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. 1
B. 2
C. 3
D. 4

Answer

a

Explanation

Let `epsilon` be the emf of cell and `R` be the total resistance of the circuit
Let `n` cell be wrongly connected Net emf of battery `= (12- 2n)epsilon` when `2` other identical cells are connecting so that these aid the battery net emf
`= (12 - 2n) epsilon + 2 and I = 3A`
so `((12 - 2n) epsilon + 2 epsilon)/(R) = 3`.....(i)
where`2` cell oppose the battery net emf
`(12 - 2n) epsilon + 2 epsilon`
As per the question
Current `= ((12 - 2n) epsilon + 2 epsilon)/(R) = 2`....(ii)
Dividing (i) and (ii) we get `n = 1`