Tính cường độ dòng điện qua các điện trở R1=4Ω, R2=10Ω,R3=12Ω, R4=15Ω ?

a, (R1//R2)nt(R3//R4)

\(R_1\)//\(R_2\Rightarrow R_{12}=\dfrac{R_1.R_2}{R_1+R_2}=\dfrac{4.10}{4+10}=\dfrac{40}{14}=\dfrac{20}{7}\Omega\)

\(R_3\)//\(R_4\Rightarrow R_{34}=\dfrac{R_3.R_4}{R_3+R_4}=\dfrac{12.15}{12+15}=\dfrac{180}{27}=\dfrac{20}{3}\Omega\)

R12 nt R 34 => \(R_{tđ}=R_{12}+R_{34}=\dfrac{20}{7}+\dfrac{20}{3}=\dfrac{200}{21}\approx9,5\left(\Omega\right)\)

b, R12 nt R 34 \(\Rightarrow I_{12}=I_{34}=I=\dfrac{U_m}{R_{tđ}}=\dfrac{15}{9,5}\approx1,58\left(\Omega\right)\)

\(R_1\)//R2\(\Rightarrow U_1=U_2=U_{12}=I_{12}.R_{12}=1,58.\dfrac{20}{7}\approx4,5\Omega\)

\(\Rightarrow I_1=\dfrac{U_{12}}{R_1}=\dfrac{4,5}{4}=1,125\left(A\right)\); \(I_2=\dfrac{U_{12}}{R_2}=\dfrac{4,5}{10}=0,45\left(A\right)\)

R3//R4\(\Rightarrow U_3=U_4=U_{34}=I_{34}.R_{34}=1,58.\dfrac{20}{3}\approx10,5\Omega\)

\(\Rightarrow I_3=\dfrac{U_{34}}{R_3}=\dfrac{10,5}{12}=0,875\left(A\right)\)\(\Rightarrow I_4=\dfrac{U_{34}}{R_4}=\dfrac{10,5}{15}=0,7\left(A\right)\)

c, Ia = 0

Khi: \(\dfrac{R_1}{R_2}=\dfrac{R_3}{R_5}\Leftrightarrow\dfrac{4}{10}=\dfrac{12}{R_5}\Rightarrow R_5=30\left(\Omega\right)\)