Capacitors ========== .. figure:: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/1280px-Capacitors_%287189597135%29.jpg :figwidth: 30% :align: right A picture of some capacitors (even some variable capacitance ones). 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.