The potential difference in open circuit for a cell is $2.2\, V$. When a $4\, \Omega$ resistor is connected between its two electrodes,the potential difference becomes $2\, V$. The internal resistance of the cell will be .............. $\Omega$.

$A$ resistor of resistance $R$ is connected between the terminals of a cell of $\operatorname{emf} E$ and internal resistance $r$. If $I$ is the current through the circuit,the terminal potential difference of the cell is given by:

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:

Given below are two statements $:$
Statement-$I$ : The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement-$II$ : The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements,choose the correct answer from the options given below.

Four cells, each of emf $E$ and internal resistance $r$, are connected in series across an external resistance $R$. By mistake, one of the cells is connected in reverse. Then the current in the external circuit is

$A$ battery consists of $n$ rows of cells connected in parallel,with each row containing $m$ cells in series. The maximum current is obtained through an external resistance of $3 \, \Omega$. If the total number of cells is $24$ and the internal resistance of each cell is $0.5 \, \Omega$,find the values of $m$ and $n$.