Understanding capacitor fundamentals
Background - Michael Faraday and the field concept.
The unit of capacitance, the farad, is named after Michael Faraday (1791 - 1867), born in England to a working class family, Faraday received limited education, nonetheless, he was responsible for many of the fundamental discoveries of electricity and magnetism. Lacking mathematical skills, (as I do J), he used his intuitive ability rather than mathematical models to develop conceptual pictures of basic phenomena. It was his development of the field concept that made it possible to map out the fields that exist around magnetic poles and electrical charges.
Unlike charges attract and like charges repel, i.e. a force exists between electrical charges. We call this region where the force acts an electric field. To visualise this field, we use Faraday’s field concept and draw lines of force (or flux lines) that show at every point in space the magnitude and direction of the force. Now, rather than supposing that one charge exerts a force on another, we instead visualise that the original charge create a field in space and that other charges introduced into this field experience a force due to the field. This concept is helpful in studying certain aspects of capacitance.
Capacitance, plate size, air spacing and breakdown voltage.
A capacitor consists of two conductors separated by an insulator. One of it’s basic forms is a parallel plate capacitor, shown below.
It consists of two plates separated by a non conducting material (an insulator) called a dielectric. The dielectric maybe air, oil, plastic, ceramic or any suitable insulating material.
Since the plates of a capacitor are metal, they contain huge numbers of free electrons. In there normal state, however, they are uncharged, that it, there is no excess or deficiency of electrons on either plate.
If a DC source is applied, electrons are pulled from one plate (leaving a deficiency) and deposited on the other plate (providing an excess). In this state, the capacitor is said to be charged. Note that no current can pass through the dielectric and thus between the plates.
Definition of Capacitance
The amount of charge Q that a capacitor can store depends on the applied voltage. Experiments show that fro a given capacitor, Q is proportional to voltage. Let the constant of proportionality be C, then :
Equation 1 Q = CV
Re-arranging the terms yields
Equation 2 C = Q / V (farads, F)
The term C is defined as the capacitance of the capacitor. As indicated, its’ unit is the farad. By definition, the capacitance of a capacitor in one farad if it stores one coulomb of charge when the voltage across it is one volt.
The farad, however, is a very large unit. Most practical capacitors range in size from picofarads (pF or 10 -12) to microfarads (µF or 10 -6). The larger the value of C, the more charge the capacitor can hold for a given voltage.
Effective area
From equation 2, capacitance is directly proportional to charge. This means that the more charge you can put on a capacitors plates for a given voltage, the greater will be its capacitance. Therefore capacitance is directly proportional to plate area.
Effect of spacing
OK considering above, since the top plate has a deficiency of electrons and the bottom plate an excess, a force of attraction exists across the gap. For a fixed spacing (fig A), the charges are in equilibrium. Now if we move the plates closer together (fig B), as the spacing decreases, the force of attraction increases, pulling more electrons from within the material of plate B to its top surface. This creates a deficiency of electrons in the lower levels of B. to replenish these, the source (E) moves additional electrons around the circuit, leaving A with an even greater deficiency and B with an even greater excess. The charge on the plates therefore increases and hence, according to equation 2 so does the capacitance, and visa versa.
Effect of Dielectric
Capacitance also depends on the dielectric.
Consider above, which shows an air-dielectric capacitor. If you substitute different materials for air the capacitance increases.
Capacitance of a parallel plate capacitor.
From the above, we can see that capacitance is directly proportional to plate area, inversely proportional to plate separation and dependent on the dielectric. So….
Equation 3 C = € A / d (farads)
Where area A is in square metres and d is in metres.
Dielectric Constant
The constant € is the absolute dielectric constant of the insulating material. It’s units are farads per metre (F/m). For air or vacuum,
€ has a value of €0 = 8.854 x 10 -12 F/m.
For other materials, € is expressed as the product of the relative dielectric constant, €1 times €0,
that is € = €1 €0
Consider again, equation 3.
C = € A / d = €1 €0 A / d
Note that €0 A / d is the capacitance of an air or vacuum capacitor. Denote it by C0, then for any other dialectic C = €1 C0
In practice
Calculate the capacitance of a parallel plate capacitor with plates 10cms by 20cms, separation 5mm
1. an air dielectric
2. a ceramic dielectric with a relative permittivity of 7500
Solution.
Convert all dimensions to metres, thus
A = (0.1m)(0.2m) = 0.02m2
d = 5 x 10-3 m
So for air dielectric:
C = €0 A / d
= (8.854 x 10-12)((2 x 10-2)/(5 x 10-3))
= 35.4 x 10-12 F
= 35.4 pF
and for a ceramic dielectric with €1 = 7500
C = 7500 ( 35.4 pF)
= 0.266 µF
Voltage Breakdown
If the voltage in fig 2B is increased beyond a critical value, the force on the electrons is so great they are literally torn from orbit. This is called dielectric breakdown and the electric field intensity at breakdown is called the dielectric strength of the material. For air, breakdown occurs when the voltage gradient reaches 3KV / mm. The breakdown strengths of other dielectrics is different.
So where do go from here?
OK we now have an understanding of the fundamental properties of capacitors, all info above has been gleamed from the web, I have enjoyed some learning while putting this post together J
In a later post I shall attempt to design a homebrew capacitor to suit the Cumbrian Magnetic Loop.