Match List-I with List-II
| List-I | List-II | ||
| Physical Quantity | Dimensions | ||
| (A) | Capacitance | (I) | \( [ML^{3}T^{-3}A^{-1}] \) |
| (B) | Electric flux | (II) | \( [M^{-1}L^{-2}T^{4}A^{2}] \) |
| (C) | Electric potential | (III) | \( [M^{-1}L^{-3}T^{4}A^{2}] \) |
| (D) | Permittivity of free space | (IV) | \( [ML^{2}T^{-3}A^{-1}] \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (II), (B) - (I), (C) - (IV), (D) - (III)
Write each quantity through its defining relation, using \( [V] = [\text{work}]/[\text{charge}] = [ML^{2}T^{-2}]/[AT] \).
(A) Capacitance — this matches (II) \( [M^{-1}L^{-2}T^{4}A^{2}] \). Capacitance is charge per unit potential.
\( \displaystyle [C] = \frac{[Q]}{[V]} = \frac{[AT]}{[ML^{2}T^{-3}A^{-1}]} = [M^{-1}L^{-2}T^{4}A^{2}] \)
(B) Electric flux — this matches (I) \( [ML^{3}T^{-3}A^{-1}] \). Flux is field times area, and the field is force per unit charge.
\( \displaystyle [\phi_{E}] = [E][A] = \frac{[MLT^{-2}]}{[AT]}\,[L^{2}] = [ML^{3}T^{-3}A^{-1}] \)
(C) Electric potential — this matches (IV) \( [ML^{2}T^{-3}A^{-1}] \). Potential is work done per unit charge.
\( \displaystyle [V] = \frac{[ML^{2}T^{-2}]}{[AT]} = [ML^{2}T^{-3}A^{-1}] \)
(D) Permittivity of free space — this matches (III) \( [M^{-1}L^{-3}T^{4}A^{2}] \). From Coulomb’s law, \( \varepsilon_{0} = q_{1}q_{2}/(4\pi Fr^{2}) \).
\( \displaystyle [\varepsilon_{0}] = \frac{[A^{2}T^{2}]}{[MLT^{-2}][L^{2}]} = [M^{-1}L^{-3}T^{4}A^{2}] \)
Note: This question is from beyond the NCERT textbook and it appears to be out of the CUET 2026 Physics syllabus.