Question

${\epsilon }_1$ and ${\epsilon }_2$ are two batteries having emf of $34$V and $10$V respectively and internal resistance of $1\Omega$ and $2\Omega$ respectively. They are connected as shown in Figure. Using Kirchhoff's Laws of electrical networks, calculate the currents $I_1$ and $I_2$.

Answer 1

Using Kirchhoff's loop law in loop BEFA :
$34-4I_1-5(I_1+I_2)-7I_1-1I_1=0$
$⟹17I_1+5I_2=34$ ....(1)
Using Kirchhoff's loop law in loop BEDC :
$10-4I_2-5(I_1+I_2)-7I_2-2I_2=0$
$⟹5I_1+18I_2=10$ ......(2)
Equation (1) $\times 5$ - equation (2) $\times 17$, we get
$-281I_2=0$
$⟹I_2=0A$
From (1), $17I_1+5\times 0=34$
$⟹I_1=2A$