structural:scholar_edition, information:classification
Mutual capacitance

A common form is a parallel-plate capacitor, which consists of two conductive plates insulated from each other, usually sandwiching a dielectric material. In a parallel plate capacitor, capacitance is very nearly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

If the charges on the plates are + q {\textstyle +q} and − q {\textstyle -q}, and V {\textstyle V} gives the voltage between the plates, then the capacitance C {\textstyle C} is given by C = q V, {\displaystyle C={\frac {q}{V}},} which gives the voltage/ current relationship i (t) = C d v (t) d t + V d C d t, {\displaystyle i(t)=C{\frac {dv(t)}{dt}}+V{\frac {dC}{dt}},} where d v (t) d t {\textstyle {\frac {dv(t)}{dt}}} is the instantaneous rate of change of voltage, and d C d t {\textstyle {\frac {dC}{dt}}} is the instantaneous rate of change of the capacitance. For most applications, the change in capacitance over time is negligible, so the formula reduces to: i (t) = C d v (t) d t, {\displaystyle i(t)=C{\frac {dv(t)}{dt}},}

The energy stored in a capacitor is found by integrating the work W {\textstyle W}: W charging = 1 2 C V 2. {\displaystyle W_{\text{charging}}={\frac {1}{2}}CV^{2}.}