When a resistance of $2\,\Omega$ is connected across the terminals of a cell,the current is $0.5\,A$. When the resistance is increased to $5\,\Omega$,the current is $0.25\,A$. The internal resistance of the cell is ............. $\Omega$.

Two cells with the same e.m.f. $E$ and different internal resistances $r_1$ and $r_2$ are connected in series to an external resistance $R$. The value of $R$ so that the potential difference across the first cell is zero is

Twelve cells,each having emf $E$ volts,are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This $12$-cell battery is connected in series with an ammeter,an external resistance $R$ ohms,and a two-cell battery (two cells of the same type used earlier,connected perfectly in series). The current in the circuit when the $12$-cell battery and $2$-cell battery aid each other is $3 \text{ A}$,and it is $2 \text{ A}$ when they oppose each other. Then,the number of cells in the $12$-cell battery that are connected wrongly is:

$A$ 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 $n$.

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 ................ $A$.

What is meant by the series connection of cells? Derive the equation for the equivalent electromotive force $(emf)$ of two cells with $emf$ $\varepsilon_1$ and $\varepsilon_2$ connected in series.