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 respectively. (a) [F] = [CM⁻¹L⁻²T²] (b) [F] = [C²M⁻²L²T²] (c) [F] = [C²M⁻¹L⁻²T²] (d) [F] = [CM⁻²L⁻²T⁻²]

Answer: (c). C = Q/V and V = W/Q, so C = Q²/W. [W] = [ML²T⁻²] [C] = [C²][ML²T⁻²] = [C²M⁻¹L⁻²T²] So the answer is (c).

Which one of the following is the correct dimensional formula for the… | JEE Main 2025 (22 Jan, Shift 2)

Q10JEE Main 2025 · 22 JAN · SHIFT 2Easy

Units & Dimensions

Which one of the following is the correct dimensional formula for the capacitance in F? $\mathrm{M, L, T}$ and $C$ stand for unit of mass, length, time and charge respectively.

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Answer: (c)

$C = \frac{Q}{V}$ and $V = \frac{W}{Q}$ , so $C = \frac{Q^2}{W}$ .
$[W] = [\mathrm{ML^2T^{-2}}]$
$[C] = \frac{[\mathrm{C^2}]}{[\mathrm{ML^2T^{-2}}]} = [\mathrm{C^2M^{-1}L^{-2}T^{2}}]$
So the answer is (c).

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