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.