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

Explanation

Power for `R_(1) rarr P_(1) = ( epsilon^(2) R_(1))/((R_(1)+r)^(2))`
Power for `R_(2) rarr P_(2)= ( epsilon^(2) R )/( ( R_(2)+r)^(2))`
As pwer question `P_(1)+P_(2)`
`implies (epsilon^(2)R_(1))/((R_(1)+r)^(2))= (epsilon^(2) R_(2))/((R_(2)+r)^(2))`
`implies sqrt(R_(1))(R_(2)+r)= sqrt(R_(2))(R_(1)+r)`
`implies sqrt(R_(1))R_(2)+sqrt(R_(1))r= sqrt(R_(2))R_(1)+sqrt(R_(2))r`
`implies r (sqrt(R_(1))-sqrt(R_(2))) = sqrt(R_(1)R_(2)) ( sqrt(R_(1)) - sqrt(R_(2)))`
`implies r = sqrt(R_(1)R_(2))`