Capacitance of a capacitor
Capacitance of a capacitorDate of publication: 11-03-2022 🕒 5 min read
What is a capacitor?
A capacitor is a component that has the ability to store energy in the form of an electrical charge. Capacitors come in many different forms, from submilimeter-sized ceramic capacitors to polypropylene capacitors for industrial applications that may weigh dozens of kilograms. A capacitor consists of electrodes between which there is a dielectric, i.e. an insulating material such as waxed paper, mica, ceramic, plastic or, in the case of electrolytic capacitors, liquid gel. Despite the presence of the insulating layer between the plates of the capacitor, a negligible current may occur, which is regarded as an imperfection of the capacitor.
A capacitor, when connected to a direct current source, accumulates an electrical charge inside and retains this charge even when disconnected from the source. It can, therefore, act as a “reservoir” for electrical energy, very much like a rechargeable battery. The process of discharging and recharging is very fast here, it is only limited by the capacitor’s internal parameters and the resistance through which the capacitor is discharged. Capacitors allow to separate AC signals from DC signals. They are also used to block sudden peaks that could trigger digital circuits in an uncontrollable manner.
The capacitor symbols used in diagrams are shown below.
The first one is the symbol of a non-polarised capacitor.
The next symbol indicates a polarised capacitor which should be connected into a circuit with the polarity of terminals indicated in the diagram.
Sometimes, you can also see a symbol of a non-polarised capacitor with a plus sign in the diagram. Then, it should be treated as a symbol of a polarised capacitor.
Opposite situations also occur, when symbols of polarised capacitors are without a plus sign, which does not mean that polarisation of these elements does not apply..
How does a capacitor work?
Electrons flow into the plate connected to the negative pole of the battery and then repel electrons belonging to the other plate. This leads to the formation of “electron holes” in the other plate, which can be treated as positive charges. When we disconnect the capacitor from the battery, the electrons become trapped in the electric field, which is a consequence of the accumulation of electrons on one electrode and their deficiency on the other. It should be remembered, however, that over time, the potential difference between the plates will decrease due to leakage, which is a very slow flow of charges from one plate to another, possibly due to imperfections in the dielectric material and other substances surrounding the plates.
The capacitance of a capacitor
Capacitance is an electrical property of a capacitor. It is the ratio of the stored charge to the voltage. The unit of capacitance is the farad (F), named after British physicist Michael Faraday. Most often, we come across capacitors with capacitances much smaller than 1F, although certain industries use supercapacitors, which offer capacitances of thousands of farads. As a general rule, we define sub-multiple (smaller) units: millifarads (1 mF= 10-3 F), microfarads (1 µF= 10-6 F), nanofarads (1 nF= 10-9 F) and picofarads (1 pF= 10-12 F). There are many websites on the Internet that convert units, including the capacitance of capacitors. It is also worth remembering that in the USA it is sometimes (although rarely) possible to find “mF” as an alternative form of notation for microfarads (μF). This can lead to serious misunderstandings, as mF is in fact the correct notation for the unit of millifarads. The bigger the surface of capacitor’s plates and the smaller the distance between them and the higher the electrical permeability of the dielectric material used, the greater the capacitor’s capacitance.
How to calculate the capacitance of a capacitor? Basic formulae.
Capacitance
Properties such as the size and shape of the plates affect the value of the stored charge, even if exactly the same voltage (U) is applied. The capacitance of a capacitor is therefore defined as the ratio of the maximum charge (Q) that can be accumulated in the capacitor to the voltage (U) applied to the plates. In other words, capacitance is the maximum charge per 1V of voltage.
Capacitance of a flat vacuum capacitor
In the case of a flat capacitor, the capacitance depends on the surface area (S) of two identical plates that are separated by a distance (d). The constant ε is the permeability of the vacuum, equal to 8.85⋅10−12F∕m.
Capacitance of a cylindrical vacuum capacitor
A cylindrical capacitor consists of two coaxial conducting cylinders, i.e. an inner cylinder of a radius (R1), which may be hollow or solid in the centre, and the outer cylinder, which is a shell of an inner radius (R2). We will define the length of each cylinder as l.
Capacitance of capacitors connected in series
For a system of series-connected capacitors, the reciprocal of the equivalent capacitance is the sum of the reciprocal of the capacitances of the component capacitors.
Capacitance of capacitors connected in parallel
For a system of capacitors connected in parallel, the equivalent capacitance is the sum of the capacitances of the component capacitors.
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