Houjun Liu


A capacitor changes, then resists being charged further. Their rules work opposite to resistors.

capacitor in series

\begin{equation} \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \end{equation}

and yet,

capacitor in parallel

\begin{equation} C_{eq} = C_1 + C_2 + C_3 \end{equation}

energy stored by a capacitor

\begin{equation} E = \frac{1}{2} CV^{2} \end{equation}

where, \(E\) is the energy stored, \(C\) the capacitance, and \(V\) the voltage across the capacitor.

Which, subbing the formula below:

\begin{equation} U = \frac{1}{2} \frac{Q^{2}}{C} \end{equation}

voltage across and max charge stored on a capacitor

\begin{equation} C = \frac{Q}{V} \end{equation}

where, \(Q\) is the change and \(V\) the voltage

“the more change the capacitor can store given a voltage, the higher the capacitance.”

\begin{equation} Q = CV \end{equation}