A cell of constant e.m.f. first connected to a resistance `R_(1)` and then connected to a resistance `R_(2)`. If power delivered in both cases is then the internal resistance o f the cell is

Options

A. `sqrt(R_(1) R_(2))`
B. `sqrt(R_(1)/R_(2))`
C. `(R_(1)-R_(2))/2`
D. `(R_(1) +R_(2))/2`

Answer

A

Explanation

`P_(1) = P_(2) rArr (E/(r + R_(1))^(2) R_(1)) = (E/(r + R_(2)))^(2) R_(2)`
`rArr (r + R_(2))^(2)R_(1) =R_(2)(r + R_(1))^(2)`
`rArr r^(2)R_(1) + R_(1)R_(2)^(2) + 2rR_(1) R_(2) = R_(2)r^(2) + 2rR_(1)R_(2) + R_(2)R_(1)^(2)`
`rArr r^(2)(R_(1) - R_(2)) =R_(1)R_(2) (R_(1) - R_(2)) rArr r = sqrt(R_(1)R_(2))`