N identical cells whether joined together in series or in parallel, give the same current, when connected to an external resistance of 'R'. The internal resistance of each cell is:-

Options

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

Answer

D

Explanation

The circuit are shown in the figure. In series combination of cells, Internal resistance are In series.

`I_S=(E+E)/(r+r+R)=(2E)/(2r+R)`
In parallel combination of cells, Internal resistance are in parallel with each other.
`therefore` Effective Internal resistance
`R_"eq"=(rxxr)/(r+r)=r^2/(2r)=r/2`
`therefore" "I_p=E/(R+r/2)=(2E)/(2R+r)`
As per questions, `I_S=I_p`
`therefore" "(2E)/(2r+R)=(2E)/(2R+r)rArr2r+r=2R+r`
`rArr" "r=R`