In the box shown current $i$ enters at $H$ and leaves at $C$. If $i_{AB} = \frac{{\text{i}}}{6}$ , $i_{DC} = \frac{{\text{2i}}}{3}$ ,$i_{HA} = \frac{{\text{i}}}{2} , i_{GF} = \frac{{\text{i}}}{6} , i_{HE} = \frac{{\text{i}}}{6}$ , choose the branch in which current is zero
Diffcult
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Applying junction law at $H$
$I_{H G}=i-\left(\frac{i}{2}+\frac{i}{6}\right)=\frac{i}{3}$
Applying junction law at $G$
$I_{H G}=\frac{i}{6}+I_{G B} \Rightarrow I_{G B}=\frac{i}{6}$
Applying junction law at $B$ .
$I_{B C}=I_{G B}+\frac{i}{6}=\frac{i}{3}$
Applying junction law at $C$
$I_{B C}+\frac{2 i}{3}+I_{F C}=i \Rightarrow I_{F C}=0$
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