a) R2//R3
\(\Rightarrow R_{23}=\dfrac{R_2.R_3}{R_2+R_3}=\dfrac{30.20}{30+20}=12\left(\Omega\right)\)
\(R_1ntR_{23}\Rightarrow R_{tđ}=R_1+R_{23}=60+12=72\left(\Omega\right)\)
b) \(I=I_1=I_{23}=\dfrac{U_{AB}}{R_{tđ}}=\dfrac{12}{72}=\dfrac{1}{6}\left(A\right)\)
\(U_{23}=U_2=U_3=I_{23}.R_{23}=12.\dfrac{1}{6}=2\left(V\right)\)
\(\left\{{}\begin{matrix}I_2=\dfrac{U_2}{R_2}=\dfrac{2}{30}=\dfrac{1}{15}\left(A\right)\\I_3=\dfrac{U_3}{R_3}=\dfrac{2}{20}=0,1\left(A\right)\end{matrix}\right.\)
c) \(U_1=I_1.R_1=\dfrac{1}{6}.60=10\left(V\right)\)
\(R_{23}=\dfrac{R2.R3}{R2+R3}=\dfrac{30.20}{30+20}=12\Omega\)
\(\Rightarrow R_{123}=R_1+R_{23}=60+12=72\Omega\)
\(I=U:R=12:72=\dfrac{1}{6}A\)
\(I=I_1=I_{23}=\dfrac{1}{6}A\left(R_1ntR_{23}\right)\)
\(U_1=R_1.I_1=60.\dfrac{1}{6}=10V\)
\(\Rightarrow U_{23}=U-U_1=12-10=2A\left(R_1ntR_{23}\right)\)
\(\Rightarrow U_{23}=U_2=U_3=2V\)(R2//R3)
\(\left\{{}\begin{matrix}I_2=U2:R2=2:30=\dfrac{1}{15}A\\I3=U3:R3=2:20=\dfrac{1}{10}A\end{matrix}\right.\)
a.\(Rtđ=R1+\dfrac{R2.R3}{R2+R3}=60+\dfrac{30.20}{30+20}=72\)
b.\(I=I1=I23=\dfrac{UAB}{Rtđ}=\dfrac{12}{72}=\dfrac{1}{6}\)
U2=U3=UAB-U1=UAB-I1.R1=12-\(\dfrac{1}{6}\).60=2(V)
\(I2=\dfrac{U2}{R2}=\dfrac{2}{30}=\dfrac{1}{15}\)
I3=I23-I2=\(\dfrac{1}{6}-\dfrac{1}{15}=0,1\)
U1=I1.R1=\(\dfrac{1}{6}.60=2\)
U2=I2.R2=\(\dfrac{1}{15}.30=2\)
U3=I3.R3=0,1.20=2
