The current provided by a battery is maximum when:

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 $P_1$. When the same batteries are connected in parallel across $R$,the rate of heat produced is $P_2$. If $P_1 = 2.25 P_2$,then the value of $R$ is (in $Omega$)

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

Ten identical cells each of potential $E$ and internal resistance $r$ are connected in series to form a closed circuit. An ideal voltmeter connected across three cells will read $...........E$.

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} = $

Two cells $E_1$ and $E_2$ having equal $EMF$ $E$ and internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively are connected in series. This combination is connected to an external resistance $R$. It is observed that the potential difference across the cell $E_1$ becomes zero. The value of $R$ will be