Cells in Series and in Parallel

Two cells of voltage $10 \mathrm{V}$ and $2\mathrm{V}$ and Internal resistances $10 \mathrm{\Omega } ,5 \mathrm{\Omega }$. respectively, are connected In parallel with the positive end of $10\mathrm{V}$battery connected to negative pole of $2\mathrm{V}$ battery (Figure). Find the effective voltage and effective resistance of the combination.

Two cells of same emf $\mathrm{E}$ but internal resistance $r_1$; and $r_2$ are connected in series to an external resistor $R$(Figure)What should be the value of $R$so that the potential difference across the terminals of the first cell becomes zero ?

The circuit in Figure shows two cells connected In opposition to each other. Cell $E_1$ is of emf $6\mathrm{V}$ and Internal resistance $2\mathrm{\Omega }$; the cell $E_2$ is of emf $4\mathrm{V}$ and Internal resistance $8\mathrm{\Omega }$. Find the potential difference between the points A and B.

Two batteries of emf ${\epsilon }_1$, and ${\epsilon }_2\left({\epsilon }_2>{\epsilon }_1\right)$and internal resistances $r_1$ and $r_2$ respectively are connected in parallel as shown in figure