Hello, I'm Nathan Parrish, and welcome back to our course on linear circuits.
Today we're going to be talking about resistance.
And so the aim for this lesson is to help you identify the relationship between
current and voltage in resistive materials.
This is the first lesson, [INAUDIBLE] content lesson of the second module,
which covers resistive circuits. And so the first thing we're going to be
covering, is this idea of resistivity, and what that actually means.
The objectives for this lesson are to, first of all, we're going to define what
resistance is, then we'll calculate conductance and resistance.
And then we'll use Ohm's Law to be able to solve for currents and voltages and
resistances, based upon the information that we have.
We'll also calculate the resistance of a material, using both its electrical
properties as well as its geometry and dimensionality of the device.
So, the first thing we're covering is Ohm's Law.
Ohm's Law is something that you'll end up using a whole lot through circuits, it's
one of the most essential things for you to understand.
And it gives us a way of describing the relationship between a current and a
voltage. So, Ohm's Law basically states that, the
voltage is equal to a current times this thing called a resistance.
But in order for us to make sure our answers are consistent, reference
instructions, again, come into play and were very important.
So, when we have it in what's sometimes referred to as the passive configuration,
or when the current arrow's pointing from the plus to the minus.
Then we just say v is equal to i times R. However, if the arrow is pointing from
the minus to the plus, we flipped their respective reference directions.
And so to keep our values consistent, we multiply by a negative one.
So, in this case, v is equal to negative i times R.
keep close track of your reference directions or you'll find yourself
getting weird answers. Resistance is essentially the ratio of
the voltage to the current. We measure it in units of Ohms, which is,
again, named after a scientist. And one ohm is equal to one volt per
ampere, or one volt per amp. When we are using equations, we're going
to represent it with a capital R. And so we can also say that R is equal to
v divided by i. There's another way we can look at this
problem. We can also look at it as, how willing is
this material, to let current flow through it?
We call this conductance, conductance is measured in units of Siemens.
And this is named after the same Siemens as the man that started the company
Siemens. We represent Siemens with a capital S,
which one Siemen is equal to one amp per volt.
But sometimes when you're writing out your, your equations, it's difficult to
distinguish a lower-case s representing seconds and a capital S representing
Siemens. So, sometimes people go back to the older
version, which was the Mho. And a Mho is basically an ohm backwards,
so it will be represented by an upside-down omega.
They're both equal to the same thing, one amp per volt.
When we're doing calculations, we'll represent these values with a capital G.
And so, G then is going to be equal to the ratio of the current to the voltage.
And again, remember that reference directions here do matter.
So, what is it that gives these materials this resistance?
What are the properties that make this happen?
And, so, to better understand this, what we're going to do is we're going to look
at the periodic table of the elements. When looking at the periodic table if
you've taken chemistry you know that all of these atoms want to be like noble
gases. They somehow want to have a full outer
shell. And so, electrically, the same thing
holds true. So, to help us understand, we're going to
look at a few different examples of some elements.
And, see what kind of electrical properties they show.
First of all, we look at lithium and chlorine.
So, lithium is right here. And chlorine is right here.
Chlorine's pretty close to be a noble gas argon.
But it has seven electrons in its outer shell.
It wants to get one more, like this, to make it like argon.
But when it does that, first of all, it gets a charge, a negative 1 charge.
But because it It so wants to be like a noble gas, it's somewhat willing to
accept electrons. And so it's something of a conductor.
lithium, lithium wants to become like neon.
And to do that it needs to get rid of that outer electron.
So, when that happens, it gets a positive one charge because there's more protons.
In the nucleus of the atom than electrons in the shell.
And so, it really comes down to, how tied are the atoms to their electrons, that
lets this get some concept of their resistance.
Another one we're going to look at is copper, which is a really good conductor.
Copper's right here. Now, it has a lot of electrons in this
shell here, that it's not particularly tightly bound to.
But that electron in particular, it, it would like to get rid of because it's
just all by itself in this outer shell. And when it does that, again because it's
losing an electron, it's going to get a positive charge.
But because this electron is just so far out and copper is so weakly bound to it,
copper ends up becoming a very good conductor.
As are, things like silver and gold. All of the things in this, this chain
here. There's another class, that we'll look
at, silicon. And silicon is right here.
Now, you'll see that it has four electrons in it's outer shell.
So, it could either get four more, to make it like argon or it could get rid of
four to make it like neon. It's kind of torn in the middle.
So, consequently, this is not a particularly good conductor, this class
of materials is known as semiconductors. Because the way, how willing they are to
accept or cast off electrons, is very closely related to the other materials
that are around them. And these semiconductors end up becoming
a very important class of atoms, when dealing with electrical circuits.
As we were talking about electrons flowing through these systems, the way
that electrons flow through systems is that they kind of get passed from one
atom to another. So, in this system, we'le have a bunch of
purple atoms and a little blue electron. As we send the little electron in, this
first atom absorbs the electron, and becomes negatively charged.
