Question

In the circuit shown, current (in $A$ ) through the $50V$ and $30V$ batteries are, respectively

• A. $2.5$ and $3$
• B. $4.5$ and $1$
• C. $5.5$ and $2$
• D. $3.5$ and $2$

Answer 1

Answer: (B)

Applying Kirchoff's loop rule in $ABCDA$
$50-20I_1=0$
$\therefore {\text{I}}_1=2\cdot 5\text{A}$
Applying Kirchoff's loop rule in $EGHFE$
$-10I_2+30=0$
$\therefore {\text{I}}_2=3\text{A}$
Applying Kirchoff's loop rule in $CEFDC$
$-5(I-I_1)-10I_2-5(I-I_1)+20I_1=0$
$-10\left(\text{I}-2\cdot 5\right)-30+\left(20\times 2\cdot 5\right)=0$
$-10\text{I}+25-30+50=0$
$\text{I}=4\cdot 5\text{A}$
$\text{I}-{\text{I}}_1-{\text{I}}_2=4\cdot 5-2\cdot 5-3=-1$
$4.5A$ and $1A$