$100$ cells, each of $e.m.f.$ $5\, V$ and internal resistance $1\, \Omega$, are to be arranged to produce maximum current in a $25\, \Omega$ external resistance. Each row must contain an equal number of cells. The number of rows should be:

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 $P$ and $Q$ each of emf $2.16 \text{ V}$ are connected in series with a resistor of $19.6 \text{ } \Omega$. An ideal voltmeter reads $2 \text{ V}$ when connected across the cell $P$ and $1.92 \text{ V}$ when connected across the cell $Q$. The ratio of the internal resistances of the cell $P$ and $Q$ is

When a resistor of $11 \,\Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \, A$. Instead,when a resistor of $5 \,\Omega$ is connected to the same electric cell in series,the current increases by $0.4 \, A$. The internal resistance of the cell is ................ $\Omega$.

Two identical batteries, each of $e.m.f.$ $2\,V$ and internal resistance $1.0\,\Omega$, are available to produce heat in an external resistance $R = 0.5\,\Omega$ by passing a current through it. The maximum Joulean power that can be developed across $R$ using these batteries is ............. $W$.

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 .............. $V$.