Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• relate your model of flow to actions in adding elements to a loop
• relate your model of flow to actions in adding loops
• connect toolkits for thinking with physical experiences with circuits
• not conflate analogies with toolkits that can make predictions

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How to:

• keep emphasising that the charged particles are only set in motion by the battery
• separate charge flow and energy shifting
• exploit your chosen toolkit to make predictions about the effects of changes to circuits
• keep the focus on whole loops
• link the ideas of something being used up to the flattening of the battery

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

More batteries

The fact that adding a second battery in series results in the bulb being brighter makes intuitive good sense to most pupils. Pupils reason that the double source (or battery) is now supplying just one consumer (or bulb) and therefore gives a bigger effect.

A more detailed explanation is, however, more demanding for pupils and is based on two effects which occur simultaneously:

With an extra battery, the positive terminal of the battery becomes more positively charged and the negative plate becomes more negatively charged, and this exerts a bigger force on the charged particles.

As a result:

• More charged particles pass through the filament each second.
• Each charge shifts more energy during its passage.

In other words, adding a battery both increases the current and increases the energy that is shifted by each charge passing.

Push and current

Wrong Track: More current flows out of the extra battery.

Right Lines: Extra batteries provide a bigger push on all of the charged particles in the circuit. When a second battery is added to the circuit, the positive side of the combined battery becomes more positive with respect to the negative side. A bigger force is therefore acting on all of the charged particles in the circuit, as they are pushed away from one side of the battery and attracted towards the other. Adding a battery, therefore, results in the same charged particles (in battery, bulb and connecting wires) moving around the circuit more quickly. More charged particles pass each point per second. In other words, the current increases.

Charged particles don't come from the battery

Thinking about the teaching

This incorrect line of reasoning is rooted in the idea that the battery is the source of the charged particles which make up the electric current.

Here you should emphasise that:

Teacher: The charged particles don't come from the battery. They start off in the battery, connecting wires and bulb. The bigger current is due to those charged particles moving around more quickly.

Expressed in terms of the rope loop:

Teacher: It's like with the rope loop. The rope didn't come from me in the first place. The loop is already there and, as when a second battery is added, I simply moved the same loop around more quickly.

Thinking about the learning

When moving from one to two batteries in a circuit, pupils often anticipate (sensibly) that the current will double in strength. What happens in practice is that the current certainly increases, but not to the extent of doubling. The reason for this is that as the current in the bulb increases, the filament heats up more and its resistance increases. The increased thermal agitation of the atoms of the filament makes it harder for the charged particles to pass.

A good teaching question

Good teaching questions that challenge pupils' understanding and encourage discussion can often be generated by considering extreme cases.

So:

Teacher: Is there any limit to how large the current can become as more batteries are added to the circuit?

In (simple) theory as more batteries are added, the charged particles in the circuit are simply pushed round more quickly, so the size of the electric current increases. In practice, there is a limit to the size of electric current through the bulb – the filament melts.

Teacher Tip: Explore edge cases to investigate what a model predicts about a situation.

But do take care: when moving from one to two batteries in a circuit, pupils often anticipate (sensibly) that the current will double in strength. What happens in practice is that the current certainly increases, but not to the extent of doubling. The reason for this is that as the current in the bulb increases, the temperature of the filament is higher and its resistance increases. The increased thermal agitation of the atoms of the filament makes it harder for the charged particles to pass.

The more batteries, the more energy

Wrong Track: Adding batteries gives more energy to the charges.

Right Lines: The charged particles flow at a greater rate and the bulb is warmed more by their working – just like the rope loop being pulled through your hands at a greater rate when I pull harder.

Adding batteries makes the bulbs glow more

Thinking about the learning

The idea that adding batteries increases the rate at which energy is being supplied to the circuit makes intuitive good sense to most pupils.

However you should avoid any temptation to suggest that the charged particles are given more energy. They are not. The rope loop is very useful here, as it correctly presents the idea that what is going on is a kind of remote working. The electrical loop links the shifting of energy from the chemical store of the battery to the shifting of energy to the thermal store of the surroundings as the bulbs glow and the radiating warms their environment.

