Definition
A capacitor is a component that stores electric charge once a voltage source is connected to it. The more charge a capacitor can store per applied voltage, the larger its capacitance, which is defined by
\[
\boxed{C = \frac{Q}{U}}
\]
The unit of capacitance is the farad (F).
Plate Capacitor
In the simplest case, a capacitor consists of two metal plates placed parallel to each other with a small separation. When a voltage is applied across the plates, electrons flow from the negative terminal of the voltage source to the connected plate, while electrons leave the plate connected to the positive terminal and move toward the source.
The charges arrange themselves in such a way that the energy is minimized.
This occurs when the electric field lines between the plates are parallel, forming a homogeneous electric field inside the capacitor. Outside the capacitor, however, the field lines are more complex. To maintain parallel field lines, charges accumulate on the surfaces of the plates. Inside the capacitor, the relationship between the voltage and the electric field simplifies to:
\[
U = Ed
\]
Substituting this into the capacitance formula gives:
\[
C = \frac{Q}{Ed}
\]
From Gauss’s law, the relationship between charge and field strength is:
\[
\frac{Q}{\varepsilon_0 \varepsilon_r} = EA
\]
Here, edge effects are neglected and only the plate area $A$ between the plates is considered. Canceling $E$ yields the expression for the capacitance of a parallel-plate capacitor:
\[
\boxed{C = \varepsilon_0 \varepsilon_r \frac{A}{d}}
\]
Thus, the capacitance is larger when the plate area $A$ increases and smaller when the plate separation $d$ increases.
In practice, foil capacitors are often used. These are made of two long rolled-up metal foils enclosed in a casing. Between the foils lies a dielectric, which both increases the capacitance and provides electrical insulation.