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 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 $n > 4$):

An electric eel generates an electric current using biological cells called electroplaques. The eel has a total of $5000$ electroplaques arranged in $100$ rows. This arrangement is shown in the figure. Each electroplaque has an $emf$ of $0.15\ V$ and an internal resistance of $0.25\ \Omega$. The water surrounding the eel completes the circuit between its head and tail. If the resistance of the water is $500\ \Omega$,the electric current generated by the eel in the water is .......... $A$.

Two cells of equal $e.m.f.$ $E$ and of internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ are connected in series. Now they are connected to an external resistance $R$. It is observed that the potential difference across the first cell becomes zero. The value of $R$ will be:

In the previous problem,if the cells had been connected in parallel (instead of in series),which of the above graphs would have shown the relationship between total current $I$ and $n$ (number of cells)?

Two cells of same emf $E$ but different internal resistances $r_{1}$ and $r_{2}$ are connected in series with a resistance $R$. The value of resistance $R$,for which the potential difference across the second cell is zero,is