Now, at this point, its neighbor might want to have that little electron.
So, it could get passed from that, atom into the next one, like this.
As we start to put more atoms, or more electrons into our atoms.
We start to see a difference in charge density and voltage.
And this voltage leads to an electric field.
So, as that happens, all of these atoms kind of know what's going on.
And this field is going to cause the electrons to kind of keep moving.
Now I call this the electron bucket brigade, because bucket brigades were a
way of putting out fires before fire engines.
Where people would gather buckets and they would [UNKNOWN] a big stream from a
source of water to a fire. And they would fill up the bucket and
kind of pass it down the chain. You don't need to wait for the first
bucket to get all the way to the end of the chain, before passing the second
bucket. And the same is true with electrons.
With this electrical field, now that all of the atoms kind of know what's going
on, these electrons can then be passed simultaneously.
So, now all of these atoms can then just exchange the electrons at once.
And all of this is transmitted by using this electrical field.
And it turns out that because we don't care if the electron that we get out is
the same as the electron we get in. That the electrons themselves could flow
very slowly through materials. Even though the currents can be very
large. Now we're going to actually figure out
how to calculate a resistance based on some things that we know.
So, the first thing we are going to need to be able to do this is some idea of how
willing is this material to let current pass through it.
Now you could do this by finding out, how many free electrons there are and doing
some things like that. But to simplify all this out, we use one
value, the resistivity. And we represent the resistivity with a
lowercase rho, a Greek character that kind of looks like a lowercase p.
This lets us know how willing the material is, to allow electrons to pass
through it. When we want to calculate the resistance
we can do so, by saying the resistance is equal to the resistivity, rho, times the
length of the material, all divided by the area.
And this is because it's a lot easier to, well and you can think of this kind of
like a water analogy. It's a lot easier to get water to pass
through a big, fat pipe that's short, than a really long pipe, that is narrow.
And the same basically holds true with, these resistances.
So, to calculate this, it's very simple, you just kind of plug in the numbers.
So, I've placed the numbers here, the area is 1, square millimeter, the length
is 50 millimeters, and the, resistivity is 10 ohm meters.
Which is the units that we use for resistivity.
So, I'm going to give you a second to try to calculate this yourself.
I'm going to put up a little pause button, so you can pause the video.
And then after you've had a chance to calculate it, then go ahead and start the
video again and we'll check your answer. So, what did you come up with?
Let's go through analysis, and see what we can, what result we get.
So, the first thing we have is the equation R, is rho L, over A.
Now you might have to calculate what the A is, for example if I had just given you
the diameter, you might have to use. The, equation for the area of a circle.
But I just gave you the area here. So, we can just plug in our numbers.
I have 10 ohm meters for our resistivity. We're going to multiply that by our
length, which is 50 millimeters and divide all of that by one square
millimeter. So, first of all we have millimeters up
here at the top. And millimeters down here on the bottom.
Here we have a meter, so that cancels out with this meter.
And so now we have a 10 to the negative 3rd on the bottom.
So, it's the same thing as multiplying by 10 to the negative 3rd on the top.
So, we get 10 times 10 to the 3rd, or, 10 kilo ohms as the resistance.
So, how did you do? You get it right?
So, fairly simple problem. and if the geometry gets a little more
complicated, then it might be a little bit harder to solve.
But, essentially this is all you need to do to find the resistance.
Through a wire or any other material. To help you get a little bit better idea
of the orders that we see when we're talking about resistance, we've included
this little table. so conductors, things like aluminum and
copper have resistivities on the order of 10 to the negative 8.
so lots of free electrons, very low resistance.
Things like silicon have a lot of variety, based on who its neighbors are
as to what kind of resistance you see, resistivity.
It's on the order of 10 to the negative 5th to 1 there's a lot of variety that
you can see there. Insulators also show a lot of variety,
even within the same piece of material different parts of the material can have
varying resistivities. But, to give you some idea.
We've had things on order of 10 to the 12th to 10 to the 22nd.
Really, really, big resistivities. So, as you can see there is a, a great
divide, between insulators that don't allow current to flow well.
And conductors which do. In summary, we used our background
material from the first module of this course to see how voltage and current
relate. Through these materials.
And then we introduce Ohm's Law, which you're going to be using frequently
throughout the course. We'll also discuss the physical cause
that gives us resistance as well as we calculated the resistance using the
dimensionality and this ideas of resistivity of the material.
So in the next lesson, we're going to look at the laws which describe the
relationship between devices is systems. So, this was looking at single devices
these resistive devices, now, we're going to start putting them into systems.
And looking at some laws, that describe how all of these things interact with one
another. If you have any questions about the
material we covered in this class. I encourage you to go to the forums and
post there, so that either Doctor Perry and I, or the TAs or even some of your
fellow students. Might be able to help answer the
questions that you might have. Until next time.