5.2.8. Capacitors

Fig. 5.14 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:

\[i(t) = C \frac{d u(t)}{dt}\]

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:

\[Z_C = \frac{1}{j\omega C}\]

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