Bài 4.
Cấu tạo mạch điện:
+Khi K mở: \([\left(R_1ntR_3\right)//\left(R_2ntR_4\right)]ntR_A\)
+Khi K đóng: \(\left(R_1//R_2\right)nt\left(R_3//R_4\right)ntR_A\)
a)Khi K mở:
\(R_{13}=R_1+R_3=20+20=40\Omega\)
\(R_{24}=R_2+R_4=30+80=110\Omega\)
\(R_{1234}=\dfrac{R_{13}\cdot R_{24}}{R_{13}+R_2}=\dfrac{40\cdot110}{40+110}=\dfrac{88}{3}\approx29,33\Omega\)
\(R=R_A+R_{1234}=2+\dfrac{88}{3}=\dfrac{94}{3}\approx31,333\Omega\)
Khi K đóng:
\(R_{12}=\dfrac{R_1\cdot R_2}{R_1+R_2}=\dfrac{20\cdot30}{20+30}=12\Omega\)
\(R_{34}=\dfrac{R_3\cdot R_4}{R_3+R_4}=\dfrac{20\cdot80}{20+80}=16\Omega\)
\(R'=R_A+R_{1234}=R_A+R_{12}+R_{34}=2+12+16=30\Omega\)
b)Khi K đóng: \(I_{12}=I_{34}=I_A=0,5A\)
\(U_{AB}=I\cdot R=0,5\cdot30=15V\)
\(U_{12}=I_{12}\cdot R_{12}=0,5\cdot12=6V\Rightarrow U_1=U_2=U_{12}=6V\left(R_1//R_2\right)\)
\(\Rightarrow I_1=\dfrac{U_1}{R_1}=\dfrac{6}{20}=0,3A;I_2=\dfrac{U_2}{R_2}=\dfrac{6}{30}=0,2A\)
\(U_{34}=I_{34}\cdot R_{34}=0,5\cdot16=8V\Rightarrow U_3=U_4=U_{34}=8V\)
\(\Rightarrow I_3=\dfrac{U_3}{R_3}=\dfrac{8}{20}=0,4A;I_4=\dfrac{U_4}{R_4}=\dfrac{8}{80}=0,1A\)
