Q156 / 180 · COMEDK 2023 (Memory Based) · Physics

If $C$ be the capacitance and $V$ be the electric potential, then the dimensional formula of $\mathrm{CV}^2$ is

  • Correct answer
    A
    $\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^0\right]$
  • B
    $\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-1}\right]$
  • C
    $\left[\mathrm{M}^0 \mathrm{LT}^{-2} \mathrm{~A}^0\right]$
  • D
    $\left[\mathrm{ML}^{-3} \mathrm{TA}\right]$

Solution

We know that energy, $E=\frac{1}{2} C V^2$ Dimensions of $C V^2=$ Dimensions of energy, $E$ $=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^0\right]$

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

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