A potentiometer wire 10 m long has a resistance of \( 40\,\Omega \). It is connected in series with a resistance box and a 2 V storage cell. If the potential gradient along the wire is 0.1 mV/cm, the resistance in the box is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 760\,\Omega \)
The potential gradient gives the potential drop across the whole wire; this fixes the current, and the cell's emf then fixes the total resistance of the series circuit (the storage cell is taken as ideal).
\( \displaystyle k = 0.1\,\mathrm{mV\,cm^{-1}} = \frac{0.1\times10^{-3}\,\mathrm{V}}{10^{-2}\,\mathrm{m}} = 0.01\,\mathrm{V\,m^{-1}} \)
\( V_{\mathrm{wire}} = k L = 0.01 \times 10 = 0.1\,\mathrm{V} \)
\( \displaystyle I = \frac{V_{\mathrm{wire}}}{R_{\mathrm{wire}}} = \frac{0.1\,\mathrm{V}}{40\,\Omega} = 2.5\times10^{-3}\,\mathrm{A} \)
The same current flows through the wire and the box in series:
\( \displaystyle R_{\mathrm{wire}} + R_{\mathrm{box}} = \frac{E}{I} = \frac{2}{2.5\times10^{-3}} = 800\,\Omega \)
\( R_{\mathrm{box}} = 800 - 40 = 760\,\Omega \)
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.”