Dear Student
Let r be the internal resistance of the cell and E its EMF. When connected across the resistance R
1 in the circuit, current passing through the resistance is
i = E/R1 + r
So, P1 = i2R1 = [E/(R1+r)]2R1
Similarly P2 = [E/(R2 +r)]2 R2
Given that P1 = P2
Substituting the values, we get,
r = √(R1R2)
Regards
Arun (askIITians forum expert)
