Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l} = \kappa \) (both\(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length \(l\). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte) \(\Lambda _m =\kappa V\)
If the length 'l' in the column of an electrolytic cell is halved and its area of cross-section is tripled then conductance (G) would become:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 times
The conductance of a column of solution is directly proportional to its area of cross section (A) and inversely proportional to its length (l):
G = κA/l
With the length halved and the area tripled (κ unchanged):
G′ = κ(3A)/(l/2) = 6 × κA/l = 6G
NCERT (2026-27 edition):
Conductance of Electrolytic Solutions – “… The inverse of resistance, R, is called conductance, G, and we have the relation:”
\( \displaystyle G = \frac{1}{R} = \frac{A}{\rho\, l} = \kappa\frac{A}{l} \) (2.18)