Question

n identical cells, each of e.m.f. E and internal resistance r, are connected in series. Later on it was found out that two cells ‘X’ and ‘Y’ are connected in reverse polarities. Calculate the potential difference across the cell ‘X'.

Answer 1

Number of cells = n 

EMF of each cell = E

Internal resistance of each cell = r

All the cells are in series.

Thus, total internal resistance, R = nr 

Total EME (e) = nE

As the two cells are connected in reverse polarity, these two cells will cancel-out the contribution of other two cells in the loop.

Then, the net EMF across the circuit will be:

E_eq = nE − 4E

The current I in the circuit = `(nE - 4E)/(nr)`

Voltage across the opposite connected batteries,

V = E − Ir

V = `E - (E(n - 4))/(nr) xx r`

V = `(4 E)/n`