Formal definition of capacitance
The capacitance (C) of an electrostatic system is the ratio of the quantity of charge separated (Q) to the potential difference applied (V).
\[C=\frac{Q}{V} \]
The SI unit of capacitance is the farad [F], which is equivalent to the coulomb/volt [C/V].
\[\left [F=\frac{C}{V} \right ] \]
One farad is generally considered a large capacitance.
Energy storage
\[u=\int_{0}^{Q}Vdq = \int_{0}^{Q} \frac{q}{C}dq = \frac{1}{2}\frac{Q^{2}}{C} \]
Since Q = CV, and also since C = Q/V
\[u=\frac{1}{2}CV^{2}= \frac{1}{2}\frac{Q^{2}}{C}=\frac{1}{2}QV \]
