The dimensions of $C{V^2}$ matches with the dimensions of
${L^2}I$
${L^2}{I^2}$
$L{I^2}$
$\frac{1}{{LI}}$
The dimensions of $C{V^2}$ matches with the dimensions of
Both are the formula of energy . $\left( {E = \frac{1}{2}C{V^2} = \frac{1}{2}L{I^2}} \right)$