Question

Obtain expression for effective emf and internal resistance when two different cell connect parallel

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)