Question

In the circuit shown, current (in $A$ ) through the $50 \, V$ and $30 \, V$ 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 $CEFDC$
$−5(I−I_1)−10I_2−5(I−I_1)+20I_1=0$
$- 10 \left(\text{I} - 2 \cdot 5\right) - 3 0 + \left(2 0 \times 2 \cdot 5\right) = 0$
$- 10 \text{I} + 2 5 - 3 0 + 5 0 = 0$
$\text{I}=4\cdot 5 \, \text{A}$
$\text{I}-\text{I}_{1}-\text{I}_{2}=4\cdot 5-2\cdot 5-3=-1$
$4.5 \, A$ and $1 \, A$