A cell of e.m.f E is connected to a resistance `R_(1)` for time t and the amount of heat generated in it is H. If the resistance `R_(1)` is replaced by another resistance `R_(2)` and is connected to the cell for the same time t, the amount of heat generated in `R_(2)` is 4H. Then the internal resistance of the cell is

Options

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

Answer

B

Explanation

`H= i^(2)Rt`
`=(E/(r + R_(1))^(2) (R_(1)t)`

`4H = (E/(r + R_(2))^(2)) (R_(2)t))`
`1/4 =(1/(r + R_(1))) R_(1) xx (r + R_(2))^(2)/R_(2)`
`rArr sqrt(R_(2))(R_(1) +r) = 2sqrt(R_(1)) (R_(2) + r)`
`sqrt(R_(1)R_(2)) (2sqrt(R_(2)) - sqrt(R_(1)))/(sqrt(R_(2))- 2sqrt(R_(1)))`