Bo: Hey, guys.
Bobby: Hey, Bo.
(bell rings)
Bo: Oh.
Billy: Oh, good! The bell!
♫ (lyrics) Flipping physics ♫
Mr. P: Ladies and gentlepeople, the bell has rung,
therefore class has begun.
Therefore, today we're going to learn about current,
and we're going to do an example problem.
Current is the movement of charges.
It is the rate at which charges flow.
It is, generally we talk about current on a wire,
so if we talk about a wire,
if we were able to see the charges moving on the wire,
we could go, 1, 2, 3, 4, 5 ...
We could count the charges as they go by.
We take and count the number of charges, add those up,
divide by the amount of time it took to do that,
and that would give us the current.
Let's walk through the equation for current.
The equation for current is current, I,
equals delta Q, or the change in charge,
over delta t, the change in time.
Again, current equals delta Q over delta t.
I equals the change in charge over the change in time.
Billy, why don't you help us figure out
the dimensions for current?
Billy: The dimensions for current.
Then we need the dimensions for the change in charge
over the change in time.
Delta Q is in Coulombs,
and delta t is generally in seconds.
Mr. P: That's right.
It's in coulombs per second.
We have a special name for a coulomb per second.
It's after a guy by the name of Andre Marie Ampere,
but I'm terrible at pronouncing things,
so let's have my wife pronounce that name.
Mrs. P: Andre Marie Ampere.
Mr. P: Thank you.
So, we have amps or Ampere, this is ...
This guy, Andre Marie Ampere, he's a famous ...
famous scientist and mathematician from the late 1700s.
He's generally considered to be
the founder of classical electromagnetism.
We have a special dimension for him.
It is 'amps', and in fact, amps are a base SI dimension,
that's an important thing to realize.
Now let's talk about the direction of current flow.
Generally what we talk about is something called
conventional current.
In conventional current, you're talking about
the direction that positive charges would flow.
Again, the direction of conventional current
is the direction that positive charges would flow,
and that would flow is an important piece.
Let's write it down.
Conventional current, the direction that
positive charges would flow.
Let's talk about that 'would'.
Bo, remind me about the classical model of the atom.
Niels Bohr, the classical model.
Bo: The classical model of the atom.
That's where there are protons and neutrons in the nucleus,
and electrons outside in the orbital shells, right?
Mr. P: That's right.
According to Niels Bohr and the classical model,
we have protons and neutrons in the nucleus of the atom,
and the electrons are in the orbital shells,
and the electrons are much easier to take out of an atom,
and therefore, it's the electrons that generally flow.
What truly is happening is you have electrons
that are flowing in a negative direction,
so you have a negative charge flowing
in a negative direction,
which is a negative times a negative,
which is a positive.
Class, do positive charges generally flow?
Bo: No.
Mr. P: Billy, what actually happens?
Billy: Negative charges flow in the negative direction.
Mr. P: That's right.
Negative charges flow in a negative direction.
Great.
Now let's talk about the two different types of current.
There is alternating current and direct current.
Let's start with alternating current.
In alternating current, as you can see,
we have the current on the Y-axis,
and time on the X-axis.
The current changes as a function of time.
You can see, it has a specific frequency,
and generally it is like a sine or cosine wave.
As opposed to direct current,
which looks like this.
You could see in direct current.
The current is constant as a function of time.
It actually does not change.
Now, you would think that direct current would be
what would be coming to your house,
but unfortunately, no.
the problem with direct current
is that there is a power loss over distance,
a significant power loss over distance.
Therefore, alternating current
doesn't have this power loss,
so the stuff that comes to your house
is alternating current,
but the stuff that generally,
most of your appliances use is direct current.
That's why you have these guys.
This right here is the power converter
for the AC/DC power converter for my Macbook Pro,
and as you can see,
you can actually read on it right here.
It says the input is 1.5 amps at 50-60 hertz,
that is the frequency of the alternating current,
and the output is actually about 17 volts or so
and it has a maximum of 4.5 amps.
you could see this right here is your AC to DC,
alternating current to direct current power converter.
A lot of things that you actually use
have an AC to DC power converter.
Now let's go through an example problem
so we can practice things, that we just learned.
Bo, can you read the problem,
and Billy, can you please translate.
Bo: A charge of 13 mC.
mC, is that millicoulombs or microcoulombs?
