Adrian was a participant in the Understanding Science project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them". So I asked him was resistance was:
So what exactly is resistance?
Resistance is, erm (pause, c.3s) Resistance is current over, voltage, I think. (Pause, c.3s) Yeah. No.
Not sure?
I can’t remember formulas.
So Adrian's first impulse was to define resistance using a formula, although he did not feel he was able to remember formulae. He correctly knew that the formula involved resistance, current and voltage, but could not recall the relationship. Of course if he understood qualitatively how these influenced each other, then he should have been able to work out which way the formula had to go, as the formula represents the relationship between resistance, voltage and current.
So I then proceeded to ask Adrian how he would explain resistance to a younger person, and he suggested that resistance is how much something is being slowed down or is stopped going round. After we had talked about that for a while, I brought the discussion back to the formula and the relationship between R, V and I:
And what about this resistance in electricity then, do you measure that in some kind of unit?
Yes, in erm (pause, c.2s) In ohms
So what is an ohm?
Erm, an ohm is, the unit that resistance is measured in.
Fair enough.
It comes from ohm's law which is the erm formula that gives you resistance.
Ah okay, so what’s the ohm's law formula then?
That is erm (pause, c.2s) R = I over (pause, c.5s) I over V, but I don’t think (pause, c.2s) voltage is amps, (unclear phrase) current is (pause, c.2s) I don’t know.
Not sure about that?
No.
As Adrian considered resistance as slowing down or stopping current I thought he might be able to rationalise how a higher resistance would lead to less current for a particular potential difference ('voltage').
Okay. Let’s say we had erm two circuits, and they both have resistance and you wanted to get one amp of current to flow through the circuits, and you had a variable power supply.
Okay.
And the first circuit in order to get one (amp) of current to flow through the circuit.
Yes.
You have to adjust the power supply, until you had 10 volts.
Okay.
So it took 10 volts to get one amp to flow through the circuit. And the second (unclear) the circuit, when you got up to 10 volts, (there is) still a lot less than one amp flowing. You can turn it up to 25 volts, and only when it got to 25 volts did you get one amp to flow through the circuit.
Yes, okay.
In mathematical terms, the resistance of the first circuit is (R = V/I = 10/1 =) 10Ω, and the second is (25/1 =) 25Ω, so the second - the one that requires grater potential difference to drive the same current, has more resistance.
Do you think those two circuits would have resistance?
Erm (pause, three seconds) Probably yeah.
Same resistance?
No because they are not the same circuit, but - it would depend what components you had in your circuit, if you had different resistors in your circuit.
Yeah, I've got different resistors in these two circuits.
Then yes each would have a different resistance.
Can you tell me which one had the bigger resistance? Or can’t you tell me?
No, I can’t do that.
You can’t do it?
No I don’t think so. No.
Adrian's first response, that the circuits would 'probably' have resistance, seemed a little lacking in conviction. His subsequent responses suggested that although he knew there was a formula he did not seem to recognise that if different p.d.s were required to give the same current, this must suggest there was different resistance. Rather he argued that different circuits would be likely to have different components which would lead to them having different resistances. This was a weaker argument, as in principle two different circuits could have the same resistance.
I shifted my approach from discussing different voltages needed to produce the same current, to asking about circuits where the same potential difference would lead to different current flowing:
Okay, let me, let me think of doing it a different way. For the same two circuits, erm, but you got one let's say for example it’s got 10 volts across it to get an amp to flow.
Yeah. So yes okay so the power supply is 10 volts.
Yeah. And the other one also set on 10 volts,
Okay.
but we don’t get an amp flow, we only get about point 4 of an amp, something like that, to flow.
Yeah, yeah.
Any idea which has got the high resistance now?
The second would have the higher resistance.
Why do you say that?
Because less erm - There’s less current amps flowing around the circuit erm when you have the same voltage being put into each circuit.
Okay?
Yes.
This time Adrian adopted the kind of logic one would hope a physics student would take. It was possible that this outcome was less about the different format of the two questions, and simply that Adrian had had time to adjust to thinking about how resistance might be linked to current and voltage.
