The number of dry cells,each of $e.m.f.$ $1.5\,V$ and internal resistance $0.5\,\Omega$,that must be joined in series with a resistance of $20\,\Omega$ so as to send a current of $0.6\,A$ through the circuit is:

Two cells with the same e.m.f. $E$ and different internal resistances $r_1$ and $r_2$ are connected in series to an external resistance $R$. The value of $R$ so that the potential difference across the first cell is zero is

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 ............. $W$.

Eight identical cells,each having an electromotive force $E$ and internal resistance $r$,are connected in series to form a closed circuit. An ideal voltmeter is connected across $2$ cells. The voltmeter will read ........ $E$.

Explain the 'Mixed Connection' of cells and derive an expression for its equivalent emf and current.

Two cells of emfs $1$ $V$ and $2$ $V$ and internal resistances $2 \Omega$ and $1 \Omega$ respectively are connected in parallel and provide a current of $1$ $A$ through an external resistance. If the polarity of one cell is reversed, the current through the external resistance becomes $\frac{\alpha}{5}$ $A$. The value of $\alpha$ is . . . . . . .