Which of the following gives the correct expression for potential gradient in terms of the resistivity \( (\rho) \) of the wire?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( k = I\rho A^{-1} \)
The potential gradient is the fall of potential per unit length of the wire, \( k = V/l \). By Ohm's law \( V = IR \), and the resistance of the wire is \( R = \rho l/A \).
\( \displaystyle V = IR = \frac{I\rho l}{A} \)
\( \displaystyle k = \frac{V}{l} = \frac{I\rho}{A} = I\rho A^{-1} \)
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 – “… A current I flows through the wire which can be varied by a variable resistance (rheostat, R) in the circuit. 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.”