Question

A cell develops the same power across two resistances `R_(1)` and `R_(2)` separately. The internal resistance of the cell is

Answer 1

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)/(R_(1)+r),thereforeP_(1)=i^(2)R=((E)/(R_(1)+r))^(2)R_(1)`
similarly `P_(2)=((E)/(R_(2)+r))^(2)R_(2)`, Given that `P_(1)=P_(2)`
Substituting the values we get ,`r=sqrt(R_(1)R_(2))`