Five cells, each of emf (E) and internal resistance (r), are connected in series. If out of these five cells, one of the cells is connected with opposite polarity, the equivalent emf and internal resistance of the combination, respectively, will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3E, 5r
In a series combination of cells the emfs add with sign (a reversed cell subtracts), while the internal resistances always add, whatever the polarity, because the current still passes through every cell.
\( \displaystyle E_{\mathrm{eq}} = 4E - E = 3E \)
\( \displaystyle r_{\mathrm{eq}} = r + r + r + r + r = 5r \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Cells in Series and in Parallel – “… The rule for series combination clearly can be extended to any number of cells:
(i) The equivalent emf of a series combination of \( n \) cells is just the sum of their individual emf’s, and
(ii) The equivalent internal resistance of a series combination of \( n \) cells is just the sum of their internal resistances.
This is so, when the current leaves each cell from the positive electrode. If in the combination, the current leaves any cell from the negative electrode, the emf of the cell enters the expression for \( \varepsilon_{eq} \) with a negative sign, as in Eq. (3.47).”