Hi. It’s Mr. Andersen and this AP Physics
essentials video 73. It is on resistors and capacitors. A resistor is drawn like this
in a circuit diagram and what it does is it restricts the flow of current in the circuit.
A capacitor is drawn like this and what it does is it stores charge in a circuit. An
then it is not going to be a circuit unless we have some kind of an energy source. So
we have an emf or in this case it is going to be a DC power source. So if we connect
them like this you should know not only what are the resistor and capacitor doing, but
what makes a good resistor. What makes a good capacitor. And so to understand that you really
have to understand at the gut level how a circuit works. And an analogy works best for
this. And so we are going to use an analogy of water flow to explain how a circuit works.
So the first thing you need is an energy source. Or an electromotive source. In this case I
will represent that with a water pump. So as you are pumping that water, the water,
we will, say is going to flow in this direction. It is going to go all the way around the circuit.
Let’s say it is in pipe. And then it is going to be drawn up into the pump again.
And so what is the first thing we could measure? Well we could measure the potential difference.
I could put my hand here. And I could put my hand here. And I would measure the potential
difference between the two. There is going to be way more potential energy up here. And
so if it is an electric circuit we call that the voltage or the potential difference across
that emf. What is the other thing you could measure? We could measure how much water is
actually flowing. And in electricity we call that I or current. So it is how much, we know
it is electrons that are moving through the circuit itself. So what is a resistor? A resistor
is anything that we add to that circuit that’s going to resist flow of current. We could
restrict that in a water pipe by simply making the pipe smaller. It is harder for that current
to flow. We are going to have a higher resistance. Now what is a capacitor look like using this
analogy? It is almost like a dam that obstructs the flow of that current. But imagine a dam
where we have a rubber sheet that goes right across it. So as the current flows into it
it builds up a huge amount of potential energy so there is charge there. But the current
cannot continue to flow. And so in a circuit you should understand resistors and capacitors.
Not only what they do but how do you make a good resistor, how do you make a good capacitor.
And so with a resistor, we want to increase the resistance. And so one way to do that
is through the material it is made up of. And so if we have high resistivity that is
going to slow the movement of that current and we are going to have a better resistor.
But you could also build it in a different way. It could have different geometry. And
so there is a direct relationship between the length of the resistor and the amount
of resistance it offers. And then there is an indirect relationship between the cross-sectional
area. So what does that mean? If we make our resistance longer, then we are going to have
greater resistance. But if we make it wider we are actually going to have less resistance.
And so if you want a good resistor, we want high resistivity. We want a long resistor.
And then we want a really narrow cross-sectional area. Now how does a capacitor work? A capacitor
is based on the material as well but it is between the two plates of the capacitor itself.
We call that the dielectric. And so the higher that dielectric constant is the greater the
capacitance of the capacitor is. But geometry affects it as well. And so the larger that
cross-sectional area is or the area of these two plates on either side, the greater the
capacitance is. And then there is an indirect relationship between the separation between
the plates. So the more narrow we make that gap the greater the capacitance is going to
be. Now to measure the current that goes through a resistor, we simply use Ohm’s law. So
to figure out the current through a resistor you simply divide the voltage, so the potential
difference divided by the resistance. And then on a capacitor we are going to measure
the charge that actually sits on the capacitor. And that is simply equal to the capacitance
times the voltage inside the circuit itself. So let’s start with resistors and resistance.
