Question

If $C$ denotes capacitance and $V$ denotes potential difference across the capacitor, the dimensions of $C{V}^2$ are

• A. Not expressible in $\text{M L T}$
• B. $\text{M L T}{}^{-2}$
• C. $\text{M}{}^2\text{L T}{}^{-1}$
• D. $\text{M L}{}^2\text{T}{}^{-2}$

Answer 1

The correct option is D $\text{M L}{}^2\text{T}{}^{-2}$

Energy stored in the capacitor is $\frac{1}{2}C{V}^2$
Units of $C{V}^2$ will be equivalent to units of energy.
Hence dimensional formula of $C{V}^2$ is $\text{M L}{}^2\text{T}{}^{-2}$