When an external resistance of $5\text{ }\Omega$ is connected across the terminals of a cell, a current of $0.25\text{ A}$ flows through it. When the $5\text{ }\Omega$ resistor is replaced by a $2\text{ }\Omega$ resistor, a current of $0.5\text{ A}$ flows through it. The internal resistance of the cell is . . . . . . $\Omega$.

When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flowing in the opposite direction produces a potential difference of $15\, V$, the $emf$ of the battery is .............. $V$.

Thousand cells of same emf $E$ and same internal resistance $r$ are connected in series in the same order without an external resistance. The potential drop across $399$ cells is found to be ......... $E$.

A circuit consists of three batteries of emf $E_{1} = 1 \text{ V}$, $E_{2} = 2 \text{ V}$, and $E_{3} = 3 \text{ V}$ and internal resistances $1 \Omega$, $2 \Omega$, and $1 \Omega$ respectively, which are connected in parallel as shown in the figure. The potential difference between points $P$ and $Q$ is: (in $\text{ V}$)

To get maximum current through a resistance of $2.5\,\Omega$,one can use $m$ rows of cells,each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega$. What are the values of $n$ and $m$ if the total number of cells is $45$?

Two cells of emf $1 \ V$ and $2 \ V$ and internal resistance $2 \ \Omega$ and $1 \ \Omega$,respectively,are connected in series with an external resistance of $6 \ \Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to the same external resistance. In this case,the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is . . . . . . .