Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ ($E_2 > E_1$ and $r_2 > r_1$) respectively,are connected in parallel as shown in the figure. The equivalent emf of the combination is $E_{eq}$. Then

Given below are two statements $:$
Statement-$I$ : The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement-$II$ : The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements,choose the correct answer from the options given below.

Two cells of internal resistance $r_{1}$ and $r_{2}$ and of the same emf are connected in series across a resistor of resistance $R$. If the terminal potential difference across the cell of internal resistance $r_{1}$ is zero,then the value of $R$ is

Two cells,having the same $e.m.f.$ $E$,are connected in series through an external resistance $R$. The cells have internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. When the circuit is closed,the potential difference across the first cell is zero. The value of $R$ is

Write the equation for the equivalent electromotive force (emf) of a series connection of cells.

Four identical cells, each of $2 \, V$ e.m.f., are connected in parallel. They supply current to an external circuit consisting of two $15 \, \Omega$ resistors connected in parallel. The terminal voltage of the equivalent cell, as measured by an ideal voltmeter, is $1.6 \, V$. Calculate the internal resistance of each cell in $\Omega$.