In the following circuit, the current through $6 \Omega$ resistor is

$A$ cell of emf $10 \text{ V}$ and internal resistance $3 \Omega$ is connected in parallel with another cell of emf $7 \text{ V}$ and internal resistance $\frac{3}{5} \Omega$,such that their positive terminals are joined together and their negative terminals are joined together. Their combined positive terminal is joined with the negative terminal,and their combined negative terminal is joined with the positive terminal of a third cell of emf $20 \text{ V}$ with internal resistance $2 \Omega$. The combination can be replaced by a battery of emf $E$ and internal resistance $r$. The values of $E$ and $r$ are respectively:

Two non-ideal identical batteries are connected in parallel. Consider the following statements:
$(i)$ The equivalent e.m.f. is smaller than either of the two e.m.f.s.
$(ii)$ The equivalent internal resistance is smaller than either of the two internal resistances.

When cells are connected in parallel,then

For a cell with non-zero (finite) internal resistance,write the relation between the terminal voltage $(V)$ and the electromotive force $(E)$ of the cell.

Two cells with same emf $E$ but different internal resistances,$r_1$ and $r_2$,are connected in series to an external resistance $R$. If the potential difference across the first cell is zero,then the value of $R$ is