In a potentiometer arrangement a cell of 1.5 V gives a balance point at 45.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 75.0 cm, what is the emf of the second cell?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2.5 V
In a potentiometer the wire has a uniform potential gradient, so the emf of a cell is proportional to its balance length, \( \varepsilon \propto l \).
\( \displaystyle \frac{\varepsilon_2}{\varepsilon_1} = \frac{l_2}{l_1} \Rightarrow \varepsilon_2 = 1.5\,\mathrm{V}\times\frac{75.0}{45.0} = 2.5\,\mathrm{V} \)
A longer balance length means a larger emf, so \( \varepsilon_2 \) must be more than 1.5 V.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Exercises – …
