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Question: Answered & Verified by Expert
In the electrical circuit shown in the figure, the current through the $4 \Omega$ resistor is
PhysicsCurrent ElectricityWBJEEWBJEE 2013
Options:
  • A $1 \mathrm{A}$
  • B $0.5 \mathrm{A}$
  • C $0.25 \mathrm{A}$
  • D $0.1 \mathrm{A}$
Solution:
1760 Upvotes Verified Answer
The correct answer is: $0.5 \mathrm{A}$
The current through the various branches of the circuit will be shown as

According to Kirchhoff's second law in closed circuit $B C D E B$
$$
\begin{array}{r}
2 I_{1}+4 l_{1}+2 l_{1}-8\left(1-l_{1}\right)=0 \\
\Rightarrow \quad 16 l_{1}-81=0
\end{array}
$$
$\Rightarrow \quad l_{1}=\frac{8 l}{16} \Rightarrow l_{1}=\frac{1}{2} l$
In closed circuit ABEFA
$$
-9+3 l+8\left(1-l_{1}\right)+2 l=0
$$
$\Rightarrow \quad 13l-8 I_{1}=9 \Rightarrow 13 /-8\left(\frac{1}{2} I\right)=9$
$\Rightarrow \quad I=\frac{9}{9}=1 \mathrm{A}$
So current through $4 \Omega$ resistor $l_{1}=\frac{1}{2} \times 1=0.5 \mathrm{A}$

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