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 ................ $\Omega$.

When two cells of emfs $E_1$ and $E_2$ and different internal resistances $r_1$ and $r_2$ are connected in series with an external load resistor $R$,the current through the load is $5 \ A$. If the polarity of the cell of emf $E_2$ is reversed,then the current through the load is $2 \ A$. Then $\frac{E_1}{E_2} = $

$A$ group of $N$ cells whose $emf$ varies directly with the internal resistance as per the equation $E_N = 1.5\, r_N$ are connected in series as shown in the figure. The current $I$ in the circuit is ........... $A$.

Four identical cells,each having an electromotive force $(e.m.f.)$ of $12\,V$,are connected in parallel. The resultant electromotive force $(e.m.f.)$ of the combination is .............. $V$.

$10$ cells,each of $emf$ $E$ and internal resistance $r$,are connected in series to a variable external resistance. The figure shows the variation of the terminal potential difference of their combination with the current drawn from the combination. The $emf$ of each cell is ................ $V$.

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: