\(R_{234}=\dfrac{R_2R_3R_4}{R_2R_3+R_3R_4+R_2R_4}=\dfrac{10\cdot15\cdot30}{10\cdot15+15\cdot30+10\cdot30}=5\left(\Omega\right)\)
\(R_{tđ}=R_1+R_{234}=6+5=11\left(\Omega\right)\)
a,\(I=\dfrac{U}{R_{td}}=\dfrac{110}{11}=10\left(A\right)\)
b,\(I=I_1=I_{234}=10\left(A\right)\)
\(U_2=U_3=U_4=U_{234}=I_{234}R_{234}=10\cdot5=50\left(V\right)\)
\(I_2=\dfrac{U_2}{R_2}=\dfrac{50}{10}=5\left(A\right);I_3=\dfrac{U_3}{R_3}=\dfrac{50}{15}=\dfrac{10}{3}\left(A\right);I_4=\dfrac{U_4}{R_4}=\dfrac{50}{30}=\dfrac{5}{3}\left(A\right)\)
c,\(U_1=I_1R_1=10\cdot6=60\left(V\right)\)
\(U_2=U_3=U_4=U_{234}=I_{234}R_{234}=10\cdot5=50\left(V\right)\)
a,\(\Rightarrow\dfrac{1}{R234}=\dfrac{1}{R2}+\dfrac{1}{R3}+\dfrac{1}{R4}\Rightarrow R234=5\Omega\Rightarrow Im=\dfrac{U}{R1+R234}=\dfrac{110}{5+6}=10A\)
b,\(\Rightarrow Im=I1=I234=10A\Rightarrow U234=U2=U3=U4=I234.R234=50V\)
\(\Rightarrow I2=\dfrac{U2}{R2}=\dfrac{50}{10}=5A\Rightarrow I3=\dfrac{U3}{R3}=\dfrac{50}{15}=\dfrac{10}{3}A\Rightarrow I4=\dfrac{U4}{R4}=\dfrac{5}{3}A\)
c,\(\Rightarrow U2=U3=U4=50V,\Rightarrow U1=U-U2=60V\)