الخميس، 12 أبريل 2018

Composite Dielectric Capacitors


       When a parallel plate capacitor has two dielectrics or more between the plates, it is said to be composite capacitor. The various types of such composite capacitor exists in practice. Let us study few types of such composite capacitors.
      Type 1: In this type, number of dielectric having different thicknesses and relative permittivities  are filled in between the two parallel plates. The composite capacitor with three different dielectrics with permittivities  εr1, εr2 and εr3 and thicknesses t1, t2 and t3 is shown in Fig. 1.

      Let V be the voltage applied across the capacitor.
      It can be seen that there exists three capacitors in series. The values of three capacitors are different. Hence, the equivalent capacitance across the terminals A-B is,

      In general, for a composite with 'n' dielectrics,

      The voltage across each dielectric will be different,

       Where E1, E2 and E2 are the values of electric intensities in the different dielectrics.
Type 2 : In this type, in the same thickness, 't', the two dielectrics are arranged as shown in the Fig. 2.

       Let the relative permittivity values for the two dielectrics be εr1 and εr2. The Thickness for both is same but the areas different. It can be seen from the equivalent circuit that there exists two capacitors in parallel due to two different dielectrics.

       If one of the two dielectrics is air, then the corresponding relative permittivity is one, to be used in the above expression.
       For 'n' dielectrics arranged in same thickness 't',

Type 3 : In  practice we can have the capacitor which is combination of above two types. One such capacitor is shown in the Fig. 3.

       Basically it is type 2 capacitor, consisting of type 1 capacitor. So there are two capacitors in parallel. The C1 is having thickness t1, relative permittivity εr1 and area A1.

      Now the capacitor C2 is again a composite capacitor of Type 1 which itself is made up of two capacitors in series. From the result of Type 1 we can write,

      Hence the total capacitance is the parallel combination of C1 and C2,

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