Welcome back to our course on linear 
circuits where today we're going to be 
talking about inductance. 
To, in this class we're going to be 
introducing a little bit about inductors 
and how they work. 
And we're going to calculate current and 
voltage in inductors. 
And as part of this, we'll also be 
discussing magnetic fields and how 
electricity and magnetism relate with one 
another. 
So, from a previous class we talked about 
capacitance, capacitors, and, we're able 
to do some derivations. 
The slide's that we're presenting now, 
this is inductance, then the next one 
will be inductors. 
And they are established in a very 
parrallell way to what the capacitence 
and capacitors were. 
The objectives of this lesson are to 
allow you to describe the construction 
and behavior of an inductor. 
And find the current through an inductor, 
as well as the voltage across an 
inductor. 
And then explain how you can get a 
voltage created at the cross of the 
conductor. 
So first off what are inductors? 
This is the first time that we actually 
need to know something about magnetism 
and in respect circuits that we are 
analyzing and it's going to start playing 
a role. 
What you essentially do is you have a 
current, coming from a current source 
that goes through a wire that is put in a 
particular geometric configuration. 
And when you do that, you get a magnetic 
field within this wire. 
And so just like an electric field in a 
capacitor stored up energy, you get a 
magnetic field and an inductor that 
stores up energy. 
And it establishes some current going 
through your inductor. 
Which you can then attach to some other 
device. 
And this current is going to keep trying 
to push through the device. 
And so we're going to kind of see how all 
of these things work together. 
today. 
So, where we presented before with 
capacitance, how currents and voltage is 
related, we are going to do the same 
thing with inductors. 
One of the things about inductors is 
they're sometimes drawn slightly 
differently, depending upon what you're 
looking at. 
So both of these are examples of how 
inductors are sometimes drawn. 
All of them kind of looks like this where 
they have bumps or curls. 
And what that is essentially showing is 
the curls of the wires that are being 
placed. 
And we'll talk a little more about that 
when we speak about the physical 
construction of inductors. 
The voltage in an inductor is equal to L 
times the didt where L is an inductance. 
Inductance is a unit that's measured in 
henry's. 
We are going to use L in our calculations 
to reference it and like when we are 
talking about capacitance referring to 
how well a material is holding an 
electric field. 
This relates to how well it's holding a 
magnetic field. 
And then again, if you want to invert 
that operation and find the current, then 
it's 1 over L. 
And then you're integrating the voltage 
with respect to time. 
To understand how these inductors are 
actually working behaviorally though, we 
need to know something about this 
electromagnetism that I mentioned. 
And so we're going to learn about 
Ampere's Law. 
Ampere's Law states that if I have a 
current moving through a material, that 
moving charge generates the magnetic 
field. 
And the magnetic field is going to be 
generated in a ring around your wire like 
this. 
And the way you can tell the direction is 
by using what's called the right hand 
rule. 
So, this dot could be seen as current 
coming out of the page. 
So if you point your thumb out of a page, 
and this is your right thumb, mind you, 
because it's the right hand rule. 
Then the curves of these arrows arrows 
are going to match the curves of your 
fingers. 
The direction that your fingers are 
pointing. 
So, that's how you can identify the 
direction. 
And these lines represent magnetic fields 
of a particular strength. 
Magnetic fields drop off the same way 
that electric fields kind of do, with 
this inverse square type of a property. 
So, as you move further and further away, 
the magnetic field is going to become 
weaker and weaker. 
And it's going to happen very drastically 
and very quickly. 
So, how do we actually use this to do 
something with a device? 
Well this is how we construct an 
inductor. 
Here this kind of a bluish gray material, 
is a ferrous core. 
Now for an inductor it doesn't need to be 
there, but it makes the inductor work 
better. 
And we'll see exactly what that means, 
here, shortly. 
And then we have a wire here that's going 
to wrap around. 
Now if you see an actual inductor, you'll 
see something that looks like it's just 
bare wire that's wrapped around. 
its usually just a copper color sometime 
it's just reddish it's not actually bare 
wire, it is insulated. 
But with thin insulation so this wire is 
normally called a magnet wire. 
