Teaching Electricity; The Rope Model

This is a slightly adapted version of a post made on the #cogscisci mailing list.

Acknowledgements:

• Rachel Hartley (Institute of Physics teaching and learning coach, who first properly showed me the rope model)
• The IoP’s supporting physics teaching website (which can be a bit dense but is really, really useful)
• many, many posts on the Physics Teaching News and Comment (PTNC) email list – too many to mention all by name, but especially Pete Gravell who has made some great points about analogies in teaching electricity.
• many people on twitter especially @emc2andallthat for many enlightening conversations. Follow him! I would also recommend you also read his blog on electricity models for a different point of view to mine.

 

 

When teaching electricity at KS3, 4 and 5, I think there are six fundamental ideas which underpin most of any electricity topic. I think the first two should be pretty well covered in primary science, leaving secondary science to formalise the latter four.

1. The idea of electricity involving a ‘flow’ (of … something… see 3!)
2. The idea of a ‘complete circuit’ being necessary for the flow to occur (in a battery-powered circuit)
3. The idea of charge (what flows in circuits)
4. The idea of current (the rate of flow of charge)
5. The idea of potential difference (the cause of the flow – ideas about how PD links to transferred energy should be developed much later in KS4 and 5 I think)
6. The idea of resistance (a measure of the ‘opposition’ to the flow of charge)

 

Many people have discussed the importance of beginning an electricity topic with the concept of charge. Ben Rogers has a section in his excellent book (also here) about the importance of distinguishing the scientific meanings of this word from other ‘everyday’ meanings.

At my current school, we restructured our Y7 so students are taught the structure of the atom (it’s not hard, it’s pattern spotting, and Y7s love it!) twice, before they do their Y7 electricity topic  (once as an add-on to the end of the ‘particles’ topic, and then again in our Y7 ‘chemical elements/periodic table’ topic). That means they already know about protons, neutrons and electrons (in shells) BEFORE starting the electricity topic. Its then a much smaller cognitive jump to say that ‘in some materials, like metals, some of the electrons are free/delocalised’ (with the appropriate explicit vocabulary instruction for delocalised, of course!) – and then to say that ‘something called a potential difference has to be applied across the ends of a metal, to make the free electrons (which are already there, within the metal) flow’. Applying a PD across an insulator has no effect as there is nothing within the insulator which can flow (no mobile charge, no free electrons, all electrons are bound). 

However, the main subject of this post is to write about the use of different models in the electricity topic, which are essentially the different ways we are teaching students to picture/think about electricity.

There’s discussion amongst physics teachers about whether its helpful or not to present students with numerous different models or electricity. From a CogSci point of view you could argue that multiple models unnecessarily increases cognitive load. Lots of physics teachers (including Ben Roger’s excellent book) disagree, which is fine. The argument given is that its good for students to evaluate the strengths and weaknesses of different models. But, I think students can only do this [evaluate models of electricity] when they already have a good understanding of the physics that is being modelled. If you teach electricity by saying  ‘electricity is like X’ but then ask ‘Right – now I want you to think about how electricity is not like X’ I think students will struggle – as you’re confusing the fragile new schema which they’ve tentatively been building about this topic they don’t know much/anything (technical) about yet.

In the past I’ve seen (and certainly, taught myself too!) lessons where a teacher has explained/demonstrated a model to ‘explain circuits’ and then immediately asked students to evaluate the weaknesses of  the model – they can’t do it because they don’t yet understand electricity well enough to understand what aspects of electricity the model shows well and what aspects are not shown well. I’m not saying this kind of model-evaluation activity is impossible to do, I just think it’s often performed far too early before students have developed good enough ‘electricity-schema’ to be able to evaluate the models effectively.

Secondary to this, I’d argue the point of the electricity topic is to teach students how electricity works; I think teaching students different models of electricity and their strengths and weaknesses has the potential to slightly side-track the point of the topic. If you were writing a list of what you want students to know by the end of the electricity topic, I doubt you’d include statements like “in the ‘water model’ of electricity a battery potential difference is modelled by a difference in fluid pressure“. But I’m sure you would include something like ‘In a circuit, a potential difference is required, to cause the charge/free-electrons to flow‘. Fundamentally, the core knowledge we want students to gain is about electricity itself, whereas knowledge of various electricity models is, to me, distinctly secondary.

