Question

Answer 1

\(\Rightarrow\left\{{}\begin{matrix}a,R1ntR2\Rightarrow Ia=\dfrac{U}{R1+R2}=\dfrac{18}{9+15}=0,75A\\b,\Rightarrow R1nt\left(R2//R3\right)\Rightarrow I2=0,5I3\\\Rightarrow I1=I2+I3=1,5I3=1,5\left(\dfrac{I1.R23}{R3}\right)=\dfrac{1,5.I1.R23}{R3}\\\Rightarrow I1=\dfrac{1,5I1.R23}{R3}\Rightarrow R3=1,5R23\Rightarrow R3=\dfrac{15R3}{15+R3}.1,5\Rightarrow R3=7,5\Omega\end{matrix}\right.\)

\(\Rightarrow Rtd=R1+\dfrac{R2R3}{R2+R3}=14\Omega\Rightarrow I1=I23=\dfrac{U}{Rtd}=\dfrac{18}{14}=\dfrac{9}{7}A\Rightarrow IA=\dfrac{U3}{R3}=\dfrac{I23.R23}{7,5}=\dfrac{\dfrac{9}{7}\left(\dfrac{15.7,5}{15+7,5}\right)}{7,5}=\dfrac{6}{7}A\)