Two cells of equal $e.m.f.$ $E$ and of internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ are connected in series. Now they are connected to an external resistance $R$. It is observed that the potential difference across the first cell becomes zero. The value of $R$ will be:

Five identical cells each of internal resistance $1\, \Omega$ and $emf$ $5\, V$ are connected in series and in parallel with an external resistance $R$. For what value of $R$ will the current in the series and parallel combination remain the same? (in $\Omega$)

For a cell,the terminal potential difference $(P.D.)$ is $2.2\;V$ when the circuit is open and reduces to $1.8\;V$ when the cell is connected to an external resistance of $R = 5\;\Omega$. Determine the internal resistance $(r)$ of the cell.

$A$ cell sends a current through a resistance $R$ for time $t$. Now the same cell sends current through another resistance $r$ for the same time. If the same amount of heat is developed in both the resistances,then the internal resistance of the cell is:

$A$ $10\,V$ battery with internal resistance $1\,\Omega$ and a $15\,V$ battery with internal resistance $0.6\,\Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to ................ $V$.

Twelve cells,each having emf $E$ volts,are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This $12$-cell battery is connected in series with an ammeter,an external resistance $R$ ohms,and a two-cell battery (two cells of the same type used earlier,connected perfectly in series). The current in the circuit when the $12$-cell battery and $2$-cell battery aid each other is $3 \text{ A}$,and it is $2 \text{ A}$ when they oppose each other. Then,the number of cells in the $12$-cell battery that are connected wrongly is: