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)))/(2sqrt(R_(2))-sqrt(R_(1)))`
D. `sqrt(R_(1)R_(2))(sqrt(R_(2))-sqrt(R_(1)))/(sqrt(R_(2))-sqrt(R_(1)))`

Answer

B