Capacitors
==========

.. figure:: /figures/capacitors.*
   :figwidth: 30%
   :align: right

   A picture of a capacitor made from two metal parallel plates and
   the electronic symbols used for inductors.


In its simplest form a capacitor is made from two parallel metal
plates. Obviously a DC current cannot flow from one plate to the
other. For DC voltages the capacitor functions as an insulator. Again,
as for the inductors, things change when considering a time varying
voltage.

For the capacitor fysicists can tell us that the current 'through' the
capacitor is proportional to the time derivative of the voltage
accross the capacitor:

.. math::
   i(t) = C \frac{d u(t)}{dt}


where $C$ is the capitance measured in Farad. Consider
$u(t)=\exp(j\omega t)$ then $i(t) = j\omega C u(t)$ and thus for the
complex impedance for the capacitor we have:

.. math::
   Z_C = \frac{1}{j\omega C}

Again carefully note that the relation between voltage and current
expressed with the complex impedance is only valid for sinusoidal
functions.