$A$ cell $E_{1}$ of $emf 6 V$ and internal resistance $2 \Omega$ is connected with another cell $E_{2}$ of $emf 4 V$ and internal resistance $8 \Omega$ as shown in the figure. The potential difference across points $X$ and $Y$ is............ $V$.

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:

What will be the ratio of the equivalent electromotive force (emf) of two cells connected in series to the equivalent emf of two cells connected in parallel?

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 $J_1$. When the same batteries are connected in parallel across $R$,the rate is $J_2$. If $J_1 = 2.25 J_2$,then the value of $R$ in $\Omega$ is

Two batteries with different $e.m.f.$ are connected in parallel. Consider the following statements: $(i)$ The equivalent $e.m.f.$ is less than the individual $e.m.f.s$. $(ii)$ The equivalent internal resistance is less than the individual internal resistances.

Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ ($E_2 > E_1$ and $r_2 > r_1$) respectively,are connected in parallel as shown in the figure. The equivalent emf of the combination is $E_{eq}$. Then