When cells are connected in parallel having EMF E1 E2 and so on but the resultant EMS is e so I want to ask why EMF is not additive in this case why in series combination EMF gets added

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Solution

We have two cells E1 and E2 with internal resistance r1 and r2 connected in parallel with a resistor R.
Let, I1 and I2 be the current through E1 and E2 respectively.
By applying KCL(Kirchhoff's Current Law),
I = I1 + I2
Let there resultant EMF is Eeff and resultant resistance be Req.
By KVL(Kirchhoff's Voltage Law)
Potential across R = Eeff - IReq
Potential across upper branch = E1 - Ir1
Potential across Lower Branch = E2 - I*r2
After solving we will get
**Eeff = (E1/r1 + E2/r2)Req

If two cells are identical, Eeff= (E/r + E/r)2r = E

While, Resultant of two cells connected in series = E1+ E2

If n number of similar cells are connected in series , then Eeff= nE**

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