Bo: Hey guys.
Both: Hey Bo.
(bell ringing)
Bobby: Oh good, the bell.
♫ (lyrics) Flipping physics ♫
(bell ringing)
Mr. P.: Ladies and gentle people, the bell has rung
therefore class has begun.
Therefore, today, we're going to define resistance,
we're going to talk about the difference
between ohmic and non-ohmic.
We're going to take a graphical look at
electric potential energy in a battery
and in a circuit.
Then, we're also going to define electric power
and look at that equation.
So, let's start with resistance.
Resistance is literally a resistance to current flow.
It's exactly what you think it would be.
The higher the resistance, the lower the current
kind of, we'll get to all of that stuff.
But the basic definition we'll start with
is resistance equals the electric potential difference
over the current.
Let's write the equation down.
The symbol, then, for resistance is a capital R.
The equation, again, is resistance
equals the electric potential difference
over the current, or delta V over I.
That's not how we usually see it,
so I'm going to rearrange the equation
but that will help us to get the dimensions.
Usually you see it as the electric potential
difference equals the current times the resistance.
Bobby, why don't you help me figure out
the dimensions for resistance.
Bobby: The dimensions for resistance.
Well, delta V is electric potential difference
and the dimensions for that are volts.
Current is in amps so resistance would be
in volts per amp.
Mr. P.: Yeah, so resistance equals electric potential difference
over current or volts per amp.
If you haven't worked with me before,
this little symbol here is an arrow,
it just means that this leads to that.
So we can get from the resistance equals
electric potential difference over the current
we can get from that
the dimensions volts per amp.
And a volt per amp has a specific name,
it is called an ohm.
The symbols for ohms is the Greek letter, omega.
Capital omega.
The way you spell ohm is O-H-M.
I find that a lot of students have a hard time
remembering the dimensions for resistance,
so I present this to you.
The symbol for resistance is an upside down horseshoe.
Why upside down, you may ask?
Bo: Because all the luck has fallen out of it.
Bobby: I don't get it.
Why does it fall out?
Billy: Bobby, if that horseshoe were right side up,
it would be shaped like a bowl and could hold soup.
Just as an example.
Bobby: Um, okay.
Mr. P.: That's right Bo.
The reason why, is because all the luck
has fallen out of it.
And I present you with this simple little story
so that you can remember that the dimensions
for resistance are ohms, an upside down horseshoe
because all the luck has fallen out of it.
See, look.
It all fell out.
Now, we're going to talk about the reason
we call this an ohm.
After the guy by the name of Georg Ohm,
who was alive in the early 1800's.
Did a lot of experiments with the concept of resistance.
He discovered that there were two different
types of substances.
One of them we call ohmic.
The graph for an ohmic substance looks like this.
On the Y axis, we have electric potential difference in volts.
On the X axis we have current in amps
and you end up with a linear relationship.
Let's figure out what the slope of this line is.
Billy, remind me, what is the equation for slope?
Billy: The equation for slope is rise over run.
Mr. P.: That's right, it's rise over run.
Let's write that down.
So, if you look at this equation,
we have rise over run.
The rise is the electric potential difference.
The run is the current.
And if you look at that, you can see
that that is equal to the resistance.
So, when you graph a substance that is ohmic,
you get a linear relationship.
It follows Ohm's Law.
This is called Ohm's Law and, therefore,
you get a linear relationship and the slope
of the line is the resistance of the substance.
We can also have something that does not
follow Ohm's Law.
A graph of that might look like this.
So, that's just one example of something
that would not follow Ohm's Law.
Bobby, what do you think this type of substance
would be called?
Bobby: Not ohmic?
Or un-ohmic.
Anti-ohmic?
No, no, no wait!
I bet it's non-ohmic.
That's it.
Non-ohmic.
Mr. P.: You are absolutely right.
These are called non-ohmic.
And pretty much we assume that substances
follow Ohm's Law unless otherwise stated
because so many of the substances we work with
in circuits are ohmic, especially in
algebra based physics.
We're going to assume that substances are ohmic
unless otherwise stated.
Now, I'm going to draw a circuit that has a battery
and a light bulb and we're going to talk about
the resistance of the wires and what happens
with the energy in this circuit.
So, what we have here is I've drawn a battery.
This is not a circuit diagram, I'm just drawing
a picture so you can get to that,
we'll get to circuit diagrams a little bit later.
So, we have a battery and a light bulb
and these are the two wires.
So what we have are the two terminals on the battery.
So this is our battery.
And this is our light bulb.
And we have one wire going from one terminal
of the battery going to one side of the light bulb.
Then we have the other wire going from one side
of the light bulb to the battery.
What we're going to talk about here,
I've labeled them as 1, 2, 3, and 4
so we can identify what happens in terms
of energy in this circuit.
We have a graph with electric potential energy
in joules on the Y axis, and location 1, 2, 3, and 4
on the X axis.
As you go from the battery to the light bulb
we have no loss in electric potential energy.
Therefore, we have a horizontal line
because we're not losing any electric potential energy.
As we go across the light bulb from 2 to 3
we have that electric potential energy
being converted to other types of energy
so the electric potential energy actually decreases.
Then, as you go, again, from 3 to 4 we have
no change in electric potential energy.
Now, the reason we have no change in electric potential energy
from 1 to 2 and from 3 to 4 is because
those are across wires.
