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Two cells of emf e1 and e2 ,internal resistance r1andr2,conected in parallel. The equivalent emf of the combination is?

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Two cells of emf e1 and e2, internal resistance r1 and r2 connected in para

Two cells of emf e1 and e2, internal resistance r1 and r2 connected in parallel. The equivalent emf of the combination is

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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 - I*Req

Potential across upper branch = E1 - I*r1

Potential across Lower Branch = E2 - I*r2

After solving we will get

Eeff = (E1/r1 + E2/r2)*Req

and

Req = r1*r2/(r1 +r2)