Thinking about the teaching

The rope loop model is likely to be useful here in helping the pupils to picture what is going on:

Teacher: So, with the rope loop, I worked harder to pull the rope around with a bigger force. I seem to remember that Anita felt the benefit of my efforts as her hand warmed up. It's a good job I didn't have to keep going for too long!

Two lines of thinking converge

Thinking about the learning

The challenge for the pupils here is to recognise the two effects which follow from increasing the number of batteries and lead to the increased brightness of the bulb:

• The bulb is brighter because the current is bigger – more charged particles per second.
• The bulb is brighter because the extra battery shifts more energy for each charge.

You'll have to decide how to do this most effectively.

Thinking about the teaching

We return to thinking about how to draw on the three key elements in sequencing this part of the teaching.

Here our advice is to start with observations and measurements (notice and record what actually happens) and then account for these observations and measurements in terms of the electric circuit model and a teaching model.

Exploiting the teaching model

This approach is the reverse of that taken in episode 01, where the teaching started with making predictions from the model.

With the approach taken here, the teaching model supports the observations and helps pupils see that they are reasonable.

Teacher: OK, so what can you tell me about the current when a second battery was added?

Teacher: Right, the current was bigger and that the bulb was brighter.

Teacher: Now, can anybody picture what's going on here in terms of the rope model?

Teacher: That's exactly right! I pulled the rope around more quickly and Julia felt her hands being heated up more.

Teacher: Now who can talk through that in terms of charge and energy?

Teacher: Excellent! As the second battery is added, the charged particles move around the circuit more quickly and twice as much energy is shifted by each charge.

Reflecting on teaching models

Thinking about the teaching

All teaching models and analogies have their strengths and weaknesses and it is important to be aware of what these are, and how they'll help or impede pupils as they try and come to terms with electric circuits. We don't think that all (teaching) models are of equal value to learners. We have advocated consistent use of a rope loop model, and given some of its advantages. You'll have to decide on one (and we think it should be one – or else the pupils need a very deep understanding of electrical loops to be able to select from amongst the models available to them, to apply the situation at hand), and we think you should be prepared to justify your choice.

We think it is not good to teach electric circuits as a collection of to-be-memorised rules, as this undermines pupils' confidence in their ability to make sense of the phenomena.

When using a teaching analogy in class, we find it very helpful to talk about it as a picture and to avoid calling it a model. This helps distinguish between helpful pictures (teaching analogies) and models: things you can reason with and that have predictive power. Both the electric circuit model (the scientific model the pupils are beginning to understand) and the rope model are worthy of that name.

We suggest you aspire to develop a model, with which the pupils can reason. Then use the model consistently. We don't recommend flipping around amongst models, because in such a case the short time that they have to study circuits will not be enough to acquire fluency with any one model. We certainly don't suggest that this is a good area for pupils to be asked to discriminate amongst models – there are far too many conceptual tripwires in this topic (and some models guide pupils into the trip zone).

One other common model involves energy being given to the charged particles as they leave the battery, which is in turn given to the bulbs. Energy may be modelled as loaves of bread given to breadvans (so the vans are the charged particles) or sweets given to pupils. All of these might be grouped as donation models.

A strength of the donation analogies is the way in which they distinguish between energy and current. The point was made earlier that pupils can easily mix up current and energy, so the teaching analogy directly addresses this problem.

However experience shows that this can also be achieved with the rope loop model.

A significant weakness of the donation analogies is that it paints the picture of charged particles collecting energy only in the battery and giving out energy in the bulb. As detailed earlier, this is not the case. The physical reasoning is wrong, even if the sums done later exhibit similar structure. The analogy does misrepresent the physics – think back to lessons of the big circuit, and is likely to reinforce many of the wrong tracks identified in this topic.

