A potentiometer is supplied a constant voltage of 5 V. A cell of emf 1.4 V is balanced by the voltage drop across 280 cm of the potentiometer wire. The total length of the potentiometer wire will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 m
A uniform potentiometer wire has a constant potential gradient \( k = V/L \), where \( V \) is the voltage across the whole wire of length \( L \). At balance, the emf of the cell equals the drop across the balancing length \( l \).
\( \displaystyle \varepsilon = k\,l = \frac{V}{L}\,l \;\Rightarrow\; L = \frac{V\,l}{\varepsilon} \)
Here the supply voltage of 5 V is taken to be across the whole wire.
\( \displaystyle L = \frac{5\,\mathrm{V} \times 280\,\mathrm{cm}}{1.4\,\mathrm{V}} = 1000\,\mathrm{cm} = 10\,\mathrm{m} \)
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):
Potentiometer – “… Since the wire is uniform, the potential difference between A and any point at a distance l from A is
\( \displaystyle \varepsilon(l) = \phi\, l \qquad (3.89) \)
where φ is the potential drop per unit length.”