[tex]E_1=E_2=E_3=E_4=3 \ V; \\ r_1=r_2=r_3=r_4=1 \ \Omega; \\ R=2 \ \Omega; \\ \bold{a)}\ E_T=E_{12}=E_{34}=E_1+E_2=E_3+E_4 \\ \Rightarrow E_T=3 \ V+3 \ V \\ \Rightarrow \boxed{E_T=6 \ V}; \\ \bold{b)} \ I_1=\frac{E_1}{R_1+r_1}; \\ R_1=r_2+R_2; \\ \frac{1}{R_2}=\frac{1}{r_3+r_4}+\frac{1}{R}=\frac{1}{1 \ \Omega +1 \ \Omega}+\frac{1}{2 \ \Omega}=\frac{2}{2 \ \Omega} \\ \Rightarrow R_2=1 \ \Omega; \\ \Rightarrow R_1=1 \ \Omega+1 \ \Omega=2 \ \Omega; \\ \Rightarrow I_1=\frac{3 \ V}{4 \ \Omega}=\boxed{0,75 \ A};[/tex]
[tex]\bold{c)} \ I=\frac{U}{R} \ \Rightarrow \ U=I \cdot R; \\ I=I_{12}+I_{34}; \\ I_1=I_2=I_3=I_4=I_{12}=I_{34} \\ \Rightarrow I=2 \cdot 0,75 \ A=1,5 \ A; \\ \Rightarrow U=1,5 \ A \cdot 2 \ \Omega \\ \Rightarrow \boxed{U=3 \ V}; \\ \bold{d)} \ r_0=1 \ \Omega; \\ I_0=I \\ R_0=R+R_{1234}; \\ \frac{1}{R_{1234}}=\frac{1}{r_1+r_2}+\frac{1}{r_3+r_4}=\frac{2}{2 \ \Omega} ; \\ \Rightarrow R_{1234}=1 \ \Omega; \\ \Rightarrow R_0=2 \ \Omega+1 \ \Omega=3 \ \Omega; \\ I_0=\frac{E_0}{R_0+r_0};[/tex]
[tex]\Rightarrow E_0=I_0 ( R_0+r_0) \\ \Rightarrow E_0=1,5 \ A(3 \ \Omega+1 \ \Omega)=1,5 \ A \cdot 4 \ \Omega \\ \Rightarrow \boxed{E_0=6 \ V}.[/tex]
