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.