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.

One electric cell (having emf of $2 \ V$ and internal resistance of $0.1 \ \Omega$) and another electric cell (having emf of $4 \ V$ and internal resistance of $0.2 \ \Omega$) are connected in parallel to each other. The equivalent emf will be . . . . . . $V$.

Two non-ideal identical batteries are connected in parallel. Consider the following statements:
$(i)$ The equivalent e.m.f. is smaller than either of the two e.m.f.s.
$(ii)$ The equivalent internal resistance is smaller than either of the two internal resistances.

$N$ identical cells are connected in series or in parallel. When an external resistor $R$ is connected to them,they provide the same current. The internal resistance $r$ of each cell is:

$12$ cells,each having the same $emf$ $E$ and internal resistance $r$,are connected in series,but some cells are wrongly connected. This arrangement is connected in series with an ammeter and two additional cells (each of $emf$ $E$ and internal resistance $r$). The current is $3 \, A$ when the cells and the battery aid each other,and it is $2 \, A$ when they oppose each other. The number of cells wrongly connected is:

The terminal potential difference of a cell is greater than its $e.m.f.$ when it is