Capacitance

In a capacitor, the charge Q (amount of electricity) is proportional to the voltage E. The expression for this relationship can be written as

Q = CE

where C is a constant called capacitance. The capacitance of any electrical equipment, including capacitors, may be calculated from their geometry.

(a) Parallel-plate air capacitor and (b) parallel-plate capacitor with dielectric material.

A capacitor in its most simple form is the parallel-electrode air capacitor as shown in Figure. The capacitance of such a capacitor can be calculated by the following formula:

where

- A is the area between the electrodes
- d is the thickness of the insulation (spacing between the electrodes)
- K is the dielectric constant of the insulation (air)

The dielectric constant (K) of air is practically unity and the dielectric constant of the other insulation materials is defi ned in terms of air or vacuum.

Table gives the dielectric constant values for most common types of insulating materials.

In cases where the geometry of the electrical equipment is simple and known, capacitance can be calculated mathematically. In the majority of cases, however, most insulation’s geometry is usually too complex and not well-enough understood to derive a reliable calculation of capacitance mathematically.

Dielectric Constant of Insulating Materials

Insulation as a Capacitor

A perfect insulator can be represented by an ideal capacitor as shown in Figure. However, all electrical equipment insulation have losses and therefore an insulator is not a pure capacitor. Thus, the electrical circuit of a  practical insulator can be represented by a capacitor with a small resistance in parallel with it, as shown in Figure.

The nature of insulation materials is such that 60 Hz current does not easily flow through them and therefore their purpose is to guide the current to the inside of the conductor. When voltage is applied to the conductor, two fields are established; one due to the current fl ow (magnetic field) and the other due to the voltage (dielectric or electrostatic field). The lines of magnetic flux around the conductor are concentric circles, whereas the lines of the dielectric flux around the conductor are radial. The resulting voltage stress due to the dielectric field varies inversely with the distance between equipotential lines.

The dielectric constant of an insulator is an indication of how much dielectric flux the insulation will allow through it. Under identical conditions insulation with a higher dielectric constant will pass more dielectric fl ux through it than another insulation having a lower dielectric constant. The dielectric constant for most commercial insulations varies from 2.0 to 7.0 as indicated in Table. It should be noted that the dielectric constant of water is 81 and generally when insulation becomes wet, its dielectric constant increases along with its capacitance, thus resulting in greater dielectric loss.

An ideal insulation can be represented as a capacitor because its behavior is similar to that of a capacitor. Two of the most common configurations considered for insulators are parallel-plate and cylindrical capacitors. For example, the parallel- plate capacitor represents an insulation system of a transformer or a machine winding, whereas the cylindrical capacitor represents an insulation system of a cable or a bushing.