[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