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 answerA$\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^0\right]$
- 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'.