To get maximum current through a resistance of $2.5\,\Omega$,one can use $m$ rows of cells,each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega$. What are the values of $n$ and $m$ if the total number of cells is $45$?

Five cells each of emf $E$ and internal resistance $r$ are connected in series. Due to oversight,one cell is connected wrongly. The equivalent internal resistance of the combination is ........... $r$.

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

Two identical cells each of emf $E$ and internal resistance $r$ are connected in parallel with an external resistance $R$. To get maximum power developed across $R$,the value of $R$ is

Two cells $P$ and $Q$ each of emf $2.16 \text{ V}$ are connected in series with a resistor of $19.6 \text{ } \Omega$. An ideal voltmeter reads $2 \text{ V}$ when connected across the cell $P$ and $1.92 \text{ V}$ when connected across the cell $Q$. The ratio of the internal resistances of the cell $P$ and $Q$ is

As shown in the figure,a group of $N$ cells is connected in series,where the $emf$ of each cell $E_n$ varies with its internal resistance $r_n$ according to the relation $E_n = 1.5 r_n$. The current $I$ in the circuit is ................ $A$.