$A$ cell of internal resistance $r$ is connected to an external resistance $R$. The current will be maximum in $R$,if

$A$ battery consists of $n$ rows of cells connected in parallel,with each row containing $m$ cells in series. The maximum current is obtained through an external resistance of $3 \, \Omega$. If the total number of cells is $24$ and the internal resistance of each cell is $0.5 \, \Omega$,find the values of $m$ and $n$.

Two cells of equal $e.m.f.$ $E$ and of internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ are connected in series. Now they are connected to an external resistance $R$. It is observed that the potential difference across the first cell becomes zero. The value of $R$ will be:

$(a)$ Six lead-acid type of secondary cells each of $emf$ $2.0 \;V$ and internal resistance $0.015 \;\Omega$ are joined in series to provide a supply to a resistance of $8.5\; \Omega$. What are the current drawn from the supply and its terminal voltage?
$(b)$ $A$ secondary cell after long use has an $emf$ of $1.9 \;V$ and a large internal resistance of $380\; \Omega$. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

Four identical cells, each of $2 \, V$ e.m.f., are connected in parallel. They supply current to an external circuit consisting of two $15 \, \Omega$ resistors connected in parallel. The terminal voltage of the equivalent cell, as measured by an ideal voltmeter, is $1.6 \, V$. Calculate the internal resistance of each cell in $\Omega$.

The terminal potential difference of a cell is greater than its $e.m.f.$ when it is