Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio `((R)/(r))` is

Options

A. 2
B. `1//2`
C. `1//5`
D. 1

Answer

D

Explanation

Here emf of each cell = E
internal resistance of each cell =r
Number of cell s , n= 5
in series .
The current through the external resistance R is
`I = (nE) /( nr +R) =(5 E) /( 5r ) +R …(i) `
in parallel
the current through the external resostance R is
` I = (E )/( (t) /( n)+R) =(nE ) /( r +nR) =(5E ) /( r +5R ) ..(ii) `
as per question I=I
`(5E ) /( 5r +R ) =( 5E )/(r+5R) or . 5R +R = r + 5R `
or R = r or `(R ) /( r ) = 1 `