Physics - Unit & Dimension Question with Solution | TestHub

$C=\frac{q}{V}$ gives farad $=\frac{\text{ coulomb }}{\text{ volt }}$;
$U=\frac{1}{2}C{V}^2$ gives farad $=\frac{\text{ joule }}{(\text{ volt }{)}^2}$;
$\tau =RC$ gives farad $=\frac{\text{ second }}{\text{ ohm }}$.
$\frac{\text{ volt-second }}{\text{ coulomb }}=\text{ ohm }$, which has the dimensions of resistance, not farad.