A circuit consists of a resistance R connected to n  similar cells.  If the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance r of each cell is given by

r = R 

$ \text{ If n cells are connected in series then } I = \frac{nE}{R + nr}$

$ \text{If n cells are connected in parallel } I'= \frac{E}{R + r/n}$

$ I = I' $

$ \frac{nE}{R + nr} = \frac{E}{R + r/n}$ 

$ nR + r = R + nr $

$ R = r$