I feel there is a danger that students (and teachers – especially non-specialist teachers of physics) might end up spending too much time thinking about the different models rather than thinking about electricity itself. This is important because, as we know from Willingham (and elsewhere), what students are thinking about is really important as that is what they’ll remember. If they spend too much time thinking about comparing ropes and waterpipes and trains/carriages this could run the risk of diverting attention from thinking directly about electricity and how electricity works.

So – the focus of the electricity topic should be on how electricity works (duh!). Any models/analogies referred to should clearly illustrate/be analogous to/help students to ‘see’/accept what happens within circuits. So what models should you use? I (and, from what I understand, also the Institute of Physics) happen to prefer one model in particular – the rope model – I’d like to take the opportunity to explain why.

With water models – students end up thinking that when you add a parallel branch to a circuit, the original water (current) then splits. This is incorrect. When you add a parallel branch to a circuit, additional current now flows and it is this new, greater current that splits at junctions in parallel circuits. In the water model, adding a parallel branch isn’t like adding an extra (empty) pipe, its like adding an extra pipe-that’s-already-full-of-water – so there’s now more water flowing in the circuit. Whilst some students ‘get’ this, I find that what was a quite simple model has not become a bit complicated. I’m also not sure it’s intuitively obvious that the ‘current’ (rate of flow of water) increases in the ‘return to the battery’ part of circuit when the two parallel paths rejoin.

Radiator models – have the same issues as water models. Also –do students really understand central heating systems well enough to use them as a reference for understanding electricity? I’d argue not.

‘Donation’ or ‘carrier’ models – these are like @emc2andallthat‘s CTM model – which, admittedly, is excellent at showing some aspects and developing quantitative reasoning. Another common ‘donation’ model is the teacher handing out tokens/sweets (energy) to students (charge) walking around the classroom, which are then ‘dropped off’ at bulbs.

I think there are many issues with donation models…

• How do the charges know how much energy to drop off at each bulb? Answer – they don’t – because this isn’t how the mechanism of electrical energy transfer (electrical working) works (see the ‘rope model’ for what I think is a better explanation/demonstration of this)
• What happens to the energy in the loaded carts if the flow suddenly stops? I don’t think it’s helpful for students to picture the energy still being there in the wires on one half of the circuit, but not on the other half of the circuit.
• Donation models imply there is a difference between the charges on either side of the circuit. There isn’t, really. Energy is just a number you calculate, and not a real thing that can be ‘carried’.
• AND – how do you explain AC?  mains electricity – arguably the most common way electricity is encountered by students in everyday life – is left as a total mystery!

The rope model – a bad way to do it

I’ve realised over the last few weeks that when some teachers hear of the rope model they picture 10-20 students all holding onto a rope loop at different points. This is not a good way to do it – they’ll all be gripping and pulling on the rope, either gripping too hard to disrupt the demo or pulling too hard in response the person next to them gripping the rope. The teacher ends up having a battle just to get the rope to do what s/he wants it to do. Also – in terms of CogSci – they’re probably thinking about gripping the rope or not getting a rope burn, rather than paying attention to the things you (the teacher) wants them to pay attention too.

The rope model – a much better way to do it.

• You need a loop of rope. Tie a length of rope (say, 3m) into a loop. Or even better – with a nylon rope, you can melt the ends together – so there is no knot that gets in the way.
• Ask for one student volunteer. They are the bulb. Get them to barely grip the rope at all – with only one hand – so the rope slips through easily.
• The teacher is the battery – they “provide a potential difference” by making the rope circulate. Ask students where the current started flowing first. Everywhere at once!
• The rope should be speckled – the free electrons are already there, in the metal wires of the circuit. They all start moving at once, with the same (speed) rate of flow everywhere around the loop.
• Direct students attention to the part of the rope close to your “bulb” – the rope travels no faster towards them than away from them. The rate of flow – the current – is the same everywhere in the circuit.
• What is happening to the “bulb’s” hand? It’s getting hotter. Energy transfer is occurring – the battery’s store of energy is decreasing, the thermal store of energy at the bulb is increasing – but not because one side of the rope is ‘carrying energy’ to the hand and the other side of the rope is returning (‘empty’) to the battery – energy is being transferred by the circulation of the system as a whole.
• How long did it take from the PD being applied (the teacher pulling the rope) for energy to ‘get’ to the bulb? No time at all – as soon as the rope starts circulating, energy is transferred. You don’t have to wait any time at all for charge to ‘carry’ energy around the circuit – because energy is not transferred from battery to bulb by charges ‘carrying’ energy; rather, energy is transferred by the motion of the system as a whole.

