Capacitors#
\[q(t) = C v(t)\]
\[v(t) = \frac{1}{C}q(t)\]
Energy#
Theorem: Energy
The total change in the energy of a capacitor whose charge changes from \(Q_{\text{initial}}\) to \(Q_{\text{final}}\) is given as follows:
\[\frac{1}{2C}(Q_{\text{final}}^2 - Q_{\text{initial}}^2)\]
The total change in the energy of a capacitor whose voltage changes from \(V_{\text{initial}}\) to \(V_{\text{final}}\) is given as follows:
\[\frac{1}{2}C(V_{\text{final}}^2 - V_{\text{initial}}^2)\]
Proof
TODO