In the expression \( \displaystyle R=\frac{l}{\kappa A} \), κ represents
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Conductivity
The resistance of a conductor is directly proportional to its length l and inversely proportional to its area of cross-section A:
\( \displaystyle R=\rho\,\frac{l}{A} \)
The constant ρ is the resistivity. Its reciprocal is the conductivity (κ):
\( \displaystyle \kappa=\frac{1}{\rho}\ \Rightarrow\ \rho=\frac{1}{\kappa} \)
\( \displaystyle R=\frac{1}{\kappa}\times\frac{l}{A}=\frac{l}{\kappa A} \)
So in the given expression, κ is the conductivity.
Why the other options are incorrect
Option (2) Conductance — Incorrect. Conductance is G = 1/R, the reciprocal of the whole resistance, not the constant in this formula.
Option (3) Molar conductivity — Incorrect. It is Λm = κ/c, the conductivity divided by concentration; it does not appear in R = l/κA.
Option (4) Resistivity — Incorrect. Resistivity (ρ) multiplies l/A (R = ρl/A); in the given form the constant sits in the denominator, so it is 1/ρ, the conductivity.
NCERT (2026-27 edition):
Conductance of Electrolytic Solutions – “… The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross section, A. That is,
\( \displaystyle R \propto \frac{l}{A} \quad\text{or}\quad R=\rho\,\frac{l}{A} \qquad (2.17) \)
The constant of proportionality, ρ (Greek, rho), is called resistivity (specific resistance). … The inverse of resistance, R, is called conductance, G, and we have the relation:
\( \displaystyle G=\frac{1}{R}=\frac{A}{\rho l}=\kappa\,\frac{A}{l} \qquad (2.18) \)
… The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa).”