Choose the correct statements :
(A) If two non ideal batteries are connected in series, then equivalent emf is larger than either of the two
(B) If two non ideal batteries are connected in series, then the equivalent internal resistance is smaller than either of the two.
(C) If two non ideal batteries are connected in parallel, then the equivalent emf is smaller than either of the two
(D) If two non ideal batteries are connected in parallel then the equivalent internal resistance is smaller than the two internal resistances
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) Only
For cells of emf \( \varepsilon_1, \varepsilon_2 \) and internal resistances \( r_1, r_2 \) the combinations follow from Kirchhoff’s rules.
Series (cells aiding each other)
\( \varepsilon_{\mathrm{eq}} = \varepsilon_1 + \varepsilon_2,\qquad r_{\mathrm{eq}} = r_1 + r_2 \)
Parallel
\( \displaystyle \varepsilon_{\mathrm{eq}} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2},\qquad r_{\mathrm{eq}} = \frac{r_1 r_2}{r_1 + r_2} \)
(A) If two non ideal batteries are connected in series, then equivalent emf is larger than either of the two — Correct. The emfs add.
(B) If two non ideal batteries are connected in series, then the equivalent internal resistance is smaller than either of the two. — Incorrect. The resistances add, so it is larger than either.
(C) If two non ideal batteries are connected in parallel, then the equivalent emf is smaller than either of the two — Incorrect. The equivalent emf is a weighted average, so it lies between \( \varepsilon_1 \) and \( \varepsilon_2 \).
(D) If two non ideal batteries are connected in parallel then the equivalent internal resistance is smaller than the two internal resistances — Correct. \( \frac{1}{r_{\mathrm{eq}}} = \frac{1}{r_1} + \frac{1}{r_2} \) is larger than either \( \frac{1}{r_1} \) or \( \frac{1}{r_2} \).
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.”
Cells in Series and in Parallel – “… Next, consider a parallel combination of the cells (Fig. 3.14). … We can put these equations in a simpler way,
\( \displaystyle \frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} \qquad (3.56) \)”