What should be null for drawing maximum current from the cell?

Two cells of the same EMF $E$ but different internal resistances $r_1$ and $r_2$ are connected in series with an external resistance $R$ as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance $R$ must then be:

A battery of e.m.f $12 \mathrm{V}$ and internal resistance $0.5 \mathrm{\Omega }$ is charged by a battery charger which supplies a $132 \mathrm{V}$ d.c. supply using a series resistance of $11.5 \mathrm{\Omega }$. What is the terminal voltage of the battery during charging?

A battery of $emf 12V$ and internal resistance $3\Omega$ is connected to a resistor. If the current in the circuit is $0.5A$,.Calculate terminal voltage of the battery when the circuit is closed.

The internal resistance of an accumulator battery of emf  $6 \mathrm{V}$ is $10 \mathrm{\Omega }$ when it is fully discharged. As the battery gets charged up, its internal resistance decreases to $1 \mathrm{\Omega }$. The battery in its completely discharged state, is connected to a charger which maintains a constant potential difference of $9 \mathrm{V}$. Find the current through the battery

$\left(a\right)$ just after the connections are made and $\left(b\right)$ after a long time when it is completely charged.