How the internal resistance be related to extrnal resistance of a closed circuit such that current in the circuit is the maximum?

Find relation between emf and internal resistance of a cell.

A cell of emf (E) and of internal resistance (r ) is connected across an external resistance (R ). Deduce the condition for current in the ciruit to be maximum.

A battery of e.m.f epsilon and internal resistance r is connected to an external resistance R to complete the circuit. Show that the battery of delivers the maximum power to R, when R=r.

Calculate the main current in the given circuit.