[BLANK_AUDIO]. Welcome back to our continuing course in
linear circuits. At this point, we've finished talking
about resistive circuits, and we're going to be moving on now to reactive
circuits. And we'll describe a little bit more
about what that means today. Themes for this lesson where we were
talking about capacitance is to allow you to describe the behavior of a device
called the capacitor. By calculating the charge that's stored
on the capacitive plates, the current that flows through the capacitor, the
voltage across a capacitor and the capicitance of the capacitor.
In the previous classes we've finished completing, the resisance circuits
section. And then Dr Ferry wrapped up that section
and then also presented an overview of this new module, the reactive circuits
module. And then today we'll be talking about the
first of these reactor devices capacitors.
But, this is actually going to be discussing two different lessons.
A, which some of the properties then physics about how these things operate.
And then the next class well talk about the actual devices that we know as
capacitors. The objectives for this lesson are to
allow you to describe the construction of a capacitor.
To find the amount of charge that's stored on a capacitor, find the current
that goes through the capacitor, find the voltage across a capacitor.
Calculate the capacitance of the capacitor and then explain how current
flows through a capacitor. In short we're discussing a lot of things
about how capacitors work. And this is similar to our resistive
circuits section, when we talked about resistance.
And we're going to be talking about how voltages and currents react within a
single device. And in the next lesson, we'll start
discussing about how they interact when we put them into a system.
A capacitor is essentially two conductive plates that's separated by a material
that's an insulator. Sometimes known as the dielectric.
So here, we can see that we have th-, a top grey plate and a bottom grey plate,
separated by, in this case, kind of a blue glassy looking thing.
If we connect this capacitor to a voltage source, what's going to happen?
Well the voltage source is going to be trying to move charges around because of
this difference in charge, density that a voltage source is going to create.
So consequently, what happens is, negative charges are placed on the bottom
of the capacitor. And when those negative charges are
collecting on that bottom plate. They push negative charges off of the top
plate. Making the top plate positively charged.
Since all of those atoms now have more protons than they have electrons.
And so we start to see an electric field is created inside of that dielectric
material. The insulator in between the 2 plates.
So, this electric field can actually be quite useful.
Because it's holding all of these charges on the plates.
And those charges can then, in turn, be used to do something interesting.
So if we need a whole lot of current on demand, well now we have a big well of
current that, well, charges that can then be used to create a current.
So if we connect a capacitor to some kind of a device, we'll see that a current is
going to start flowing to try to equalize that charge density difference.
On that capacitor. So we see the current that will be
flowing from the positve to the negative. And as that happens, unlike a battery
capacitor doesn't have any type of process that keeps this reaction going.
Once those electrons are gone then that electric field disappates and it kind of
finds itself to a steady state. We actually identify how much charge is
on the capacitive plates, by using this handy equation where the charge q is
going to be equal to c times v. And here c represents capacitance and
we're going to be talking a little bit more today about exactly what capacitance
means. And we see here we've got a capacitor
connected to a voltage source and independent voltage source.
And so the negative side of the capacitor is going to be where the negative
terminal of the source is connected. The strength of the boltage across this
capacitor will match. The strength of the source because that's
what causing these charges to be moved around.
There's some kind of pressure being applied to make this happen.
If we remove the source then those charges are going to start to try and
dissipate by making themselves diffused throughout the material so that there's
no longer a difference in charge density. Just like resistance had Ohm's law to
allow us to know how the currents and the voltages related to one another, we have
something that's analogous for capacitors.
But with capacitors, it's not quite so simple.
At this point ,we're going to start seeing that time becomes more and more of
a component. Because of the way the capacitors work as
we place more and more charge onto the plates we see that the voltage is going
to increase. And so voltage conseqently is an
integration where its equal to one over c times the integral from t not to t of the
current. With respect to time, plus whatever the
initial voltage happens to be. We can then derive the current equation
by taking the derivative of that, and we see that the current is equal to C dv dt.
So as the voltage changes that lets us know how much current is flowing through
the capacitor. So it's actually what capacitor lets us
know is how much charge is required to get a particular electric field through
the dielectric. So if it has a high capacitance, then
that means that we have a whole lot of charge on that capacitor that's available
when we apply a small voltage. So, small voltages can lead to a lot of
current that's on demand very, very quickly.
But we have to put those charges on there beforehand so that means that it will
take longer to get a higher voltage. Because we have to put more charges on
their to establish that field. When we are discussing capacitance we're
going to be using units of ferrets which are indicated by a F and the variable
that we're going to use in all of our equations is a C.
It's quite simple to calculate capacitance.
The capac, well, assuming that we have a nice geometry.
If we have two parallel plates separated by some kind of dialectric material.
The capacitance is simply equal to epsilon times the area of the plates.
So the width times the length. All divided by the distance between the
two plates. And here, epsilon is the permittivity of
the material, of the dielectric material, or that insulator.
You might remember from before, we talked about the permittivity of free space.
And that's how willing a vacuum is to allow an electric field to be established
in it. As you change the material, the
permitivity changes. And that's one of the major things that
allows us identify how much capacitance it has, or how much charge is required to
create an electric field through that dialectic material.
Normally though, when we're talking about these perpetuities, the values that were
using are very, very, very small. As we mentioned, the permittivity of free
space is 8.85 times 10 to the negative 12 [INAUDIBLE] per meter.
And so instead of using the permittivity of the material directly, often what
we'll do is use an epsilon R, which is the relative permittivity of that
material. And then we multiply epsilon R times
epsilon ot. Define the true permittivity.
So you we give you some idea of the order of these permittivities.
We have a table here to kind of give you some kind of sense.
Eric behaves almost like a vac, vacuum, its relative permittivity is
approximately one. Teflon is a better insulator as 2.1.
A paper 3.9 and it starts to go up as we get down to things like water.
Water actually has a fairly high permittivity.
78.5. But in all of these cases the
permittivity does vary somewhat based upon things like temperature.
there are also some different properties of materials.
And, when we're talking about things like Paper.
There's a lot of variety that you can find within the paper.
So, even between different areas of the same material, that permittivity can
actually change quite a bit. Now, we've been talking a little bit
about the current that's flowing through a capacitor.
But I almost mentioned that, in between the 2 plates is an insulator.
And so it doesn't really want to let current go through.
So how is this current flowing through the capacitor?
Well, it's not really flowing through the capacitor, not a lot of the electrons are
actually crossing that gap, but what we see is if we push an electron under the
bottom plate, this way. Then what's going to happen it's going to
be pushing away a negative charge on the opposite of the plate because like
charges are going to repel one another. And so as a negative charge gets pushed
away from the other plate, it leaves a positive ion, an atom that has an extra
proton because that electron's been moved so it's no longer electrically neutral,
so it becomes positively charged. And so what we see, if we don't really
care that it's a capacitors, an electron comes in one side, and then an electron
comes out the other side. It's a different electron, but we really
don't care. And so this is the way that we say a
current flows through a capacitor even though none of these elements are
actually crossing through that dielectric.
And so that way we see this current. To summarize, we identify that something
by how these capacitors work. And so now you should have a little bit
of understanding of how these parallel plates are working; as we apply voltage,
what happens to the charges? And we were able to calculate that charge
on a capacitor using that q is equal to c times v.
We showed the relationship between current and voltage on the capacitor,
which is a differential. or based on time.
So that time derivative of voltage allows us to see the current.
And then we calculated this capacitance. And explained what we mean when we say
the current is flowing through the capacitor.
In the next class, we'll talk about capacitors as circuit devices, and we
will look at the behavior of how these capacitors behave in an actual circuit
environment. Until then