Parallel Plate Capacitor with Dielectric in Series and Parallel.
We have seen the flash of a camera when we click a photo.
When we click the photo the flash instantly release a stored energy in the form of light.
The energy released during the flashlight of a camera is stored in a capacitor in the form of charge.
This is the general form of a capacitor with two plates, one is a positive plate and another is negative plate.
And the capacity to store charge in a particular capacitor is its capacitance.
When we fill some specific material between the plates of a capacitor, the storage capacity or the capacitance increases.
The specific material we fill between the plates of a capacitor, we say it dielectric.
Let's know more about the dielectric.
The dielectric material is an electric insulator which can be polarised by an applied electric field.
When we placed a dielectric material between the capacitor, the capacitance of the capacitor increases.
Dielectric posses the ability to store charge in an electric field, we say its dielectric constant.
Now let's discuss more through an illustration.
Suppose we have four dielectrics with name
$K_{1}$
,
$K_{2}$
,
$K_{3}$
and
$K_{4}$
connected between point P and Q.
Let we assign the value of the dielectric constant as 1, 2, 3 and 4 to dielectrics
$K_{1}$
,
$K_{2}$
,
$K_{3}$
and
$K_{4}$
respectively.
And let surface is A/3 of each dielectric and the thickness is d, d, d/2 and d/2 of
$K_{1}$
,
$K_{2}$
,
$K_{3}$
and
$K_{4}$
respectively.
Suppose, we say the capacitance of the dielectrics
$K_{1}$
,
$K_{2}$
,
$K_{3}$
and
$K_{4}$
is
$C_{1}$
,
$C_{2}$
,
$C_{3}$
and
$C_{4}$
respectively.
Now we can resolve each dielectric in a separate connection between the point P and Q.
The connection between dielectric
$K_{3}$
and
$K_{4}$
is somewhat we say a series connection.
Now the equivalent capacitance of both
$K_{3}$
and
$K_{4}$
, let we its say C' is given as:
Now we put the value of
$K_{3}$
and
$K_{4}$
, where
$Ïµ_{0}$
is a constant.
By solving the above equation we get the equivalent capacitance of
$K_{3}$
and
$K_{4}$
.
Now
$K_{1}$
,
$K_{2}$
and C' is connected with P and Q in the arrangement as shown in the figure, we say it parallel connection.
Now let we solve the equivalent capacitance of parallel connection.
Let we represent the equivalent capacitance of parallel connection with C.
Now the equivalent capacitance of parallel connection is given as in figure with respective values.
This is the total capacitance of the capacitor with dielectrics in series and parallel.
Revision.
The dielectric material is an electric insulator which can be polarised by an applied electric field.
Dielectric material posses the ability to store charge in an electric field, we say its dielectric constant.
The arrangement is shown in the figure is a series connection.
And the arrangement as shown in the figure is a parallel connection.
The End