What is called the internal resistance of a cell?

The internal resistance of a cell depends on

What is meant by the series connection of cells? Derive the equation for the equivalent electromotive force $(emf)$ of two cells with $emf$ $\varepsilon_1$ and $\varepsilon_2$ connected in series.

The emfs of three cells connected in parallel are $E_1=5 \ V, E_2=8 \ V$ and $E_3=10 \ V$ and their internal resistances are $r_1=1 \ \Omega, r_2=2 \ \Omega$ and $r_3=3 \ \Omega$,respectively. By changing $E_3$ to $E_{3N}$,the equivalent emf is doubled. Then $E_{3N}$ in $V$ is:

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 $\Omega$.

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