n identical cells, each of emf `epsilon` and internal resistance r, are joined in series to form a closed circuit. One cell A is joined with reversed polarity. The potential difference across any one cell is

Options

A. `((n+1) nE-4)/(n)`
B. `(n^(2) E-4)/(n)`
C. `((n^(2) + 1) E-3)/(n)`
D. `((n+1) E-4)/(n-1)`

Answer

A

Explanation

When two cells are connected with reverse polarity then equivalent emf of the combination of the cells becomes `nE-4`, because two cells will cancel the emf of two other cells in combination. Effective internal resistance of this circuit becomes nr because all internal resistances are connected in series. Net current flowing in the circuit can be written as follows: `i= ((nE-4)/(nr))` Current will enter the positive terminal of cells, which are connected with reverse polarity. Hence terminal potential difference across them would be:
`V= E+ir = nE + ((nE-4)/(nr)) r = (n^(2)E + nE-4)/(n)`
`= ((n+1) nE-4)/(n)` Thus, option (a) is correct