Question

A parallel combination of two cells of emf e1 and e2 and their resistance

Answer 1

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)

 Eequa=(E1R2+E2R2)/(R1+R2)

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