Twelve cells each having the same e.m.f are connected in series and are kept to a closed box. Some of the cell are connected in reverse order .The battery is connected in series with an ammeter an external resistance `R` and two cells of the same type as an in the battery .The current when they and support each other is `3` ampere and current is `2` ampare when the two oppose each other. How many cells are connected in servese order ?

Options

A. 4
B. 1
C. 3
D. 2

Answer

B

Explanation

Let n number of cells wrongly connected-
`E_(eq) = (12 - 2n)E`
`r_(eq) =(12-2n)E`
`r_(eq) = 12r`
(i) When 2 additional cell (help)
`E_(eq)^(.) = (12 - 2n)E + 2E`
`r_(eq)^(.) = 12 r + 2r = 14 r`
`((12-2n)E + 2E)/(14r) = 3`....... (i)
When 2 additional cells oppose the battery
`((12-2n)E - 2E)/(14r) = 2`......... (ii)
Now, `((12-2n)E + 2E)/(14 xx 3) = ((12 - 2n)E-2E)/(14 xx 2)`
`rArr 24E - 4ne + 4E = 36 E - 6ne - 6E`
`rArr 2ne = 2E rArr n =1`