Billy: It's milli because it's an m.
If it were mu, then it would be micro.
Bo: Thanks, Billy.
Billy: You're welcome.
Bo: A charge of 13 millicoulombs passes through
a cross-section of wire in 4.5 seconds.
Billy: Please write 13 millicoulombs, 4.5 seconds.
Mr. P: That's great, Billy, but remember,
I just have a bunch of numbers here.
Really, when you translate something,
what you need to do is you need to tell me
what letters, what symbols we're using.
What, for example, is 13 millicoulombs?
what is 4.5 seconds?
Billy: Okay, then delta Q,
or the charge passing through the wire
is 13 millicoulombs,
and the change in times is 4.5 seconds.
Mr. P: And what are we looking for?
Billy: We're solving for the current,
so capital I equals '?'.
Mr. P: Well, yeah, that's part a, but what about part b?
Billy: Hm. I guess that would be
the number of electrons equals '?'.
Mr. P: Great, so we know the change in charge,
the delta Q is 13 millicoulombs.
We know the change in time is 4.5 seconds.
We know for part a, we're looking for the current,
and for part b, we're looking for the number of electrons
that pass by the wire in that time.
Great.
Billy, why don't you work on part a.
Tell me, how do we solve this?
Billy: Well, we start with the equation for current,
or current equals change in charge
over the change in time.
Oh, but we need to convert
the dimension for charge to coulombs.
There are 1,000 millicoulombs in one coulomb,
and in order to cancel out the millicoulombs,
we need to use 1 coulomb over 1,000 millicoulombs.
That gives us 0.013 coulombs for our charge.
We put that into our equation for
the change in charge of delta Q,
and then we put in our 4.5 seconds for our change in time.
That gives us 0.028 with a repeating 8 amps.
Mr. P: Great, and with sig figs?
Billy: With sig figs, our 4.5 seconds only had 2,
so we should have two on our answer,
which rounds to 0.029 amps.
Mr. P: What if we were instead to give our answer as ...
2.9, what dimensions would it have if we had 2.9 amps?
Bobby: That would be milliamps
because there are 1,000 milliamps in an amp,
just like there are 1,000 millicoulombs in 1 coulomb,
and 1,000 millimeters in 1 meter.
Mr. P: You're right.
2.9 milliamps, or 0.029 amps.
Great.
Part b.
Bo, can you please solve part B for us.
Bo: I guess.
Well, we already know the charge,
so we can use the equation Q equals N times E.
Mr. P: You're right.
We're going to use the quantization of charge equation,
Q equals N times E,
or the charge equals the number of charge carriers
times the fundamental charge.
Bo: Uhh, we need to rearrange that
to solve for the number of charge carriers, or N.
That gives us N equals charge over fundamental charge E,
so we just put in 0.013 coulombs
over the fundamental charge.
Mr. P: What is the fundamental charge?
Billy: That's 1.6 times 10 to the negative 19 coloumbs.
Mr. P: Which means we put 1.6
times 10 to the negative 19 amps
for the fundamental charge,
and we get 8.125 times 10 to the 16th electrons.
Therefore, with sig figs,
we get 8.1 times 10 to the 16th electrons.
Bobby: Can you please explain to me
why we use a positive charge
when the charge on the electron is negative?
Billy: I got this one.
Remember ...
Remember, Bobby, that unless otherwise stated,
we are always talking about conventional current,
which is the direction that the positive charges would flow.
Regardless of the fact that there were,
in this particular problem, we have electrons flowing,
in the negative direction, we use conventional current,
and that uses a positive charge.
Bobby: Thanks, Billy.
Billy: You are welcome, Bobby.
Mr. P: Now, I'd like to talk about this number.
Scientific notation is great.
It makes it much easier to write down
large and small numbers.
However, sometimes it masks what the number actually is.
Let's write down this number without scientific notation.
It will be an 81 followed by 15 zeros.
81 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 zeros.
This works out to be 81 peta electrons,
or 81 times 10 to the 15th electrons,
or if you prefer, 81 quadrillion electrons.
81 quadrillion electrons.
81 quadrillion electrons!
How long was that?
4.5 seconds?
What was our current?
2.9 milliamps.
Billy: Wow, that's a lot!
Mr. P: Just gives you an idea for
how many electrons are passing through our wires.
It is a lot.