Match List-I with List-II
|
List-I Physical property |
List-II Expression |
|
(A) G (conductance) |
(I) \( l/(RA) \) |
|
(B) R (resistance) |
(II) \( A/(ρl) \) |
|
(C) \( \kappa \) (Specific conductance) |
(III) \( \kappa/c \) |
|
(D) \( \Lambda_m \) (molar conductance) |
(IV) \( l/(\kappa A) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
The resistance of a conductor is proportional to its length l and inversely proportional to its area of cross section A: \( R = \rho\,\frac{l}{A} \), where ρ is the resistivity. Conductance, conductivity and molar conductivity are all built from this one relation, so each expression follows by rearranging it.
(A) G (conductance) — This matches (II) A/(ρl). Conductance is the reciprocal of resistance:
\( \displaystyle G = \frac{1}{R} = \frac{A}{\rho\,l} \)
(B) R (resistance) — This matches (IV) l/(κA). Since conductivity is \( \kappa = 1/\rho \):
\( \displaystyle R = \rho\,\frac{l}{A} = \frac{l}{\kappa A} \)
(C) κ (Specific conductance) — This matches (I) l/(RA). Rearranging the same relation for κ:
\( \displaystyle \kappa = \frac{1}{\rho} = \frac{l}{R\,A} \)
(D) Λm (molar conductance) — This matches (III) κ/c. Molar conductivity is the conductivity divided by the molar concentration:
\( \displaystyle \Lambda_m = \frac{\kappa}{c} \)
Shortcut: Λm = κ/c gives (D)-(III), found only in Options (3) and (4); G = 1/R = A/(ρl) gives (A)-(II), which leaves Option (4).
NCERT (2026-27 edition):
Conductance of Electrolytic Solutions – “… The inverse of resistance, R, is called conductance, G, and we have the relation: G = 1/R = A/(ρl) = κA/l … The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa).”
Measurement of the Conductivity of Ionic Solutions – “… It is related to the conductivity of the solution by the equation: Molar conductivity = Λm = κ/c”