Problem-based on Energy Density for Capacitor - I
We all might have used radios in our life.
The radio was very popular for listening to the song and the news.
The tunning knob is used to tune the channel and it is connected to the capacitor.
The capacitor is the two-terminal passive electronic device that stores electric energy in an electric field.
And that energy is calculated by the formula.
The energy stored by the capacitor per unit volume is called energy density.
It is denoted by
$u$
and calculated as,
Now, we will solve a problem based on energy density for a capacitor to know more clear about it.
Let's take a problem based on energy density for a capacitor.
Suppose we have a parallel plate capacitor.
And there is the air gap of
$1mm$
thick between the two plates.
The dimensions of the plates are given as
$40cmÃ—30cm$
.
And this capacitor is connected across a battery of
$12V$
.
Now, we need to find the capacitance of this capacitor.
And we have to also find the energy stored in the capacitor as well as the energy density for this capacitor.
Hence, the capacitance of the capacitor will be calculated by the formula.
The given data in question is,
After putting the values, we get,
Hence, the capacitance of the capacitor is,
Now, the energy stored will be calculated by the formula.
Hence, after putting the values, we get
Hence, the energy stored in the capacitor is,
Now, we can find the energy density by the formula.
So, the volume in this capacitor is,
Now, after putting the values, we get,
Hence, the energy density for this capacitor is,
Therefore, we can easily solve the problem based on energy density for a capacitor,
The End