In general, we consider wires to have
zero resistance, so they're going to have zero loss
in electric potential energy.
But then we get to the battery
and the job of the battery is to add energy
to the electrons.
So, the electrons are actually going to increase
in energy as they go from 4 back up to 1.
So, as they go from 4 to 1 and then
they're going to go back to where they started.
Back at 1.
So, this is, from 4 to 1, is across the battery.
The battery is basically a charge pump.
It increases the electric potential energy
of those little electrons.
So, remember, the electrons are moving around.
Remember, they're going to opposite direction
from the conventional current.
So, the little electrons, as they go through the battery,
they gain electric potential energy.
Then they go across the wire.
They don't lose any electric potential energy.
Then as they go across the light bulb
from 2 to 3 they lose electric potential energy
and it's basically this giant loop that keeps happening.
So let's talk for a minute about from 2 to 3
going across the light bulb.
The question is, what happens to the electric potential energy?
Where does it go?
So, Bo, where does the electric potential energy go
in a light bulb?
Bo: The electric potential energy goes to ...
Wait, I bet this is kind of like friction
in that the electric potential energy
goes to heat.
Oh, and it's a light bulb so light energy as well.
So to heat and light energy.
Mr. P.: Uh, Bo can you give me one more?
Billy: There is also sound energy.
Mr. P.: Yes Billy, light bulbs also make sound.
Some of them not so much but some of them way too much.
And what you end up with here is
this electric potential energy is actually converted
to heat, light, and sound.
So the electric potential energy, again,
it's gained in the battery, that's what the battery does.
Gives the electrons electric potential energy,
and then they lose it as they go across the light bulb.
It gets converted to heat, light, and sound.
Just so you know, the mechanical equivalent
of this right here is the basic concept of a roller coaster.
(mechanical sounds)
In a roller coaster there is a machine
that lifts the object up, you generally.
So, here it's just like the electron being given
electric potential energy.
Right here you could think about it
in our mechanical example, in a roller coaster
where you're gaining gravitational potential energy
via the work done by whatever machine
it is that's lifting you up.
Then, once you get to the very top,
you lose gravitational potential energy
and you gain kinetic energy, but you also have
via friction, energy being converted to heat and sound.
So, all the way from here to here
this is like going down on a roller coaster
where that gravitational potential energy
is actually being converted to heat and sound.
Then, of course, you get back down to the bottom
of the roller coaster and you have to gain
your gravitational potential energy
so that you can then have that gravitational
potential energy converted to heat and sound.
So this is the electrical equivalent.
Instead we have charges that gain electric potential energy
and then they lose that electric potential energy
as it's converted to heat, light, and sound.
Now, we're going to talk about the rate
at which this electric potential energy
that we were just talking about being converted
to heat, light and sound.
We're going to talk about the rate
at which that's being done.
That is called power.
Power is the rate at which energy is converted
to heat, light, and sound.
So remind me, Billy, we already have an equation for power.
We're going to figure out the one for electric power.
Billy, what is the equation we know for power?
Billy: Uh ...
Bo: I know it.
Mr. P.: Okay Bo, what is it?
Bo: Power equals work over time.
Mr. P.: That's right Bo.
Power equals work over time.
In this particular case,
we're talking about electric power
so the work we're talking about
is the change in the electric potential energy.
And we need to get the change in electric potential energy
in terms of the electric potential difference.
Bobby, what is the general equation
for electric potential difference?
Bobby: The electric potential difference
equals current times resistance,
or delta V equals I times R.
Mr. P.: Actually Bobby, that's the equation
we just learned for electric potential difference
which is equal to current times resistance.
I'm looking for the more general equation.
Billy?
Billy: Electric potential difference
equals change in electric potential energy
divided by charge.
Mr. P.: Billy, you're right.
The electric potential difference equals
the change in the electric potential energy
per unit charge.
We can rearrange that equation and get
that the change in electric potential energy
is equal to the charge times the electric potential difference.
Which means we can substitute that
into the equation we already have.
So, electric power equals the charge
times the electric potential difference
per unit time.
And remind me, what is charge per unit time?
Bobby: Charge per unit time is current.
Mr. P.: In other words, power equals current
times the electric potential difference.
And we can actually go back and use
the equation that Bobby gave us,
which is that the electric potential difference
equals the current times the resistance
and we can substitute that in.
Power equals, then, current times current
times resistance, or current squared
times resistance.
We could also rearrange this equation again
to get that the current equals the electric
potential difference over the resistance.
Therefore, we can substitute in for current here,
power equals the electric potential difference
over the resistance.
That quantity is squared times the resistance.
Or electric potential difference squared
divided by the resistance squared times the resistance.
One of our resistances cancels out
and we get the electric potential difference squared
divided by the resistance.
In other words, we have 3 different equations.
3 different equations for electric power.
Power equals current times the electric potential difference.
It equals the electric potential difference
squared, divided by the resistance.
And it equals the current squared,
times the resistance.
3 different equations for electric power
all having to do with current, resistance
and electric potential difference.
Again, power is the rate at which
electric potential energy is converted
to heat, light, and sound.
Oh, we do need the dimensions for electric power.
What are the dimensions for power Bo?
Bo: Power is in joules per second, or watts.
Mr. P.: Great.
Power is in watts or joules per second.
(quiet whistling)