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, R3 = 24
TH1: K mở =>R0 nt R2
\(=>U1=I0.R0\left(V\right)\)
\(=>Ubd=I0.Rtd=\dfrac{U1}{R0}\left(R0+R2\right)=>Ubd=U1+\dfrac{U1.R2}{R0}\)
\(=>\dfrac{U1.R2}{R0}=Ubd-U1=>R0=\dfrac{U1.R2}{Ubd-U1}\)
Th2: R0 nt (R1//R2)
\(=>U0=U2\)
\(=>Ubd=U2+I0.R12=U2+\dfrac{U2}{R0}.\dfrac{R1.R2}{R1+R2}\)
\(=>Ubd=U2+\dfrac{U2}{R0}.\dfrac{\dfrac{R2}{4}.R2}{\dfrac{R2}{4}+R2}=U2+\dfrac{U2}{R0}.\dfrac{\dfrac{R2^2}{4}}{\dfrac{5R2}{4}}\)
\(=U2+\dfrac{U2}{R0}.\dfrac{R2}{5}=>Ubd=U2+\dfrac{U2.R2}{5R0}\)
\(=>R0=\dfrac{U2.R2}{5\left(Ubd-U2\right)}\)
\(=>\dfrac{U1.R2}{Ubd-U1}=\dfrac{U2.R2}{5\left(Ubd-U2\right)}\)
\(=>Ubd=\dfrac{4U1U2}{5U1-U2}\)
a)Khóa \(K_1\) đóng, khóa \(K_2\) mở ta có CTM: \(\left(R_1ntR_2\right)//R_3\)
\(I_A=I_m=1A\)
\(R_{12}=R_1+R_2=5+5=10\Omega\)
\(R_{tđ}=\dfrac{R_{12}\cdot R_3}{R_{12}+R_3}=\dfrac{10\cdot15}{10+15}=6\Omega\)
\(U=R_{tđ}\cdot I=6\cdot1=6V=U_{12}=U_3\)
\(I_1=I_2=I_{12}=\dfrac{U_{12}}{R_{12}}=\dfrac{6}{10}=0,6A\)
\(I_3=1-0,6=0,4A\)
b)Khóa \(K_1\) mở và khóa \(K_2\) đóng ta có CTM: \(R_2//\left(R_1ntR_3\right)\)
\(R_{13}=R_1+R_3=5+15=20\Omega\)
\(R_{tđ}=\dfrac{R_2\cdot R_{13}}{R_2+R_{13}}=\dfrac{5\cdot20}{5+20}=4\Omega\)
\(I_A=\dfrac{U}{R_{tđ}}=\dfrac{6}{4}=1,5A\)
\(I_2=\dfrac{U_2}{R_2}=\dfrac{U}{R_2}=\dfrac{6}{15}=0,4A\)
\(I_1=I_3=I_{13}=I-I_2=1,5-0,4=1,1A\)