|parallel configuration:||i = (emf)/(R + r/2)|
|OR:||i(x) = 1/(1 + x/2)|
|series configuration:||i = (emf)/(r + R/2)|
|OR:||i(x) = 1/(x + 1/2)|
where the dimensionless involves a dimensionless internal resistance x=r/R and a dimensionless current which is the actual current in ratio to the current that would be present if r=0. This formulation facilitates the computer generated graph below (or whatever algebraic operations which you might wish to carry out in finding the optimal configuration).
When the load resistance is larger than internal resistance (R>r, lighter load, x<1), use the series configuration.
When load resistance is smaller than internal resistance (R<r, heavier load, x>1), use the parallel configuration.
Graph created with Origin for Windows