N batteries each of emf E and internal resistance r are first connected in series and then in parallel to an external resistance R. if current through R is same in both cases then.

Options

A. `R=r^(2)//N`
B. `R-Nr//2`
C. `R=Nr`
D. `R=r`

Answer

4

Explanation

In serie s
curren t `=(NE)/(Nr+R)`
In parallel, current `=(E)/((r//N)+R)=(NE)/(r+NR)`
since the currents in the two cases are equal,
`(NE)/(Nr+R)=(NE)/(r+NR)`
or `Nr+R=r+NR`
or `Nr-r=NR-R`
or `r(N-1)=R(N-1)`
or r=R
`therefore R=r`.