2015 AP Physics I free response 2 a and b

Some students want to know what gets used up in an incandescent light bulb when it is in series with a resistor: current, energy, or both. They come up with the following two questions: in one second, do fewer electrons leave the bulb than enter the bulb? And does the electric potential energy of electrons change while inside the bulb?

So, this first question is really a measure of current because current is how much charge per second is going through a particular part of our circuit. So, charge per second is what you could also think of as electrons per second. Current's going to measure the first one. And the electric potential energy of the electrons? Well, that's going to be voltage. Does the voltage change? Is there a voltage drop when we go from one side of the bulb to another?

The students have an adjustable power source, insulated wire, light bulbs, resistors, switches, voltmeters, ammeters, and other standard lab equipment. Assume the power supply and voltmeters are marked in terms of volt increments and ammeters are marked in hundreds of an amp increments.

All right. Describe an experimental procedure that could be used to answer questions one and two above. In your description, state the measurements you would make and how you would use the equipment to make them. Include a neat labeled diagram of your setup.

All right, so let's do part A right over here. So I have… so part A. So we're going to have a power source, and I think they said it was a variable power source. Did they say that? They say, “Yeah, the students have… the students have an adjustable power source, insulated wire, light bulbs, resistors, switches, and voltmeters.” And they wanted to know about an incandescent light bulb when it is in series with a resistor.

So, an incandescent light bulb when it is in series with a resistor—let's make an attempt at drawing this. So just the circuit, the circuit only that they care about. We could do our adjustable power source. So let me draw that. So you could do that like this. A couple… I'll do a couple here, so like this. So that would be a power source where this is the positive end and this is the negative end.

Now, let me make my circuit before any measurement tools, and then we'll add the measurement tools. So, I'm going to make it in series with a resistor. So let's put a resistor here of some resistance, and then let's keep going with our circuit. So we're going to keep going with our circuit, and now let's put our incandescent light bulb.

The symbol for an incandescent light bulb? There are actually several. I'll use this one, where I do a little bump here and then I'll continue, and I'm actually going to put a circle around that bump. So it would be just like… I'm almost there. I'm trying to do it neatly because they're telling us to do it with a neat diagram. All right, let me draw it a little bit better than that.

So it would look something like this, and then let me put a circle around this. So, putting a circle around this, this is our incandescent light bulb; this is our power source. And to show it's a variable power source, I can put an arrow across it like this that shows us that it is a variable power source.

So this is a circuit that I've just set up, but I want to use some ammeters and voltmeters in order to measure what's happening as our electrons are going through the light bulb. The standard convention is to show current going from the positive terminal to the negative terminal. But we know—and if you don't know, I encourage you to watch the KH Academy videos on it—what's actually happening is you have electrons traveling from the negative terminal to the positive one.

But in general, if we just wanted to talk about the current, you would denote it… the current would, the convention is that the current goes from the positive direction to the negative direction. You could view it as they're the positive gaps of electrons or however you want to, but the electrons are actually moving in the other direction.

So the first question is: do you have a different number of electrons moving per second before entering the light bulb than when you come out of the light bulb? Well, the way you can measure that is by measuring the current on either side of the light bulb. And the way we can measure the current on either side of the light bulb is we can insert— we can insert ammeters on either side.

And ammeters have to be inserted in series, so I'm giving it some space so I can insert my ammeters. So that is one ammeter; it's going to measure current right through that part, so I put an amp there. And then that is another ammeter right over there: ammeter. So these are going to measure current on either side of our light bulb.

Current measures current on either side, or I could say measuring current entering and exiting the light bulb—current entering and exiting the light bulb. Entering the light bulb, or I'll just say maybe… I say exiting the bulb.

And we also care about the voltage drop, so we could put a voltmeter, and the voltmeter can be put in parallel with the light bulb. So let me draw the voltmeter here. So I'm trying to draw it neatly. So this is the voltmeter, and it's going to measure the voltage drop from one side to another.

Connect this… write it over K. So this measures the voltage drop— measures voltage—measures voltage drop. So I've drawn my diagram. Let's see, what else do I need to do? So they say describe an experimental procedure that could be used to answer questions one and two above.

In your description, state the measurements you would make and how you would use equipment to make them. Include a neat labeled diagram of your setup. Okay, so I guess my description… I could say I’d put two ammeters, and ammeter in series with the bulb: one before bulb, let me write bulb one after.

If the current is the same on both, then the same number of electrons enter and exit the bulb. If the current is the same, the same on either side, then electrons per second entering and exiting will be the same. If the currents are different, then the rate of electrons passing is different—are different.

All right, so that's the first part, the first statement to try to go for this first statement. For statement one: in one second, do fewer electrons leave the bulb than enter the bulb? If the ammeters are measuring the same current, well then you have the same number of electrons per second entering and leaving the bulb. If the ammeter measures different currents, well then you got different numbers of electrons.

All right, now for statement two—so let me write this. This is statement one; statement one—that is my procedure right over there. Now for statement two: statement one test, I guess I could say— and then statement two test.

Statement two test. I think you guys get the idea by this point, but I'm just writing it out because you would have to if you were taking this AP test. I would say put voltmeter, a lowercase voltmeter, put voltmeter in parallel with… let me write it out… with bulb. If it measures voltage drop, or I could say: if and only if, so I’ll say: if measured voltage drop, then…

How do they actually phrase the statement? See, does the electric potential energy of electrons change? Then electric potential energy of electrons changes. Electric potential energy of electrons—I don't normally write this much—changes; otherwise, does not. If no voltage drop, then no change in potential energy. If no voltage drop, then no change in potential energy.

We could write potential energy, and there you go. That is part A, where I set up my neat diagram. I’m measuring the current entering and exiting the light bulb, and actually, if you view it from the electron's point of view, this one is measuring the electrons going in that direction.

This is electrons entering; electrons exiting. But either way, the electrons per second would affect current. Same current? Well then, you have the same electrons per second. A different current? Then you have different electrons per second entering and exiting the bulb.

And this measures the electric potential energy across the light bulb. If that is—if you see a—if you actually measure a voltage here, then that means that the potential energy is changing from one side of the bulb to another.

And so I'll stop there. Actually, I think I ended part B2. Explain how data from the experiment you described can be used to answer question one above. Explain how the data from the experiment you described can be used to answer question two above.

So, this is really Parts A and B. So actually, let me write this down. So this is A plus B right over here; we have the diagram. And if you're taking the test, depending on how your time pressure is, you might want to label this more. But if you're running out of time, then you might not have time to describe it in as much detail.