When a current of $2 \ A$ flows through a resistor of $2 \ \Omega$,the terminal voltage across the cell is $E/2$. The internal resistance of the cell is ........ $\Omega$.

For a cell with non-zero (finite) internal resistance,write the relation between the terminal voltage $(V)$ and the electromotive force $(E)$ of the cell.

Two sources of equal $emf$ $E$ are connected in series with an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 > R_1)$. If the potential difference across the source of internal resistance $R_2$ is zero,then the value of $R$ is:

Infinite number of cells having $emf$ and internal resistance $(E, r)$,$(\frac{E}{n}, \frac{r}{n})$,$(\frac{E}{n^2}, \frac{r}{n^2})$,$(\frac{E}{n^3}, \frac{r}{n^3})$... are connected in series across an external resistance of $\frac{nr}{n+1}$. The current flowing through the external resistor is:

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

When a battery is connected across a resistor of $16 \Omega$,the voltage across the resistor is $12 \ V$. When the same battery is connected across a resistor of $10 \Omega$,the voltage across it is $11 \ V$. The internal resistance of the battery in ohm is