Two batteries each of `E` and internal resistance `r` are connected turn by turn in series and in parallel, and are used to find current in an external resistance `R`. If the current in series is equal to that in parallel, the internal resistance of each battery is

Options

A. `R`
B. `R//2`
C. `R//3`
D. `R//4`

Answer

A

Explanation

(a)
`I_(S) = (2E)/(2r + R)` and `I_(P) = (E)/((r )/(2) + R) = (2E)/(r + 2R)`
If `I_(S) I_(P)`
`(2E)/(2r + R) = (2E)/(r + 2R)`
`2r + R = r + 2R`
`r = R`