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 -enter image description here

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 ?


In practice you cannot get zero resistance in the cells, though you could use superconductors to get zero resistance in the connectors.

If the theoretical situation where there is zero resistance in the cells and in the connections between them, then applying Ohm's Law to the circuit loop containing the cells shows that either the cells have the same EMF or there is an infinite current in the loop. If the EMF values are the same then the current in the loop could be anything (zero divided by zero). However the current multiplied by zero resistance gives zero change to the potential difference between A and F.

In practice you could have very low resistances. This would produce large currents unless the EMFs are very nearly equal. The currents would continue until the EMFs of the cells became equal, or something broke. Perhaps the cell with higher EMF would charge the one with lower EMF. Perhaps the cell with higher EMF would merely heat the cells and loop until it had discharged to the point where its EMF had dropped to the EMF of the other. Perhaps it would result in the destruction of either or both cells or the wire in the loop.


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