The relation and units of cell constant are, respectively,

The correct answer is Option (1) → cell constant = \(l/A\); units: \(cm^{-1}\)

The resistance of a conductor is proportional to its length l and inversely proportional to its area of cross-section A, \( R = \rho\,\frac{l}{A} \). Writing the conductivity \( \kappa = 1/\rho \):

    \( \displaystyle \kappa = \frac{1}{R}\cdot\frac{l}{A} \)

For a conductivity cell, l is the distance between the electrodes and A their area. The quantity l/A is the cell constant, G*. Its unit follows from the units of length and area:

    \( \displaystyle G^{*} = \frac{l}{A} \Rightarrow \frac{\mathrm{cm}}{\mathrm{cm^2}} = \mathrm{cm^{-1}} \)

So the cell constant is l/A with unit cm⁻¹ (m⁻¹ in SI units).

Why the other options are incorrect

• Option (2) cell constant = \(A/l\); units: cm — Incorrect. This is the reciprocal of the cell constant.

• Option (3) cell constant = \(l\times A\); units: \(cm^3\) — Incorrect. Length times area is a volume, which plays no part in \( R = \rho\,l/A \).

• Option (4) cell constant = \(l/A\); units: cm — Incorrect. The relation is right, but cm divided by cm² gives cm⁻¹, not cm.

NCERT (2026-27 edition):
Measurement of the Conductivity of Ionic Solutions – …