[tex]E_p=\frac{\sum\limits^n_{i=1} {\frac{E_i}{r_i} } \, }{\sum\limits^n_{i=1} {\frac{1}{r_i}}} \\\frac{1}{r_p}=\sum\limits^n_{i=1} {\frac{1}{r_i}} \\E_1=E_2=...E_i=E \\r_1=r_2=...=r_i=r\\r_p=\frac{r}{n}\\ E_p=E\\R_{12}=\frac{R_1R_2}{R_1+R_2}=\frac{4*12}{4+12}=\frac{48}{16}=3\Omega\\ R_{34}=\frac{R_3R_4}{R_3+R_4}=\frac{3*6}{3+6}=\frac{18}{9}=2\Omega\\ R_e=R_{12}+R_{34}=3+2=5\Omega=>R_e=5\Omega[/tex]
[tex]I=\frac{E_p}{R_e+r_p}=\frac{E}{R_e+\frac{r}{n} }=\frac{48}{5+\frac{10}{10} }=\frac{48}{6}=8A=>I=8 A\\[/tex]
[tex]U_1=U_2\\U_3=U_4\\U_1=U_2=I_{12}*R_{12}=3I_{12}\\U_3=U_4=I_{34}R_{34}=2I_{34}\\u=Ir_p=8*\frac{r}{n}=8 V\\ U_1+U_2+u=E<=>48-8=3I_{12}+2I_{34}<=>40=3I_{12}+2I_{34}\\I_{12}+I_{34}=I=>I_{12}+I_{34}=8\\\left \{ {3I_{12}+2I_{34}=40} \atop {I_{12}+I_{34}=8|*2}} \right. <=>\left \{ {3I_{12}+2I_{34}=40} \atop {2I_{12}+2I_{34}=16}} \right. \\I_{12}=24 A\\I_{34}=I-I_{12}=8-24=-16 A\\U_1=U_2=R_{12}I_{12}=3*24=72 V\\U_2=I_2R_2=>I_2=\frac{U_2}{R_2}=\frac{72}{12}= 6A\\t=5 min=300 s\\[/tex]
[tex]W_2=R_2I_2^2t=12*6^2*300=129600 J=>W_2=129600 J\\P=R_eI'^2=R_e(\frac{E}{R_e+r})^2=5(\frac{48}{5+10})^2=5* 10,24=51,2 W=>P=51,2 W[/tex]
