Two batteries of different $e.m.f.$ values and internal resistances are connected in series with each other and with an external load resistor. The current is $3.0 \,A$. When the polarity of one battery is reversed,the current becomes $1.0 \,A$. The ratio of the $e.m.f.$ values of the two batteries is ............

$n$ identical cells each of $e.m.f.$ $E$ and internal resistance $r$ are connected in series. An external resistance $R$ is connected in series to this combination. The current through $R$ 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:

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

Two cells,having the same $e.m.f.$ $E$,are connected in series through an external resistance $R$. The cells have internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. When the circuit is closed,the potential difference across the first cell is zero. The value of $R$ is

For two cells having the same $EMF$ $E$ and internal resistance $r$,the current passing through an external resistor of $6 \ \Omega$ is the same when both cells are connected either in parallel or in series. The value of internal resistance $r$ is . . . . . . $ \ \Omega$.