}}(\cos(1.249)+j\sin(1.249))= 200+600j$
$E_{4} = \frac{525}{\sqrt{2}}(\cos(3.222)+\sin(3.222)) = -370-30j$
$E_{6} = \frac{1390}{\sqrt{2}}(\cos(3.92)+\sin(3.92)) = -700-690j$
$\omega = 1000$
###### МКТ
$$
\begin{cases}
I_{11} = J_{3}=-4+3j \\
E_{4} = I_{22}(Z_{4}+Z_{5}+Z_{2})-I_{33}Z_{5}-I_{11}Z_{2}) \\
E_{6}+E_{1} = I_{33}(Z_{6}+Z_{5})-I_{22}Z_{5}
\end{cases}
$$
$$
\begin{cases}
-370 - 30j = I_{22}(60+60+20j-30j)-I_{33}(60+20j)-(-4+3j)(-30j) \\
-700-690j+200+600j = I_{33}(60-90j+60 + 20j)-I_{22}(60+20j)
\end{cases}
$$
$I_{22}= -3-2j$     $I_{33}=-3-4j$

$I_{1}=I_{33}-I_{11}= -3-4j+4-3j=1-7j$
$I_{2}=I_{11}-I_{22}=-4+3j+3+2j=-1+5j$
$I_{3}=J_{3}=-4+3j$
$I_{4}=I_{22}=-3-2j$
$I_{5}=I_{33}-I_{22}=-3-4j+3+2j=-2j$
$I_{6}=I_{33}=-3-4j$
###### МЦП
![[мцп.png]]
$\phi_{1} -\phi_{4}=E_1$
$$
\begin{cases}
\phi_{4}=0 \\
\phi_{1}=E_{1}=200+600j \\
\phi_{2}
\left(\frac{1}{Z_{2}}+\frac{1}{Z_{4}}+\cancelto{0}{\frac{1}{Z_{3}}}\right)
- \frac{\phi_{1}}{Z_{2}} - \frac{\phi_{3}}{Z_{4}} - \cancelto{0}{\frac{\phi_{4}}{Z_{4}}} = J_{3} - \frac{E_{4}}{Z_{4}} \\
\phi_{3}\left(\frac{1}{Z_{4}} + \frac{1}{Z_{5}} + \frac{1}{Z_{6}}\right) - \frac{\phi_{1}}{Z_{5}} - \frac{\phi_{2}}{Z_{4}} - \cancelto{0}{\frac{\phi_{4}}{Z_{6}}} = \frac{E_{4}}{Z_{4}} - \frac{E_{6}}{Z_{6}}
\end{cases}
$$
$$
\begin{cases}
\phi_{2}\left(\frac{1}{-30j} + \frac{1}{60}\right) - \frac{200+600j}{-30j} - \phi_\frac{3}{60} = -4+3j - \frac{-370-30j}{60}  \\
\phi_{3} \left(\frac{1}{60} + \frac{1}{60+20j} \frac{+1}{90j}\right) - \frac{200+600j}{60+20j} - \frac{\phi_{2}}{60} = \frac{-370-30j}{60} - \frac{700-690j}{60-90j} 
\end{cases}
$$
$\phi_{2}= 350+630j$     $\phi_{3} =160+720j$

$I_{1}=J_{5} - J_{2} = -2j+1 -5j = 1-7j$
$I_{2} = \frac{\phi_{2}-\phi_{1}}{Z_{2}} = \frac{350+630j-200-600j}{-30j} = -1+5j$
$I_{3} = J_{3} =-4+3j$
$I_{4}= \phi_{2}-\phi_{3}+E_{4} = \frac{350+630j-160-720j-370-30j}{60} = -3-2j$
$I_{5}= \frac{\phi_{1}-\phi_{3}}{Z_{5}} = \frac{200+600j-160-720j}{60+20j} =-2j$
$I_{6}= \frac{\phi_{3}-\phi_{4}+E_{6}}{Z_{6}}= \frac{160+720j-700-690j}{60-90j} =-3-4j$
###### МЭГ
$I_{6}$ — ?
$I_{6} = \frac{U_{xx}}{Z_{n}+Z_{ви}}$
1) $Z_{11}=Z_{6} = 60-90j$
2) 
$I_{11}=J_{3} = -4+3j$
$E_{4} = I_{22}\left(Z_{4}+Z_{2}+Z_{5}\right)-I_{11}Z_{2}$
$-370-30j=I_{22}(60-30j+60+20j)-(-4+3j)(-30j)$
$I_{22} = \frac{-69+16j}{29}$
###### Второй закон Кирхгова
$E_{1}+E_{6}=U_{xx}-I_{22}Z_{5}$
$200+600j-700-690j=U_{xx}-(\frac{-69+16j}{29})(60+20j) \Rightarrow U_{xx}= \frac{-18960-3030j}{29}$
3) 
![[дано без кала.png]]
$Z_{ви}=\frac{(Z_{2}+Z_{4})Z_{5}}{Z_{2}+Z_{4}+Z_{5}} = (-30j+60)\frac{60+20j}{-30j+60+60+20j} = \frac{1020-60j}{29}$
$Z_{6}= \frac{\frac{-18960-3030j}{29}}{60-90j+\frac{1020-60j}{29}} = -3-4j$
##### Векторная диаграмма для узла №3
![[2,4 и 5.png|300]]
$I_{6}=I_{4}+I_{5}$
$-3-4j=-3-2j-2j$
$-3-4j=-3-4j$
###### Показания приборов
$I_{A} = \frac{2\sqrt{2}}{\sqrt{2}}= 2A$
$E_{1}= U_{V}- I_{2}Z_{2}-I_{3}Z_{3}$
$200+600j=U_{V}-(-1+5j)(-30j)-(-4+3j)80$
$U_{V}=30+870j$
$U_{V}=\sqrt{30^{2}+870^{2}} = 870B$
#### Ответ
$$
\begin{align}
I_{1} &=1-7j \\
e_{1}(t) &=\sqrt{50}\sqrt{2}\sin(10^{3}t -1.42) \\
I_{2} &=-1+5j \\
e_{2}(t) &=-\sqrt{26}\sqrt{2}\sin(10^{3}t -1.37) \\
I_{3} &=-4+3j \\
e_{3}(t) &=-5\sqrt{2}\sin(10^{3}t -0.643) \\
I_{4} &=-3-2j \\
e_{4}(t)&=-\sqrt{13}\sqrt{2}\sin(10^{3}t+0.58) \\
I_{5} &= -2j \\
e_{5}(t) &= 2\sqrt{2} \sin(10^{3}t-1.57) \\
I_{6} &=-3-4j \\
e_{6}(t) &=-5\sqrt{2}\sin(10^{3}t +0.927)
\end{align}
$$