When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$,the rate of heat produced in $R$ is $J_1$. When the same batteries are connected in parallel across $R$,the rate is $J_2$. If $J_1 = 2.25 J_2$,then the value of $R$ in $\Omega$ is

$n$ identical cells are joined in series,with two cells $A$ and $B$ in the loop having reversed polarities. The $EMF$ of each cell is $E$ and the internal resistance is $r$. The potential difference across cell $A$ or $B$ is (where $n > 4$):

$100$ cells, each of $e.m.f.$ $5\, V$ and internal resistance $1\, \Omega$, are to be arranged to produce maximum current in a $25\, \Omega$ external resistance. Each row must contain an equal number of cells. The number of rows should be:

When a resistor of $11 \,\Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \, A$. Instead,when a resistor of $5 \,\Omega$ is connected to the same electric cell in series,the current increases by $0.4 \, A$. The internal resistance of the cell is ................ $\Omega$.

Five identical cells each of internal resistance $1\, \Omega$ and $emf$ $5\, V$ are connected in series and in parallel with an external resistance $R$. For what value of $R$ will the current in the series and parallel combination remain the same? (in $\Omega$)

If the $EMF$ of each cell is $E = 1.5 \text{ V}$ and internal resistance is $r$, as shown in the figure, what is the current $i$ flowing through the circuit (in $\text{ A}$)?