Dielectrics in Series or Parallel in Parallel Plate Capacitor

Physics

formula

Dielectrics in series

where , are the dielectric constants

definition

variable permittivity

Example : A parallel plate capacitor having square plates of edge and plate separation . The gap between the plates is filled with a dielectric of dielectric constant which varies parallel to an edge as where and are constants and is the distance from the left end.
Solution: Consider a small strip of width at a separation from the left end with area of . Its capacitance is .
The given capacitor may be divided into such strips with varying from to . All these strips are connected to parallel. The capacitance of the given capacitor is,

example

Capacitance of parallel plate capacitor with a combination of dielectrics

Example:
In the figure shown, find the effective capacitance across P and Q. (Area of each plate is )
Solution:
The above arrangement acts as the capacitor in parallel with and which are in series.

and are in series.

is in parallel with
Total capacitance