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,

(B) [\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]

(C) [\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]

(D) [\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]

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JEE Mains · Physics · STD 11 - Units,dimensions and measurement

JEE Mains 2025
Easy
MCQ

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

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Answer & Solution

Correct Answer

(A) \([\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { Energy }=\frac{Q^2}{2 C} \\ & \begin{aligned} \therefore \quad[\mathrm{F}] & =\frac{\left[\mathrm{C}^2\right]}{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ & =\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{+2}\right]\end{aligned}\end{aligned}\)

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