In the network shown,the potential difference between $A$ and $B$ is ................. $V$ $(R = r_1 = r_2 = r_3 = 1 \Omega, E_1 = 3 \, V, E_2 = 2 \, V, E_3 = 1 \, V)$.

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 . . . . . . .

The potential difference between the terminals of a cell is $20 \ V$ when a current of $2 \ A$ flows through the circuit. When the direction of current in the circuit is reversed,the potential difference between the terminals of the cell is $30 \ V$. The internal resistance of the cell is (in $Omega$)

$n$ equal cells,each having emf $E$ and internal resistance $r$,are connected in a circuit with an external resistance $R$. If the same current flows in the circuit whether the cells are connected in series or in parallel,then:

The terminal potential difference of a cell when short-circuited is ($E$ = $E.M.F.$ of the cell).

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.