And so I have a simple circuit here. So I have some batteries and a light bulb. You
can see that the light bulb is not lit. And so that is because electrons are not able
to flow through the circuit. So if I take something like gold and I put it in the middle,
then electrons can flow. And so gold has a really low resistance. Let’s add glass in
the middle. Glass, nothing happens to the light bulb. And that’s because it has high
resistance. But then we could take something like carbon, put it in the middle and it is
going to have a resistance somewhere in the middle. And so a resistor is really put together
to resist the flow of those electrons. And they have little bands on the side that tell
you how much resistance there is. And the precision of that resistor. But they are really
three parts to a resistor. We are going to have the resistivity, what the material is
made up of. We are also going to have the length of the resistor. And then finally we
are going to have the cross-sectional area. So now let’s play with the resistance of
a resistor. What I am going to do is I am going to increase the resistivity, what it
is made up of, increase in resistance. And so there is a direct relationship there. Let’s
look at length. Increase length, more resistance, decrease length, then we are going to have
decreased resistance. That is because it is in the numerator. Now let’s look at the
area. As I decrease the area, greater resistance. As I increase the area there is going to be
less resistance. So you could think to yourself, how do I make the least resistant resistor?
I am going to want a really large cross-sectional area, small length and small resistivity.
You can see the resistance goes to zero Ohms at this point. What if I wanted to have the
most resistance in a resistor? Then I am going to do the opposite. High resistivity. I am
going to have a really long length and I am going to have a short cross-sectional area.
So I am going to have a really large resistance. And so you should be able to calculate the
current across a resistor. And so this is a PHET simulation. I have a battery here.
You can see it is a 9-volt battery. I have an ammeter down here which is going to measure
the amps or the current or I in the circuit. And then you can see that I have a resistor
over here. In this case we have a 9 Ohm resistor. Well you can see here right away that this
is a 9 voltage, so I could 9 up here. What is the resistance? The resistance is going
to 9 Ohms and so I could put 9 right here. What is 9 divided by 9? I have a current of
1 amp. And you can see that reads right there. But watch what happens when I start to change
the Ohms. As I increase the resistance what is happening to my amps? It is cut in half.
If I increase it again, 27 ohms, now I am going to have way less amps. Less current
is actually making it through. You can see as I change the resistance, make it greater
there is really low amps. As I decrease it we are going to have high amps to the point
where I really shorted out my battery and we have a fire going on. Now let’s move
to the capacitor. A capacitor is two plates and a charge will start to build up on either
side of it. So we get these electric field lines. And that is where the potential energy
is. To increase the amount of capacitance we put a dielectric in the middle. And so
our equation for this is the dielectric constant, that is going to be right here. Now this is
the permitivity of just free space, so that is going to be a constant. Then we have the
area on the stop. So that is the cross-sectional area. And then we are going to have the displacement
on the numerator. And so that is going to be the distance between these two gaps. And
so the three things you should understand, number 1 is the dielectric constant. So in
the simulation I am going to take that dielectric and I am going to slide it in-between the
capacitor. Now it has a dielectric constant of 1. But see what happens as I increase the
dielectric constant with teflon, paper and glass. What is happening to the capacitance?
It is increasing. So as I increase the dielectric constant I am increasing the capacitance.
What happens as I decrease the separation between the two? I am increasing the capacitance.
Then what happens as I increase the cross-sectional area? I am increasing the capacitance. Same
thing. If I pull it apart, make it smaller. Pull out the dielectric I have gotten rid
of that capacitance. Now you also should be able to calculate the charge across a capacitor.
And that charge is simply equal to the capacitance of the capacitor times the voltage. And so
now I have a capacitor I have hooked up to a battery. As I decrease the voltage the charge
goes down. As I increase the voltage the charge goes up. Watch what happens as I change the
capacitance. There is going to be a direct relationship between the capacitance and the
charge. And so all you do if you want to figure out the charge on a capacitor is you take
the capacitance of the capacitor times the voltage and that is going to tell you how
much charge, or how much Q can build up on that capacitor. And so did you learn to make
predictions about how resistors and capacitors work in a circuit? Remember resistors resist
flow. Capacitors store energy. Could you design a capacitor and a resistor that works best?
Remember it is what material it is and then the geometry of how it is put together. Could
you analyze to figure out how changing the resistor or changing the capacitor could change
the voltage in a current inside a circuit? I hope so. And I hope that was helpful.
