Energy Stored in Parallel Plate Capacitor
We all are familiar with the ceiling fans.
It is a mechanical fan mounted on the ceiling of a room or space and used in the summer season.
We also have noticed after a long period of time, the speed of the fan has got decreased.
And when we change the capacitor attached in the fan, then, the fan gets its normal speed.
It happens, because, the capacitance of the capacitor is decreased after a long period of time.
A capacitor is a passive electronic device that stores the electric energy in an electric field.
And the effect of the capacitor is called capacitance.
Now, we will discuss the energy stored in a parallel plate capacitor.
Let's discuss the energy stored in a parallel plate capacitor.
A capacitor is charged by connecting its plate to the terminals of a cell.
Then, the charge is transferred from one of its plates to another.
And one of the plates is positively charged, whereas, another plate is negatively charged.
The positively charged plate is at a higher potential and negatively charge plate is at lower potential.
The electric field between the two plates is uniform and the positive charge is transferred from the negative plate to the positive plate.
Hence, the work is done during the transfer of charges and this work is stored in the capacitor as potential energy.
Now, the potential difference
$v$
between the plates is calculated by,
And the additional work done to transfer charge
$dq$
from one plate to another will be,
So, to get the total work done, we have to integrate it from
$0$
to
$Q$
.
Hence, this is the energy stored in the capacitor as potential Energy
$U$
.
Now, if
$V$
be the potential difference between the plates, then,
Hence, the equation will be as,
And that energy is stored in the electric field of the space between the plates.
Hence, the surface density of charge
$Ïƒ$
will be,
According to Gauss's theorem,
Since, the capacitance of the capacitor is,
Hence, the energy stored in the capacitor will be,
Now, it can be also written as,
Further, as the energy density,
$u$
of the capacitor is,
So,
$A.d$
will be the volume of the capacitor, hence, it can be written as,
Hence, this is the equation for energy density in parallel plate capacitor.
This is all about the energy stored in a parallel plate capacitor.
Revision
This is the parallel plate capacitor.
So, the energy stored in this capacitor will be,
And the energy density will be,
The end