JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Capacitance

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Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

(A) $[F] = [C^{2} M^{- 2} L^{2} T^{2}]$
(B) $[F] = [CM^{- 2} L^{- 2} T^{- 2}]$
(C) $[F] = [CM^{- 1} L^{- 2} T^{2}]$
(D) $[F] = [C^{2} M^{- 1} L^{- 2} T^{2}]$ ✓ Correct

Answer: (D)

Solution

Capacitance is defined by

C = \frac{q}{V}

. Multiplying numerator and denominator by q:

C = \frac{q ^{2}}{q V} = \frac{q ^{2}}{W}

since qV has the dimensions of work (energy) W.

Dimensions:

[q] = [C]

(the unit of charge),

[W] = [M L^{2} T^{- 2}]

[C] = \frac{[ C ] ^{2}}{[ M L ^{2} T ^{- 2} ]} = [C^{2} M^{- 1} L^{- 2} T^{2}]

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Single correct option

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