>> ALOM: We’re more reliant on batteries than ever before.
Developing better batteries is a really interesting
and exciting area of research. Students will
know that batteries, or cells, provide energy to a circuit.
However up until A level they’ll largely ignore the fact
that the cell itself has an internal resistance.
One of the core practicals for A level physics
is for students to find this internal resistance
and the EMF of a given cell, which presents some interesting
challenges for collecting good quality data.
The practical is based on the relationship
between this EMF, the terminal potential difference,
the current through the circuit, and this internal resistance.
This is the relationship.
You can see that I can rearrange this to get this.
So if I plot the terminal voltage against the current
through the circuit, I should expect a straight line
where the y intercept gives me the EMF and the magnitude
of the gradient gives me the internal resistance.
So let's take a look at how that might work.
Hi Christina, you look ready for action.
>> CHRISTINA: Yeah. Ready to go, and you can give me
a hand maybe. It's a very simple circuit, as you know.
I'm going to be investigating this AA cell, which I’ve got
connected in series with a variable resistor so we
can vary the current. This extra ten ohm resistor
limits the current generally in the circuit so the cell doesn't
get too hot which might affect its internal resistance.
>> ALOM: This seems a bit of overkill
for a ten ohm resistor.
>> CHRISTINA: Yes, well, it's what we had available
on the day. You could just use an ordinary fixed
ten ohm resistor. You've just got to check that
it's got the right power rating.
>> ALOM: OK, and it's worth getting students to think about
why you're using this additional resistor and what's going on in
the battery and so forth.
>> CHRISTINA: And reminding them that everything has resistance
including our cell. I'm also only going to connect
the circuit momentarily just to take the readings, to stop
things getting too hot.
>> ALOM: And you're not bothering with the push switch.
>> CHRISTINA: You could but I've found that actually just
connecting the lead like that works perfectly well.
We're going to be using digital multimeters which the students
do need to be able to use themselves,
so this is going to be measuring the current, and this one is for
the terminal PD.
>> ALOM: Yeah, I've made a film about those.
>> CHRISTINA: Oh yes, I think I've seen that film.
It's up there with your film on paint drying.
>> ALOM: Yep, boring but popular.
>> CHRISTINA: Okay, so shall we take some data?
Maybe you could help me by reading one of the meters
and writing down the result.
>> ALOM: Okay.
So I'll read out the current If you read the voltage.
>> CHRISTINA: Okay. And if we start at this end we’ve got
the highest resistance, which will give us the lowest
current to start with.
>> ALOM: Okay. So that's forty… thirty nine point nine.
>> CHRISTINA: One point three four.
>> ALOM: Forty-five point zero.
>> CHRISTINA: One point three two.
>> ALOM: That's eighty three point eight.
>> CHRISTINA: And one point two three. Okay.
>> ALOM: Alright.
>> CHRISTINA: You noticed I wasn't worrying too much about
taking readings at equal intervals across the rheostat,
and students can sometimes obsess about getting systematic
data but really it doesn't matter that much.
>> ALOM: And I guess the important thing is to just
make sure that you are getting a change in the voltage
as you're moving along.
>> CHRISTINA: Yeah, and making sure that you've covered
the full range.
>> ALOM: OK brilliant, shall we plot a graph.
>> CHRISTINA: Let's do it.
>> ALOM: So do one point four one five divided by.
>> CHRISTINA: Point nought eight.
>> ALOM: Point nought eight yeah.
>> CHRISTINA: And that's two point one ohm.
>> ALOM: Which is slightly more than I’d expect for an AA cell.
>> CHRISTINA: Yes, I'd normally expect it to be less
than an ohm.
>> ALOM: Yeah, okay, but that's what the data says, and the y
intercept gives us an emf of one point four one five volts.
>> CHRISTINA: And that's good, because for a cheap battery
of this sort, which has a stated value of one point five volts,
that's probably within its tolerance.
>> ALOM: So this practical seems to work very well, we've got
some good data, it's fairly straightforward to do,
and students will get practice of rearranging an equation so
they can plot the straight line graph. But, I like to push
my students a bit more and give them a bit of a challenge.
So I get them to find the internal resistance
of one of these: a button cell.
>> CHRISTINA: Okay, I'll disconnect this one.
>> ALOM: Okay, I’m just using a lump of Blutack to hold my
button cell like that. >> CHRISTINA: Okay.
>> ALOM: And I'm going to plonk this one here so
it's in contact. >> CHRISTINA: Right.
>> ALOM: Okay, so why don’t we watch what happens?
>> CHRISTINA: So that's fluctuating much more
wildly than before.
>> ALOM: That's why this is interesting,
because students are going to be challenged to think about how
they're going to cope with this fluctuation.
>> CHRISTINA: And their measurement uncertainty of it.
>> ALOM: Absolutely yeah.
>> CHRISTINA: But, I mean, how are we physically going
to cope with taking readings even with the two
of us working together?
>> ALOM: OK so the issue of taking a simultaneous reading
from both meters: I have got a solution but for that I’m
gonna use the camera on my phone.
>> CHRISTINA: But isn't your battery dead?
>> ALOM: I'm going to use the camera on your phone. So,
we're going to do pretty much the same thing that we
did last time, if you momentarily
connect the circuit, and then change the current.
I'll photograph the meters and I'll have a reading so will
do that 10 times yeah?
>> CHRISTINA: Okey-doke, so we’ll start at
this end again.
>> ALOM: So tell me when you're a go.
>> CHRISTINA: OK go! >> ALOM: Yep.
>> CHRISTINA: Go! >> ALOM: Yeah.
>> CHRISTINA: Okay? >> ALOM: Okay, so….
>> CHRISTINA: Now we plot a graph of the data.
>> ALOM: We can just plot a graph straight
from these readings. So, I’ve got…
hundred seven point oh. >> CHRISTINA: Milliamps?
>> ALOM: Yep millimps yep.
>> CHRISTINA: A hundred and seven.
>> ALOM: One point five two.
>> CHRISTINA: So how would you cope
with the measurement uncertainty?
>> ALOM: Well, the students might suggest
taking repeat readings, but as you've seen the readings
fluctuate so much that’d be really hard for them to take
a voltage reading at the same current again. So,
what I would do is repeat the whole experiment.
>> CHRISTINA: So you get the whole run
of the different current.
>> ALOM: That's right. I’d use the three sets of data
to calculate an internal resistance and an EMF, and then
I'd use those values and look at the spread of those values
and calculate the uncertainties in those.
>> CHRISTINA: And find the average overall.
>> ALOM: That's right.
So what have we got here?
>> CHRISTINA: So our EMF is three point one five volts.
>> ALOM: Which is what we'd expect from a button
cell like this.
>> CHRISTINA: And the internal resistance is… so… three point
one five minus one point two zero over point one three.
>> ALOM: Okay, so that's an internal resistance
of fifteen ohms.
>> CHRISTINA: Fifteen ohms! So that's really different from
the AA cell we measured.
>> ALOM: That's right, and that's why I think
this allows students to see that cells are much more
interesting than they might think.
I hope you found that useful. In the description below you’ll
find links to lots of other useful stuff like teacher’s
notes and worksheets, and please don't forget
to subscribe so you can watch the other films in the series.
Okay, this doesn’t feel weird at all.