You seem pretty sure about that, does that make sense to you?
Yes, it makes sense when you put it like that.
Right, but when I had it the other way, the same current through both, and one required 10 volts and one required 25 volts to get the same current.
Yes.
You did not seem to be too convinced about that way of looking at it.
No. I suppose I have just thought about it more.
Having made progress with the fixed p.d. example, I set Adrian another with constant current:
Yes. So if I get you a different example like that then…let’s say we have two different circuits and they both had a tenth of an amp flowing,
Okay. Yes.
and one of them had 1.5 volt power supply
Okay yes.
and the other one had a two volt power supply
Yeah.
but they have both got point one of an amp flowing. Which one has got the high resistance?
Currents the same, I would say they have got different voltages, yeah, so erm (pause, c.6s) probably the (pause, c.2s) the second one. Yeah.
Because?
Because there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in and therefore resistance must be more to stop the rest of that.
Yes?
I think so, yes.
Does that make sense to you?
Yeah.
So this time, having successfully thought through a constant p.d. example, Adrian successfully worked out that a circuit that needed more p.d. to drive a current had greater resistance (here 2.0/0.1 = 20Ω) than one that needed a smaller p.d. (i.e. 1.5/0.1 = 15Ω). However his language revealed a lack of fluency in using the concepts of electricity. He referred to voltage being "put in" to the circuits rather than across them. Perhaps more significantly he referred to their being "less current flowing in" where there was the same current in both hypothetical circuits. It would have been more appropriate to think of there being proportionally less current. He also referred to the greater resistance stopping "the rest" of the current, which seemed to reflect his earlier suggestion that resistance is how much something is being slowed down or is stopped going round.
My purpose in offering hypothetical answers was to see if they allowed Adrian to reconstruct the formula he could not recall. As he had now established that greater p.d. is needed when resistance is higher for a foxed current), and that less current flows when resistance is higher (for a fixed p.d.), he might have been able to recognise that his suggestion that "resistance is current over, voltage" was inconsistent with these relationships.
Okay and how does that relate to the formula you were just telling me before?
Erm, No idea.
No idea?
Erm (pause, c.2s) once you know the resistance of a circuit you can work out, or once you know any of the, two of the components you can work out, the other one, so.
Yeah, providing you know the equation, when you know which way round the equation is.
Yes providing you can remember the equation.
So can you relate the equation to the explanations you have just given me about which would have the higher resistance?
So if something has got a higher resistance, so (pause, c.2s) so the current flowing round it would be - the resistance times the voltage (pause, c.2s) Is that right? No?
Erm, so the current is resistance time voltage? Are you sure?
No.
So Adrian suggested the formula was I = R × V (rather than I = V /R ), which did not reflect the qualitative relationships he had been telling me about. I had one more attempt at leading him through the logic that might have allowed him to deduce the general form of the formula.
Go back to thinking in terms of resistance.
Okay.
So you reckoned you can work out the resistance in terms of the current and the voltage?
Yes, I think.
Okay, now if we keep, if we keep the voltage the same and we get different currents,
Yes.
Which has, Which has got the higher resistance, the one with more current or the one with less current?
Erm (Pause, c.6s) So, so, if they keep the same voltage.
That’s the way we liked it the first time so.
Okay.
Let’s say we have got the same voltage across two circuits.
Yes.
Different amounts of current.
Yes.
Which one’s got the higher resistance? The one with more current or the one with less current?
The one with less current.
So less current means it must be more resistance?
Yes.
Ok, so if we had to have an equation R=.
Yes.
What’s it going to be, do you think?
Erm (pause, c.7s) R= (pause, c.3s) I don’t know. It's too hard.
Whether it really was too hard for Adrian, or simply something he lacked confidence to do, or something he found too difficult being put 'on the spot' in an interview is difficult to say. However it seems fair to suggest that the kind of shift between qualitative relationships and algebraic representation, that is ubiquitous in studying physics at this level, did not come readily to this advanced level physics student.
Return to ECLIPSE homepage
List of science topics
Dr Keith S Taber kst24@cam.ac.uk
University of Cambridge Faculty of Education
© Keith S Taber, 2013