A potentiometer with a cell of 2.4 volt and internal resistance of \( 2\,\Omega \) maintains a potential drop across the resistance wire AB of length 2 meters and resistance \( 10\,\Omega \). A standard cell which maintains a constant emf of 'V' volt with internal resistance \( 0.2\,\Omega \) gives a balance point at 1.6 m length of the wire. The value of emf of second (standard) cell (V) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1.6 volt
In a potentiometer the driver cell sends a steady current through the wire, so the potential falls uniformly along it. At the balance point the galvanometer shows no deflection, so no current flows through the standard cell and its emf equals the potential difference across the balancing length.
The current in the wire, with the driver cell's internal resistance in series:
\( \displaystyle I = \frac{\varepsilon}{R_{AB} + r} = \frac{2.4\,\mathrm{V}}{10\,\Omega + 2\,\Omega} = 0.2\,\mathrm{A} \)
The potential drop across the wire and the potential gradient:
\( \displaystyle V_{AB} = I R_{AB} = 0.2 \times 10 = 2\,\mathrm{V} \)
\( \displaystyle k = \frac{V_{AB}}{L} = \frac{2\,\mathrm{V}}{2\,\mathrm{m}} = 1\,\mathrm{V\,m^{-1}} \)
The emf of the standard cell:
\( \displaystyle V = k\,l = 1\,\mathrm{V\,m^{-1}} \times 1.6\,\mathrm{m} = 1.6\,\mathrm{V} \)
The internal resistance \( 0.2\,\Omega \) of the standard cell does not matter, because no current flows through it at balance.
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.”