Dielectrics & Dielectric Constant Video Lecture - Civil Engineering (CE)

capacitors are very useful devices as
they allow us to store electric
potential energy within the electric
field that is created as a result of a
separation of electric charge so let's
begin by looking at these two diagrams
that have parallel plate capacitors so
in diagram a we have a parallel plate
capacitor and we also have a battery now
the battery essentially acts to charge
our parallel plate capacitor and when
that capacitor is fully charged it looks
something like this so one of the plates
has a negative charge the other plate
has a positive charge now because they
are separated by certain distance that
means we have a separation of electric
charge and that will create an electric
field midway or in between our two
plates and we can then store electric
potential energy within that electric
field which then can be used to do
useful work for example power a computer
or phone now the gap separating the two
plates of the capacitor contains air and
generally speaking air acts as an
insulating material and that means it
prevents electrons from flowing from
this region to this region now the
problem with using air is the following
at very high voltages what happens is
air becomes ionized the air molecules
lose electrons and that essentially
allows the electrons from this plate to
flow to this plate and we essentially
have a loss of separation of charge and
that destroys our capacitor so once
again the problem with using air is that
at high enough voltages the air
molecules become ionized and they begin
conducting electrons across the plate so
at low voltages the air is a good
insulator but at high voltages it
becomes ionized and allows electrons to
flow from this plate to this plate this
our capacitor now one way that we can
tackle this problem is by replacing air
with another type of insulating material
that is capable of withstanding high
voltages and this insulating material is
usually called a dielectric so we can
place some type of dielectric in between
our two plates now let's examine what
the effects are of placing a dielectric
between our two plates so one thing that
a dielectric does to a capacitor is it
increases the capacitance it increases
the quantity of electric charge that can
be stored on either one of our plates so
there are two ways that we can increase
our capacitance so one way is we can
bring our plates closer so now that we
have a very thin sheet of dielectric
between our two plates we can bring our
plates closer thereby decreasing our
distance between our two plates because
our capacitance is universally
proportional to our distance if we
decrease our distance we increase our
capacitance now even if our distance
between the two plates remains the same
the dielectrics will still increase our
capacitance by a factor of K which is
usually determined via experiment now K
is known as the dielectric constant and
it's actually depends on the type of
substance that we are using so different
substances will have different K values
now what this basically means is the
following if we define our C naught as
the capacitance when the space in
between our two plates is a vacuum then
we see that our capacitance C with our
dielectric is equal to C naught
multiplied by this factor of K now
recall that C naught the capacitance
when the space between is a vacuum is
equal to the product of the permittivity
of free space epsilon naught multiplied
by the surface area of either one of
these plates divided by the distance
separating our two plates so we can take
this equation and replace C naught with
this ratio and we get this result so the
capacitance with our dielectric is equal
to the product of the dielectric
constant K the permittivity of free
space given by epsilon naught the
surface area of either one of the plates
divided by the separation distance
between our two plates so if we now
define a new constant given by epsilon
to be the product of K and epsilon
naught then we have the following
equation so the capacitance of our
parallel plate capacitor width the
dielectric in-between is equal to
epsilon multiplied by a divided by D
where our epsilon is known as the
permittivity of our dielectric material
that we are using so once again epsilon
is a constant it's the product of the
dielectric constant and our permittivity
of free space now let's move on to the
second effect dielectrics also increase
the charge stored on our capacitive and
that makes sense because if our
capacitance increases our capacity by
definition of capacitance is now able to
store more electric charge so let's see
what that means by looking at the
following equations so recall that the
quantity of electric charge that can be
stored on our plate when there is a
vacuum in between is equal to C naught
our capacitance when there's a vacuum in
between multiplied by the voltage
difference so Q is equal to C multiplied
by V now if we take this equation
rearrange it and solve for C naught we
see that C naught is equal to C divided
by K so let's replace C naught with C
divided by K so now we have this
equation we can take K
bring it to this side we get this result
the product of the capacitance of our
dielectric capacitor multiplied by the
voltage is equal to K multiplied by Q
naught so this is simply equal to Q the
quantity of electric charge stored on
our capacitor when there is a dielectric
in between this is equal to cv which is
equal to K multiplied by Q naught so we
see Q the quantity of charge that is
stored on our capacitor with a
dielectric is equal to K the dielectric
constant multiplied by Q naught so let's
move on to the third effect that our
dielectric has on our parallel plate
capacitor so dielectrics decrease the
voltage so the voltage between our two
plates when there's a dielectric in
between is equal to V naught divided by
K where V naught is the voltage between
our two plates when there's a vacuum in
between so we see with the dielectric
the voltage drops by a factor of K so
capacitance increases by a factor of K
the charge increases by a factor of K
and our voltage drops by a factor of K
now because voltage also depends on
electric field we see that if the
voltage drops the electric field also
decreases between our two parallel
plates so we see in effect number for
the dielectrics decrease the electric
field so let's look at the case without
our dielectrics
so without dielectrics we see that the
electric field E naught is equal to V
naught divided by D so the electric
field is constant
now with dielectrics our electric field
which is just given by our E is equal to
the voltage between our two plates with
a dielectric divided by D now from this
part we know voltage is
two V naught divided by K so if we
replace our voltage with V naught
divided by K we get this result so we
see that the electric field between our
plates with our dielectric is equal to e
naught divided by K so not only will the
voltage decrease by a factor of K our
electric field will also decrease by a
factor of K so once again capacitance
increases by a factor of K the charge
increases by a factor of K the voltage
decreases by a factor of K and electric
field also decreases by a factor of K
between our two parallel plates within
this capacitor