Then

• Model the effect of increasing PD (pull the rope faster) – you get a greater rate of flow (current).
• Model the effect of increasing circuit resistance – either get your “bulb” to grip the rope tighter, or invite 1 or 2 additional “bulbs” to come up and add their resistance (grip) into the circuit – the current (rate of flow) decreases. Where does it decrease? Everywhere – not just at the place with more resistance.
• Get 2 “bulbs” in series to each grip the rope – one tightly (high resistance), one very loosely (low resistance). The current might be different now, but its still the constant all around the circuit. Whose hand gets hotter – where is more energy transferred? At the high resistance bulb. Did the rope have to know to “drop off” more energy there? No – its just obvious that more energy ‘input’ to the system is transferred there, rather than the low resistance bulb.
• Make a parallel circuit by adding an entirely new rope loop (and bulb) into the system. The battery provides the same PD to both loops. Whilst both loops might circulate at the same speed (which, in circuits, is certainly not always true) it is obvious that where the rope loops ‘overlap’ in the shared part of the circuit (just “after” the battery, and where the parallel loops ‘rejoin’ just before the “battery”) that there is now more charge flowing than before – a greater rate of flow of charge. It should also be reasonably clear that the current in the original loop is exactly the same as it was before.

 

• FINALLY – show alternating current (mains electricity – arguably the most common way electricity is encountered by students in everyday life) by constantly changing the direction of the loop motion. Energy is still transferred across the circuit, from the AC source (teacher) to the “bulb” (student’s hand) – but without any part of the rope having to travel from the AC source around to the bulb (to “deliver”) that energy.

 

I’m glad that people have found the above useful. I’m not presenting the Rope Model as a ‘silver bullet’ that will suddenly enable all to understand electricity – I just thought it might be useful to share a detailed description of my approach to using the rope model to provide a visible demonstration/analogy for tricky electricity concepts. Please do read the above in conjunction with the CTM model and the Supporting Physics Teaching materials from the IoP and make up your own mind about what will help you teach concepts in electricity best, to your classes.

 

 

Additional note –

It was suggested to me that one advantage of ‘carrier/donation’ models over the rope model, is donation models show electric potential and potential difference (the difference between one side of the circuit and the other) really clearly – but the rope model doesn’t show this very well at all.

I would agree that the rope model doesn’t show the idea of electric potential very well (i.e. intuitively) – but I think the rope model could show this. If you point at the ‘speckles’ on the rope and say they represent electrons, you could point to an arbitrary section of rope (say 10cm long – mark off this section on the rope with a sharpie if you like) and say ‘this section represents 6 billion billion electrons – one Coulomb of charge’. When that 1C passes through a “bulb” (hand gripping the rope) – you could ‘pause’ the flow and talk about the energy that was transferred by that one Coulomb of charge as it flowed through the ‘bulb’ – this ‘energy transferred/work done per Coulomb’ is the PD across the bulb.

OK – admittedly that’s not very easy/intuitive to understand and it doesn’t show a ‘difference’ between the two sides of the bulb, but it is possible to model PD in the rope model.

About that ‘difference’ between the two sides of the bulb. This is a difference in electric potential. Electric potential is a scalar field, a numerical property of every distinct point in space, due to the electric field at that point in space. (Temperature is an easy to understand example of a scalar field – we can model every point in a room (every x,y,z coordinate) as having a numerical value associated with it, which is the temperature at that point). The electric potential at a point in space tells you the stored energy that would be associated with every Coulomb of charge present at that point (energy per unit charge). This is a calculated number only and not representative of any physical difference between the electrons (charge) either side of the bulb. Yet – in carrier models, we are embedding a very clear picture of a physical difference between the charges on one side of a bulb and the other. That’s what I personally prefer not to do, and why I prefer not to use ‘carrier’ model even to get across the idea of PD. The ‘potential difference’ across a bulb is not a physical difference between the electrons on either side of the bulb, it is a difference in a calculated quantity associated with the points in space ‘in the wires’ on one side of the bulb and the points in space ‘in the wires’ on the other side of the bulb. (This is getting close to the limit of my understanding of circuits… if I’m outright wrong about any of this, do let me know…)

So what do I do instead to ‘get across’ the idea of PD? I use different coloured highlighters to highlight circuit diagrams to show parts of the circuit (different points in space) where the electric potential (the energy-per-unit-charge associated with 1C being stored there) has the same and different values. I’ll have to explain this in a separate blog post, another time! Thank you for reading.

 

Additional note 2 – some further reading…

Here’s an article that goes into the ‘donation model’ misconception in far more detail.

And here‘s another related article.