Question

R1=1

R2=R5=5

R3=R6=3

R4=R7=2

\(U_{AB}=12V\)

a) Tim \(R_{AB}\)

b)Tim \(Í_1,I_2,I_3,I_4,I_5,I_6,I_7\)

c)Tim \(U_1,U_2,U_3,U_4,U_5,U_6,U_7\)

Answer 1

CTM: \(R_7nt\left\{R_6//\left[R_5nt(\left(R_1ntR_2\right)//R_3//R_4)\right]\right\}\)

a)\(R_{12}=R_1+R_2=1+5=6\Omega\)

\(\dfrac{1}{R_{1234}}=\dfrac{1}{R_{12}}+\dfrac{1}{R_3}+\dfrac{1}{R_4}=\dfrac{1}{6}+\dfrac{1}{3}+\dfrac{1}{2}=1\Omega\Rightarrow R_{1234}=1\Omega\)

\(R_{12345}=R_5+R_{1234}=5+1=6\Omega\)

\(R_{123456}=\dfrac{R_6\cdot R_{12345}}{R_6+R_{12345}}=\dfrac{3\cdot6}{3+6}=2\Omega\)

\(R_{AB}=R_7+R_{123456}=2+2=4\Omega\)

b)\(I_7=I_{AB}=\dfrac{U_{AB}}{R_{AB}}=\dfrac{12}{4}=3A=I_{123456}\)

\(\Rightarrow U_6=U_{12345}=U_{123456}=3\cdot2=6V\Rightarrow I_6=\dfrac{U_6}{R_6}=\dfrac{6}{3}=2A\)

\(I_{1234}=I_5=\dfrac{U_{12345}}{R_{12345}}=\dfrac{6}{6}=1A\)

\(U_{12}=U_3=U_4=U_{1234}=1\cdot1=1V\)

\(\left\{{}\begin{matrix}I_3=\dfrac{U_3}{R_3}=\dfrac{1}{3}A\\I_4=\dfrac{U_4}{R_4}=\dfrac{1}{2}A\end{matrix}\right.\)

\(I_1=I_2=\dfrac{U_{12}}{R_{12}}=\dfrac{1}{6}A\)