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.
