Dielectrics in Capacitors - Electrical Engineering Video Lecture - Electrical Engineering (EE)

In most capacitors, a
non-conducting material
is placed between
the two metal pieces
that make up that capacitor.
There's two reasons for this.
For one, the
non-conducting material
prevents the pieces of metal
from touching each other, which
is important because if the
pieces of metal were touching,
no charge would ever
get stored since you've
completed the circuit.
But there's another
bonus to inserting
a non-conducting material
between the plates
of a capacitor.
It will always increase the
capacitance of that capacitor.
As long as the material
is non-conducting,
it doesn't even
matter what it is.
As long as you don't change
the area or separation
between the plates, inserting
a non-conducting material
will always increase
the capacitance.
The name we give to
non-conducting materials
place between capacitor
plates is a dielectric.
But why does a dielectric
increase the capacitance?
To find out, let's
look at this example.
When you hook up a battery
of voltage V to a capacitor,
charge will get separated.
Now let's say you
remove the battery.
The charge is stuck on the
plate since the negatives don't
have a path in which to
get back to the positives.
So even after
removing the battery,
the charge on the plates is
going to remain the same.
And the voltage will
also remain the same
as the voltage of the
battery that charged it up.
Now imagine placing a
dielectric in between the plates
of the capacitor.
The dielectric material is made
out of atoms and molecules,
and when placed in between
the plates of this charged
up capacitor, the negative
charges in the dielectric
are going to get attracted
to the positive plate
of the capacitor.
But those negatives can't
travel to the positive plate
since this dielectric is
a non-conducting material.
However, the negatives
can shift or lean
towards the positive plate.
This causes the charge in
the atoms and molecules
within the dielectric
to become polarized.
To put it another way, the atom
kind of stretches and one end
becomes overall negative
and the other end
becomes overall positive.
It's also possible that the
dielectric material started off
polarized because some molecules
are just naturally polarized
like water.
In this case, when
the dielectric
is placed between the
charged up capacitor plates,
the attraction between
the negative side
of the polarized molecule
and the positive plate
of the capacitor would cause
the polarized molecules
to rotate, allowing
the negatives to be
a little bit closer to the
positively charged capacitor
plate.
Either way, the end result is
that the negatives in the atoms
and molecules are going to face
the positive capacitor plate
and the positives in
the atoms and molecules
are going to face the
negative capacitor plate.
So how does this
increase the capacitance?
The reason this
increases the capacitance
is because it reduces the
voltage between the capacitor
plates.
It reduces the voltage because
even though there's still just
as many charges on
the capacitor plates,
their contribution to the
voltage across the plates is
being partially cancelled.
In other words, some
of the positive charges
on the capacitor plate are
having their contribution
to the voltage
negated by the fact
that there's a negative
charge right next to them now.
Similarly, on the
negative side there's
just as much negative
charge as there ever was,
but some of the negative charges
are having their contribution
to the voltage
canceled by the fact
that there's a positive
charge right next to them.
So the total charge
on this capacitor
has remained the same, but
the voltage across the plates
has been decreased because
of the polarization
of the dielectric.
If we look at the
definition of capacitance,
we see that if the
charge stays the same
and the voltage
decreases, the capacitance
is going to increase,
because dividing
by a smaller number
for the voltage
is going to result in a larger
value for the capacitance.
So inserting a
dielectric in this case,
increase the capacitance
by lowering the voltage.
Let's look at another case
of inserting a dielectric.
Imagine we, again, let
a battery of voltage V
fully charge this capacitor.
And let's insert a dielectric
between the plates.
But this time, let's leave
the battery connected.
Now what's going to happen?
Well, just like before,
the atoms and molecules
in the dielectric are going to
stretch and orient themselves
so that the negatives are
facing the positive plate
and the positives are facing
the negative plate, which again
reduces the voltage between
the two capacitor plates.
But remember, we left
the battery connected
and this battery is going
to try to do whatever
it has to do in order
to make sure the voltage
across the capacitor is the same
as the voltage of the battery
V. Because that's just
what batteries do.
They try to maintain
a constant voltage.
So since the dielectric
reduced the voltage
by canceling the contributions
from some of the charges,
the battery's just going to
cause even more charges to get
separated until the voltage
across the capacitor
is again the same as the
voltage of the battery.
So the charge stored on the
capacitor is going to increase,
but the voltage is
going to stay the same.
Looking at the definition
of capacitance,
the charge on the
capacitor increased
after we inserted
the dielectric.
But the voltage across
the capacitor plates
stayed the same,
since it's still
hooked up to the same battery.
So the effect of inserting
a dielectric again
is to increase the
capacitance, this time
by storing more charge for
the same amount of voltage.
To figure out how much you've
increased the capacitance,
you just need to know what's
called the dielectric constant
of the material that you've
inserted between the capacitor
plates.
The dielectric constant is often
represented with a Greek letter
kappa or simply a K.
The formula for finding
out how the dielectric will
change the
capacitance is simple.
If the capacitance of a
capacitor before inserting
a dielectric was C,
then the capacitance
after inserting a dielectric
is just going to be k times C.
We should note that
since a dielectric always
increases the capacitance,
the dielectric constant k
for a non-conducting material
is always greater than 1.
So for example, if a capacitor
as a capacitance of 4
farads, when you insert
a dialect with dielectric
constant 3, the capacitance
will become 12 farads.