Q65 / 75 · JEE Main 2025 (22 Jan Shift 2) · Physics

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,

  • Correct answer
    A
    $[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
  • 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
    $[\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$

Solution

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

Hence, the correct answer is option: 'A'.

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