And that's why I've colored it this kind 
of reddish to look some what like the 
magnet wire that you'd see on a real 
inductor. 
And then here, i represents the currents 
flowing through the wire. 
To see how this device is working, what 
we're going to do is take a cross section 
of this. 
Here, all of these dots represent current 
coming out of the page. 
And all of these x's represent current 
going into the page. 
As you send this current through, it 
establishes a magnetic field. 
And here we can see kind of a shape of 
what that magnetic field looks like. 
And the way that that's established is, 
each of these wires is generating 
magnetic field going around in circles 
like this. 
And since all of these are placed side by 
side, this one is also making a magnetic 
field as playing around like this and 
this one is pointing like this. 
So, start with what happens is it 
establishes a magnetic field here that's 
almost like parallel lines. 
Because its from this combination of all 
these individual magnetic fields. 
If you look at the other side as it's 
going into the page, they have the same 
looping structure. 
But now, thanks to the right hand law, we 
see that these arrows are going to point 
like this. 
So here, they're going clockwise, here, 
they're going counterclockwise. 
But if you'll notice, in the middle, all 
these arrows point the same direction. 
So, both sides of the coil are pushing 
magnetic field in the same direction. 
Now our capacitance or our inductance, 
rather is letting us know how well this 
core holds a magnetic field. 
And so often times you use a ferrous cord 
or ferrous meaning it has iron in it. 
Because things that have iron in it hold 
magnetic fields better. 
And perceptually what it means is that as 
your inductance gets larger, this 
magnetic field is going to make the 
current want to keep pushing through. 
Kind of in a constant rate. 
So now we'll start looking a little bit 
more at the implications of that. 
We've talked about wires and how we have 
no potential difference across wires. 
So [UNKNOWN] potential. 
Because voltages are created by 
differences in charge density, and if 
it's a wire then the charge is able to 
freely move 
And make its way around through the 
material until it is evenly distributed. 
So we don't see voltages across wires. 
But we do across an inductor, even though 
an inductor is essentially just a wrap of 
wire. 
And the reason we see this is because of 
magnetic fields that are being 
established. 
So to better understand how that works, 
suppose I have a current source here. 
It's been hooked up to this inductor for 
a little while and so there's a magnetic 
field. 
Here represented by these two red curves 
in this inductor. 
Now suppose I increase my current. 
Well, the thing about conductors is they 
want to keep their current flowing at a 
nice steady pace. 
And if you try and change the current 
flow, then things start to get backed up. 
So we start letting extra charge flow out 
of this source. 
But as it does that, this charge is going 
too quickly. 
It's going more quickly than this 
inductor has established that current 
should flow. 
So, these extra charges here on this end 
have to kind of wait their turn. 
And they kind of group up a little bit. 
But just like the charges were pushing in 
capacitors, that kind of behavior. 
This source still wants to pull charge 
carriers from here and as it does that we 
see we get a positive collection of 
charge. 
These are all atoms that have lost some 
of their electrons they give a positive 
charge on this side. 
And so what ends up happening? 
Well, now we can see that there starts to 
be established this difference in charge 
density. 
And so now there is a voltage, even 
though it's through a wire by the charge 
kind of getting grouped up. 
If we did it the other way, and we 
decreased the current on this source. 
[INAUDIBLE]. 
The same thing would basically happen, 
but opposite. 
This inductor would be pushing current 
through faster than the source was 
accepting it. 
So in this case, you're going to then see 
electrons grouping up on this side. 
And then positive ions on this side. 
So to summarize what we presented today. 
We talked about the equations for current 
and voltage in inductors. 
We talked about Ampere's Law, that shows 
how the flow of current gives us magnetic 
fields. 
Showing one way that electricity and 
magnetism interrelate. 
And then we showed how voltage can be 
created across an inductor, even though 
it's technically only a wire. 
Now, some of the things about these 
magnetic fields, might be something very 
new to you. 
So, if you have questions about the 
magnetic fields, and how these things are 
operating. 
go to the forums and post your questions 
there, so that we can make sure that 
you're understanding the material that's 
being presented here. 
In our next class, we'll present 
inductors as actual circuit elements, and 
see how they interact in a circuit 
environment. 
Until next time.