A further weakness of donation analogies is the reliance on ad-hoc rules. For example, using a supermarket picture, in moving from one to two bakeries, it may be plausible to suggest that each van collects twice the amount of energy, but it is not so clear as to why the vans also move round at twice the rate. For the correct working of the analogy it is essential to recognise that changes to the amount of bread carried per van and the rate at which the vans move round cannot occur independently. Similarly, in adding an extra supermarket it is necessary to accept that the bread is shared between the supermarkets and that the loop of vans is slowed down.

Adding a bulb prevents things happening

Wrong Track: The first bulb grabs the current, so that there's none left for the second.

Wrong Track: The first bulb slows down the current, and the second one slows it even more.

Right Lines: The current is the same everywhere in the loop. The bulbs both act together to reduce the flow. Ther really isn't a first and second.

One more bulb, reduced current

Thinking about the learning

The fact that adding a second identical bulb in series results in the two bulbs being dimmer makes intuitive good sense to most pupils. Their underlying reasoning is that the single source (or battery) is now being shared between the two bulbs. This idea needs both development and some refining, so that it increases in precision.

The key idea for the pupils to get hold of here is that adding an extra bulb introduces more resistance to the circuit, and this has the effect of slowing down the passage of charge around the whole circuit. The number of charged particles passing any point in the circuit is reduced; in other words, the current is reduced.

Thinking about the teaching

The rope loop teaching model is very useful in getting over the idea that the electric current goes down when a second bulb is added to the circuit.

Teacher: OK! Now I want both Julia and Anita to loosely hold the rope. I'm pulling the rope round with the same force and it's obvious that Anita's extra grip or resistance has slowed down the whole of the rope loop.

Having talked through the teaching model, attention is returned to the electric circuit model:

Teacher: When a second bulb is added, extra resistance is introduced to the circuit. This has the effect of slowing down the flow of charge all around the circuit. In other words the current is reduced.

It is worth emphasising that it is the filament of the bulb that offers the resistance to the flow of charge:

Teacher: The filament of the bulb is made from very thin tungsten wire. The filament is designed so that it is difficult for the charge to pass through and, as they do, they interact with the tungsten atoms and the whole lot heats up until the filament glows white-hot. This is rather different from what happens in the connecting leads. These are made from relatively thick lengths of copper wire that have a very low resistance and so very little heating occurs in the connecting leads.

One current set by the resistance

Wrong Track: The current is smaller in the filament of the bulb because of the very high resistance, but then speeds up and gets bigger through the conducting wires.

Right Lines: The extra resistance at a single place in the circuit has the effect of reducing the current around the whole circuit. The same amount of charge passes per second through each and every part of the circuit.

The current is reduced in the whole circuit

Thinking about the learning

A further important point to emphasise is that when additional resistance is introduced to a circuit in one place, the current is reduced everywhere in the whole circuit. This can be the source of confusion for pupils.

Thinking about the teaching

It may be helpful to think of the resistance as providing the rate-determining step for the whole circuit. The rope loop is useful in establising this. As further resistance (more pupils gripping the rope) is added to the circuit, the movement of the whole rope loop is slowed down. All parts of the rope loop move around at the same speed.

It is worth exploring the effect on the current of a full range of resistance.

Teacher: What would happen to the current if more and more bulbs were added to the circuit?

Quite simply, as more bulbs are added, the resistance in the circuit increases, the charge moves around more slowly and the current gets smaller. With an infinite resistance, the current would fall to zero. We can demonstrate this simply by making a gap in the circuit.

Teacher: What would happen to the current if all of the bulbs were removed from the circuit and we were left with a connecting lead from one side of the battery to the other?

This is called a short circuit and is to be avoided! Because there is very little resistance in the circuit (apart from that provided by the battery itself), a very large current results with the charged particles moving around very quickly. It is likely that the battery will be damaged, or the wire become so hot that it will burn you or even melt!

Don't use a model that suggests charged particles come from the battery

It's very easy to say;

Teacher: a current of 1.4 ampere flows from the supply

or

Teacher: a current of 1.4 ampere is drawn from the supply

.

Once again these words imply that the current originates in the battery and it is better to say something like

Teacher Tip: There is a current of 1.4 ampere in the wires of the big loop and in the supply.

