FUNDAMENTALS OF ELECTRIC SYSTEMS

 

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FUNDAMENTALS OF ELECTRIC SYSTEMS

CAPACITORS:

                           Figure 1 illustrates a capacitor. It consists of two insulated conductors a and b.They carry equal and opposite charges +q and -q ,respectively. All lines of force that originate on a terminate on b.The capacitor is characterized by the following parameters:

·        q, the magnitude of the charge on each conductor

·        V, the potential difference between the conductors

The parameters q and Vare proportional to each other in a capacitor, or q = CV,where

C is the constant of proportionality. It is called the capacitance of the capacitor. The capacitance depends on the following parameters:

     ●  Shape of the conductors

     ●  Relative position of the conductors

     ●  Medium that separates the conductors

The unit of capacitance is the coulomb/volt (C/V) or farad (F). Thus

                         

1 F = 1 C/V

It is important to note that:

but since, 

dq\dt = i

Thus,

This means that the current in a capacitor is proportional to the rate of change of the voltage

with time.

                                                  

Figure: Two insulated conductors, totally isolated from their surroundings

and carrying equal and opposite charges, form a capacitor.

In industry, the following submultiples of farad are used:

·              Microfarad (1 microfarad = 10^-6 F)

·              Picofarad  (1 picofarad = 10^-12 F)

Capacitors are very useful electric devices. They are used in the following applications:

·         To store energy in an electric field. The energy is stored between the conductors, which are normally called plates. The electric energy stored in the capacitor is given by:

U_E = q²/2C

·         To reduce voltage fluctuations in electronic power supplies

·         To transmit pulsed signals

·          To generate or detect electromagnetic oscillations at radio frequencies

·         To provide electronic time delays

Figure 1.2 illustrates a parallel  plate capacitor in which the conductors are two parallel

plates of area A separated by a distance d. If each plate is connected momentarily to the terminals of the battery, a charge +q will appear on one plate and a charge -q on the other.

If d is relatively small, the electric field E between the plates will be uniform. The capacitance of a capacitor increases when a dielectric (insulation) is placed between

the plates. The dielectric constant k of a material is the ratio of the capacitance with

Figure: A parallel-plate capacitor with conductors (plates) of area A.

TABLE 1: Properties of Some Dielectrics*

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Material                                   Dielectric                              Dielectric

                                                              constant                        strength(KV/mm)  

                        ---------------------------------------------------------------------------------------

dielectric to that without dielectric. Table 1 illustrates the dielectric constant and dielectric strength of various materials.

The high dielectric strength of vacuum (∞, infinity) should be noted. It indicates that if

two plates are separated by vacuum, the voltage difference between them can reach infinity without having flash over (arcing) between the plates. This important characteristic of vacuum has led to the development of vacuum circuit breakers, which have proved to have excellent performance in modern industry.

                                                         

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