Show that the rate of heat produced for ,any battery of emf E and internal resistance R will maximum for R = r

A set of n equal resistors, of value R each, are connected in series to a battery of emf E and internal resistance R. The current drawn is I. Now, the n resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10I. The value of n is

What is the maximum value of current available from a cell of emf 1.5 V and internal resistance 1 Omega ?

Two identical cells each of emf E and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the value of R is

n identical cells, each of emf e and internal resistance r, are first connected in series and then in parallel. What will be the ratio of the emfs and of the internal resistances of these two cell combinations?

What is the minimum number of cells each of emf 10 V and internal resistance 1 Omega to pass a current of 10 A through a resistance R of 3 Omega ? What is the discharging power of R?