Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• draw out the ideas that students use to make predictions
• separate ideas of current and voltage, met previously
• connect calculations done to ideas used to account for the circuits
• reinforce the difference between series and parallel connections in circuits

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:

• emphasise the necessity of representing the complete loop as a connected system
• link the phenomena to the toolkits that you use to make predictions
• make the tookits evidently intelligible and fruitful
• use teaching models systematically
• give physical reasons for changes in current as the circuit is altered

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.

Building on earlier topics

This episode builds on the SPT: Electric circuits topic, focusing on current in a single electrical loop.

As students move into 14–16 study they will have been exposed to a significant amount of teaching about electric circuits during their experiences 11–14, and even before that. This is not to say (unfortunately!) that they will have a full understanding of the ideas that they covered earlier.

In returning to work on electric circuits with the 14–16 age group, it is therefore very valuable to set a selection of short diagnostic questions for your students, to find out what they still understand from earlier studies and to help them to start thinking once again about electric circuits.

Diagnostic question on ammeter readings

The following question, on electrical current, was set to a group of students after their 11–14 teaching on electric circuits:

In this circuit the ammeter at position 1 reads 0.3 ampere. Predict the value of the current at positions 2 and 3.

Current at ammeter 2 is …

Current at ammeter 3 is …

Explain why you have predicted these values.

Correct answers:

Current at ammeter 2 is 0.3 ampere

Current at ammeter 3 is 0.3 ampere

Explanation:

The current is the same in every element round this simple series circuit. This is because the rate of flow of charge (the number of coulombs of charge passing each point every second) is the same for every point in the circuit.

Some students' answers and implications

Student 1

Ammeter 2: 0.6

Ammeter 3: 0.3

Because the energy in the charges go past the ammeter with energy in the charges then when it gets to number 2 the charges are empty so it is low.

Student 2

Ammeter 2: 0.3 ampere

Ammeter 3: 0.3 ampere

Because the flow of energy will be the same all the time and the bulbs will be dim.

Student 3

Ammeter 2: 0.3 ampere

Ammeter 3: 0.3 ampere

Because all the current has been shared equally.

Student 4

Ammeter 2: 0.3 ampere

Ammeter 3: 0.3 ampere

I predicted these values because the current stays the same speed all the time.

Student 5

Ammeter 2: 0.3 ampere

Ammeter 3: 0.3 ampere

No explanation given.

Thinking about the teaching

Although four out of five students give correct predictions of the value of the current, the explanations do not inspire confidence! At least some student answers are off down the wrong tracks.

Students 1 and 2 refer to energy in their explanations, possibly getting mixed up with ideas of voltage. The way in which student 3 refers to the current being shared seems closer to an explanation for a parallel circuit. The answer given by student 4 is more encouraging, although it would be preferable to say the charged particles drift along at the same rate everywhere.

A diagnostic question about thin wire

The following question, about the idea of electrical resistance, was set to a group of students after their 11–14 teaching about electric circuits.

In circuit B there is a thin piece of wire. The thin wire forms part of the circuit.

1. Explain why the current is smaller in circuit B.
2. What will be the brightness of the bulb in circuit B?
3. Explain your answer.

Correct answers:

1. The current is smaller in circuit B because the thin wire introduces extra resistance and reduces the rate of flow of charge (the electric current) in all parts of the circuit.
2. The bulb will get dimmer.
3. The bulb will get dimmer because the current through it is reduced. Also, the potential difference of the supply is now shared between the wire and the bulb, so there is a smaller potential difference across the bulb. The brightness of the bulb is determined by the input power (P = I × V), and both current and potential difference have been reduced.

Some students' answers and implications

Student 1:

1. Because it has to go through the bulb then go through the wire and the wire slows the charges down.
2. It will go dim.
3. Because the energy is slower than normal so it is dim because the wire is slowing the charges down.

Student 2:

1. Because the power is taking more energy to get to the bulb to make it light.
2. It will go dim.
3. Because the energy has to get through a lot of wire to power the bulb and go through an ammeter to get to the bulb.

Student 3:

1. Because the wire is slowing the charge down in the circuit.
2. It will get dimmer.
3. It will be dimmer because there is less charges getting to it.

Student 4:

1. The current is smaller in circuit B because the charges slow down when they flow through the wire.
2. The brightness of the bulb will be normal.
3. The bulb is normal because if the wire would be in front of the bulb then you could change the brightness but because it is behind you cannot.

Student 5:

1. Because the longer the wire the greater the resistance.
2. It will glow very dimly.
3. Because there is not as much energy flowing through because it is the long piece of wire it has to travel through.

Thinking about the teaching

Student answers – right lines or wrong track? Once again, the good news is that four out of five students give a correct bulb brightness prediction, but as before the explanations aren't so convincing.

