Bài 1:

a. \(R=R1+\left(\dfrac{R2.R3}{R2+R3}\right)=30+\left(\dfrac{15\cdot10}{15+10}\right)=36\Omega\)

b. \(I=I1=I23=\dfrac{U}{R}=\dfrac{24}{36}=\dfrac{2}{3}A\left(R1ntR23\right)\)

\(U23=U2=U3=I23\cdot R23=\dfrac{2}{3}\cdot\left(\dfrac{15.10}{15+10}\right)=4V\left(R2\backslash\backslash R3\right)\)

\(\rightarrow\left\{{}\begin{matrix}I2=U2:R2=4:15=\dfrac{4}{15}A\\I3=U3:R3=4:10=0,4A\end{matrix}\right.\)

Bài 2:

a. \(R=\dfrac{R1.\left(R2+R3\right)}{R1+R2+R3}=\dfrac{6\cdot\left(2+4\right)}{6+2+4}=3\Omega\)

b. \(U=IR=2.3=6V\)

\(\dfrac{1}{R}=\dfrac{1}{R1}+\dfrac{1}{R2}+\dfrac{1}{R3}=\dfrac{1}{4}+\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{5}{12}\Rightarrow R=2,4\left(\Omega\right)\)

\(\Rightarrow I=\dfrac{U}{R}=\dfrac{24}{2,4}=10\left(A\right)\)

Cấu tạo mạch: \(\left[\left(R_3//R_4\right)ntR_2\right]//R_1\)

\(U_1=U_{234}=U_m=24V\)

\(I_1=\dfrac{U_1}{R_1}=\dfrac{24}{12}=2A\)

\(R_{34}=\dfrac{R_3+R_4}{R_3\cdot R_4}=\dfrac{6+6}{6\cdot6}=\dfrac{1}{3}\Omega\)

\(R_{234}=R_2+R_{34}=9+\dfrac{1}{3}=\dfrac{28}{3}\Omega\)

\(I_2=I_{234}=\dfrac{U_{234}}{R_{234}}=\dfrac{24}{\dfrac{28}{3}}=\dfrac{18}{7}A\)

\(U_2=I_2\cdot R_2=\dfrac{18}{7}\cdot9=\dfrac{162}{7}V\)

\(U_{34}=I_{34}\cdot R_{34}=\dfrac{18}{7}\cdot\dfrac{1}{3}=\dfrac{6}{7}V\)

\(\Rightarrow U_3=U_{34}=\dfrac{6}{7}V\Rightarrow I_3=\dfrac{U_3}{R_3}=\dfrac{1}{7}A\)

\(I_A=I_1+I_3=2+\dfrac{1}{7}=\dfrac{15}{7}A\)

\(\Rightarrow\left\{{}\begin{matrix}a,R1//\left(R2ntR3\right)\Rightarrow Rtd=\dfrac{R1\left(R2+R3\right)}{R1+R2+R3}=6\Omega\\b,\Rightarrow\left\{{}\begin{matrix}U=U1=U23=24V\Rightarrow I1=\dfrac{U1}{R1}=\dfrac{8}{3}A\\I2=I3=\dfrac{U23}{R2+R3}=\dfrac{4}{3}A\\U2=I2.R2=8V\\U3=U-U2=16V\end{matrix}\right.\\c,R1//\left(R2ntRx\right)\Rightarrow Im=1,5.\dfrac{24}{6}=6A\\\Rightarrow Rtd=\dfrac{R1\left(R2+Rx\right)}{R1+R2+Rx}=\dfrac{9\left(6+Rx\right)}{15+Rx}=\dfrac{24}{Im}=4\left(\Omega\right)\Rightarrow Rx=1,2\Omega\end{matrix}\right.\)

a. \(R=R1+\left(\dfrac{R2.R3}{R2+R3}\right)=30+\left(\dfrac{15.10}{15+10}\right)=36\left(\Omega\right)\)

b. \(I=I1=I23=\dfrac{U}{R}=\dfrac{24}{36}=\dfrac{2}{3}A\left(R1ntR23\right)\)

\(U23=U2=U3=I23.R23=\dfrac{2}{3}\left(\dfrac{15.10}{15+10}\right)=4V\)(R2//R3)

\(\left\{{}\begin{matrix}I2=U2:R2=4:15=\dfrac{4}{15}A\\I3=U3:R3=4:10=0,4A\end{matrix}\right.\)

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