A battery of emf `E` and internal resistance `r` is connected to a resistor of restance `r_(1)` and Q Joules of heat is produced in a certain time `t`. When te same battery is connected to another resistor of resistance `r_(2)` the same quantity of heat is produced in the same time `t`. Then the value of `r` is

Options

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

Answer

D

Explanation

`Q=(V^(2))/(r_(1))=(E^(2)r_(1))/((r+r_(1))^(2))`
`Q=(V^(2))/(r_(2))=(E^(2)r_(2))/((r+r_(2))^(2))`