# What will be the equivalent EMF if we connect cells with 0 internal resistance in parallel?

Well we have a formula for calculating equivalent EMF of n cells with EMF $$E_1,E_2,E_3,....E_n$$ and internal resistances $$r_1,r_2,r_3,....r_n$$ as $$E= ({E_1/r_1 + E_2/r_2 + E_3/r_3)}/({1/r_1 + 1/r_2 + 1/r_3})$$ for 3 cells ,but we can extend up till n cells

What will the formula be if $$\mathrm{r_1,r_2,r_3...r_n}$$ all approach to 0. Incapable of working out multivariable limits ,I tried to derive it just like the way we can derive this formula for cells in parallel (with internal resistance ) But what i get is this -

Surprisingly it comes out to be $$\mathrm{E_1 = E_2}$$ . But isn't the EMF of cell decided by us? Why does this happens ? Or am i going wrong at any step ?