Question

In the electrical circuit shown in the figure the current through the $4\Omega$ resistor is:

• A. $1A$
• B. $0.5A$
• C. $0.25A$
• D. $0.1A$

Answer 1

Answer: (B)

$0.5A$

The current through the various branches of the circuit will be shown as given
According to Kirchhoff's second law in closed circuit $BCDEB$
$2I_1+4I_1+2I_1-8(I-I_1)=0$
$\Rightarrow 16I_1-8I=0$
$\Rightarrow I_1=\frac{8I}{16}\Rightarrow I_1=\frac{1}{2}I....\left(i\right)$
In closed circuit $ABEFA$
$-9+3I+8(I-I_1)+2l=0$
$\Rightarrow 13l-8I_1=9$
$\Rightarrow 13l-8\left(\frac{1}{2}I\right)=9$
$\Rightarrow I=\frac{9}{9}=1A...\left(ii\right)$
So current through $4\Omega$ resistor $I_1=\frac{1}{2}\times 1=0.5A$