In the circuit shown in figure,

$E_1=10V,E_2=4V,r_1=r_2=1\Omega$ and $R=2\Omega$.

Find the potential difference across battery $1$ and battery $2.$

 Net emf of the circuit $=E_1-E_2=6V$

Total resistance of the circuit $=R+r_1+r_2=4\Omega$

Current in the circuit, $i=\frac{\text{ net emf }}{\text{ total resistance }}=\frac{6}{4}=1.5A$

Now,

$V_1=E_1-i{r}_1=10-(1.5)\left(1\right)$

$=8.5V$

and

$V_2=E_2+i{r}_2=4+(1.5)\left(1\right)$

$=5.5V$