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Two cells of emfs ει & ε2 and internal resistances r1 & r2 respectively are connected inparallel. Obtain expressions for the equivalent resistance and emf of the combination

Answer»

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 + I2Let there resultant EMF is Eeff and resultant resistance be Req.By KVL(Kirchhoff's Voltage Law)Potential across R = Eeff - I*ReqPotential across upper branch = E1 - I*r1Potential across Lower Branch = E2 - I*r2After solving we will getEeff = (E1/r1 + E2/r2)*ReqandReq = r1*r2/(r1 +r2)

Eequa=(E1R2+E2R2)/(R1+R2)



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