Two identical bulbs

Wrong Track: The first bulb must get all of the energy because the charges don't know that there is a second bulb.

Right Lines: Equal quantities of energy are shifted by both bulbs as the currents in both are identical, and the resistance of both are identical. The energy shifted by the battery is is equal to the energy shifted by both bulbs.

Using the rope loop model

Thinking about the learning

Problems can arise for those pupils who think of the charges starting out from the battery and shifting all of their energy in the first bulb. We'd suggest that you undermine this by not using any model that suggests that charges leave the battery having had energy donated to them.

Thinking about the teaching

The idea to get over here is that the battery is working equally on the charges in both bulbs. There is the same current in both and both have the same resistance. There is no first bulb and second bulb. As the energy shifted from the store of the battery is equal to the sum of the energies shifted at each bulb, and these energies are equal, then the energy shifted by each bulb will be half that shifted by the battery. But this conclusion is a consequence, not a determining rule.

Once again, the rope loop can be very helpful in talking through the idea that with two bulbs there is a simultaneous and equal shifting of energy at the two sites:

Teacher: So, with both Julia and Anita holding the rope, both of them can feel their hands warming up. In fact, if they both grip the rope equally they will be equally warmed.

Teacher: Equal grip leads to equal (slipping) frictional force on each. What else could it be? There is the same amount of rope going through both Julia's and Anita's hands. So with no differences between them, what other result could there be than this?

If you encounter particular reluctance, reinforce the idea by making the rope move in the opposite direction; the position order in the circuit is not what is important.

Putting together thinking about two lamps

Thinking about the learning

The challenge for the pupils here is to be able to provide a full explanation as to why the two bulbs become equally dim:

The bulbs are now dimmer because adding the extra bulb increases the resistance and reduces the current everywhere in the whole circuit. As a result, less charge passes per second through each bulb, and each charged particle shifts less energy as it passes through each filament.

Thinking about the teaching

Once again (as in the previous episode), our advice is to start with observation and measurement (see what actually happens) and to account for these observations and measurements in terms of the electric circuit model and teaching model.

We advise this because sometimes pupils become quite fixed on the idea that the first bulb will get all of the energy when two bulbs are connected in series. With this point in mind, we think that it is a good idea to start with practical observations and measurements. The fact of the matter is that the bulbs are equally dim. Selection and effective use of a good teaching model, together with consistent and careful modelling of reasoning with this model.

Expressed in terms of the electric circuit model:

Teacher: Fewer charged particles pass through a bulb each second, as the push provided by the battery is the same, but the resistance present in the loop is greater. So less energy will be shifted by each bulb and, as a consequence, by the cell.

Getting more: paying nothing?

Wrong Track: There's no extra battery. We're getting the second bulb's worth for nothing!

Right Lines: Energy is shifted to the surroundings by the two bulbs at twice the rate and as a result the battery goes flat more quickly. When the second bulb is added in parallel it is just as bright as the first one. Energy is shifted by the two bulbs at twice the rate and so the battery does not last as long.

More energy shifted

Thinking about the learning

The fact that adding a second bulb in parallel results in the two bulbs being of normal brightness is counter-intuitive for most pupils. Their underlying reasoning is that the single source (or battery) is now being shared between the two consumers (or bulbs) and that they should therefore be dimmer, just like the bulbs in series.

At first it seems as though adding bulbs in parallel gets you something for nothing!

The incorrect idea here is that by adding a second bulb in parallel, it is possible to get twice the energy output without further energy cost.

Thinking about the teaching

We suggest two possible ways of addressing this idea of something for nothing.

Help pupils make sense of their observations in terms of the battery going flat more quickly:

Teacher: At first it seems as though we're getting something for nothing, but the drawback is that with the two bulbs in parallel the battery flattens more quickly. We shift the energy stored in the battery more quickly.

Help pupils to picture what is going on in terms of an identical flow of charge through each independent loop. As a consequence there is an increased flow of charged particles through the battery, which results in energy being shifted by the battery at an increased rate. This detailed approach is discussed in the next challenge.

