Question

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

Hint:

When a battery cell is reversed in a series circuit, its e.m.f. opposes the total e.m.f. of the circuit, reducing the overall voltage.

Answer 1

When \( n \) identical cells are connected in series, the total effective e.m.f. is: \[ E_{\text{total}} = nE \] If two cells are connected in reverse polarity, their individual e.m.f. will subtract from the total e.m.f.: \[ E'_{\text{total}} = (n-2)E \] However, the potential difference across a single reversed cell ‘X’ is equal to the sum of the e.m.f. of the reversed cells, which is: \[ V_X = 2E \] Thus, the potential difference across cell ‘X’ is \( 2E \).