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Question: Answered & Verified by Expert
If $C$ be the capacitance and $V$ be the electric potential, then the dimensional formula of $C V^{2}$ is
PhysicsUnits and DimensionsKCETKCET 2011
Options:
  • 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:
1309 Upvotes Verified Answer
The correct answer is: $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{0}\right]$
We know,
Energy, $E=C V^{2}$
Dimensions of $C V^{2}=$ Dimensions of energy
$$
=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]
$$

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