A parallel circuit is two loops

Thinking about the learning

If pupils are asked to build a circuit so that…

one battery lights two bulbs to normal brightness

… more often than not, they use the single pair of battery terminals to make two circuit loops.

When the circuit is constructed and drawn in this way as two separate loops, which share a single battery, it makes good sense to pupils that:

• Each bulb is of normal brightness.
• Each bulb has a current in it which is equal to that produced in a simple one battery and one bulb circuit.
• The battery flattens more quickly because it is providing energy for both circuits and bulbs.

These pupil insights provide a very helpful starting point for teaching about parallel circuits.

Thinking about the teaching

To help pupils understand parallel circuits as consisting of two loops, and to relate them to these conventional formats, we have found the following sequence to be very useful.

• Build a circuit with a single loop to the right of the battery, using short wires of one colour and a single bulb.
• Detach that loop from the battery, and put it to the right hand side.
• Build a circuit with a single loop to the left of the battery, using long wires of a different single colour and a single bulb.
• Detach that loop from the battery, and put it to the left hand side.
• Now attach both loops, keeping them on the same side.
• Now lift the longer loop over to the right, without breaking any connections.

By following this sequence through, the point can be made that in the parallel circuit, each bulb has the same current in it and that therefore there is a double current (the sum of the currents in each loop) in the battery. The double current shifts energy at double the rate.

Just where do the charged particles come from?

In describing what happens when a second bulb is added in parallel, it is quite common for teachers to use phrases such as:

Teacher: When the second bulb is added in parallel, twice the current is drawn from the battery.

Such expressions are potentially misleading in that they paint a picture of the battery providing the additional current. Instead, it is the additional charged particles from the second loop which flow through the battery.

It would be better simply to say:

Teacher Tip: When the second bulb is added in parallel, there is twice the current in the battery.

Different ways of drawing the same circuit

Teacher Tip: Try exploring (with pupils) other representations for parallel circuits, showing that the same circuit can be drawn with different, but equivalent, layouts.

Remember – it's only what's in the loop that's important. The whole loop functions as an integrated system: we'd suggest not trying to explain it as stories about isolated actors (journeys undertaken by one charge, the current splitting, etc.).

Only in the very simplest cases are circuits either series or parallel. For more precision, you might refer to series connections or parallel connections. Later on, pupils may well meet circuits where things are connected in both series and parallel in the same circuit. But for very simple circuits you can use the terms series circuits and parallel circuits without causing too much confusion.

More flow – the same in each loop

Wrong Track: The current leaves the battery and splits, some down each loop.

Right Lines: Each loop has a flow just as it would on its own. So each one flattens the battery just as it would on its own. There are two loops, so twice as much current, and so the battery is working twice as hard.

Flattening the battery more quickly

Thinking about the learning

When the second bulb is connected in parallel, the current in the battery doubles. This means that double the number of charged particles are flowing through the battery each second. With double the number of charged particles, energy must be shifted from the battery's store at twice the rate. So, the battery's store is depleted of energy in half the time.

Thinking about the teaching

In terms of the electric circuit model:

Teacher: OK, so with one battery and one bulb, we can picture the charged particles moving through the battery. When a second bulb is added in parallel, an extra loop of charged particles is provided. The number of charged particles passing through the battery each second is therefore doubled. So, with the second loop, the charged particles shift energy from the battery at twice the rate and the battery will go flat more quickly.

In terms of the rope loop:

Teacher: With one loop, I have to work to keep the rope moving and Julia feels her hand warming up as she grips the rope. If I add a second loop of rope, I now need to increase my rate of work to keep both loops going and both Julia and Anita feel their hands warming up. Of course, in this case I get tired more quickly!

There's a good chance you could improve your teaching if you were to:

Try these

• thinking about electrical loops
• linking what you do in setting up a loop to your reasoning about the circuit
• using model to mean a toolkit for thinking with that is capable of generating predictions
• reasoning about electrical loops as complete systems
• reasoning about parallel circuits as two complete loops
• being consistent in how you draw circuits

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• using sequential models, such as donation models
• conflating energy shifting and charge flowing
• electrical energy

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.