Question

Two cells having emf's of $10V$ and $8V$ and internal resistance of $1\Omega$ (each) are connected as shown with an external resistance of $8\Omega$. Find the current flowing through the circuit.

Answer 1

Suppose that a current $i$ flows through the external resistance ($8\Omega$) and it divides into two branches at the node $B$ as $i_1$ and $i_2$
Using KCL, $i_1+i_2=1$
Using KVL
For loop ABYXA
$(-i_1)1+(i-i_1)1=-10+8$
for loop ABQPA
$(-i_2)1+(-i)8=-10$
On solving we get
$i=\frac{18}{17}A\approx 1.06A$
$i_1=10-8i=(10-8.54)A=1.52A$
$i_2=i-i_1=-0.46A$
The negative sign for $i_2$ means that its direction its opposite to the direction that we had assumed.