Student 1 correctly refers to the wire slowing the charges down but it makes much less sense to state, the energy is slower than normal. Student 2 seems to be arguing from a current going around the circuit components in sequence point of view rather than a simultaneous all-at-once point of view (as modelled by the rope loop). Student 3 gives a correct version of the charge story but there is no reference to potential difference. Student 4 is correct in stating that the charges slow down in circuit B, but is clearly wrong in predicting a normal bulb brightness. It is quite clear that student 4 is using the same kind of sequential reasoning as student 2. Student 5 correctly refers to resistance and is the only one to do so; less convincing is the reference to not as much energy flowing.

Diagnostic question about adding a cell

The following question, relating to the effect of increasing the number of cells in a circuit, was set to a group of students after their 11–14 teaching about electric circuits.

The bulb in circuit A is glowing normally.

How is the bulb in circuit B glowing?

1. It's dim.
2. It's glowing normally.
3. It's glowing brightly.
4. It's off.

Explain your answer.

Correct answer:

The bulb is bright.

Explanation:

With two cells there is a larger current everywhere in the circuit and a bigger potential difference is created across the bulb. The power output of the bulb (which depends on the potential difference and on the current) is therefore larger.

Students' answers and implications

Student 1:

c. Bright.

This is because instead of getting 100 % energy it is getting 200 % to make light up double more than normal.

Student 2:

c. Bright.

Because there is more energy and it only has to power one bulb so the bulb will be brighter than with one battery.

Student 3:

c. Bright.

There is more charges getting to it because there are charges coming out of each battery.

Student 4:

c. Bright.

The more batteries the more charges the more energy but more bulbs it would be dim or off.

Student 5:

c. Bright.

Because there are two batteries there is double the amount of energy flowing to the bulb.

Student answers – right lines or wrong track? All of the students make a correct prediction of bulb brightness.

Students 1, 2 and 5 all refer to there being more energy for the bulb. Students 3 and 4 suggest that there are more charges getting to it. This is correct in the sense that with two cells the charge moves round the circuit at a greater rate. It is clear, however, that student 3 is thinking in terms of the extra cell supplying more charges. This is not correct, unfortunately.

Material for thought

The students' answers to these three diagnostic questions are thought-provoking. In general terms the students are able to predict correctly what will happen physically in a circuit when changes are made, but they seem much less secure in providing correct explanations for those changes. Perhaps this is to be expected. Developing scientific explanations using concepts such as charge, current, energy and potential difference correctly is quite a challenge. With this in mind, it will do no harm, when returning to this topic, to get the rope loops out once again and to go back to basics in helping students to visualise and model the working of electric circuits.

Teacher: Circuits are loops containing charged particles, all (nearly simultaneously) set in a steady average motion as a result of the action of cells and resistances in each loop.

We now turn our attention to electric current in simple loops. The fundamental teaching and learning challenge addressed here is for students to come to recognise that the size of the current in a simple electrical loop depends on the potential difference across the cell and the resistance of any component in the loop.

The flow starts simultaneously everywhere in the loop

Wrong Track: When the switch is closed, the electric current flows out of the battery, then goes through the wires, then comes to the bulb and then flows back to the battery.

Right Lines: When the switch is closed, the charged particles are set in motion in all parts of the circuit, all at very nearly the same time.

All-at-once-motion

Thinking about the learning

An absolutely fundamental point in coming to understand electric circuits is that when a circuit is completed the electric charge starts flowing in all parts of the circuit: there is a current in every element. All charged particles start their gradual drifting movement at very nearly the same time.

The wrong track thinking illustrated here is based on the idea that the battery acts as the source of action for the circuit. This basic idea is, in fact, correct: the bulb will not light without a battery. The clear point to make here is that the battery is not the source of charge. The charge that makes up the electric current do not start off in the battery – it is present in all parts of the circuit (bulbs, and wires and cells).

Thinking about the teaching

It's all too easy for the teacher to unconsciously promote the battery–as–source–of–charge model by consistently pointing, with one finger, to the battery and saying,

Teacher: So the electric current flows from the battery… round the circuit…

or

Teacher: So the electric charge flows from the battery… round the circuit…

Such descriptions are to be avoided.

A more helpful approach is to portray the all–at–once motion of the current with two hands to demonstrate the simultaneous motion of charge in all parts of the circuit.

The rope loop model introduced in the SPT: Electric circuits topic provides a very striking representation of this all–at–once motion.

Markings on bulbs serve a practical purpose

Wrong Track: This is a 2 ampere bulb: it says so on the box. So if it is used in a circuit there must be a current of 2 ampere flowing around the circuit and through the bulb.

Right Lines: The 2 ampere on the box refers to the current in the bulb when it is being used at its normal operating potential difference. A 12 volt and 2 ampere filament bulb has a current of 2 ampere in the filament when used with a 12 volt supply so that there is a 12 volt drop across the bulb (wire the bulb directly across the supply).

Teaching and learning foci

Thinking about the learning

The key point for the student to get hold of here is that, so long as the current is not large enough to make the bulb fail, the bulb will allow any current to pass: the size of the current depends on the cell voltage. For example, if a 6 volt supply is used, the current through the bulb will be rather less than the 2 ampere expected for a 12 volt supply.

Thinking about the teaching

As students first start to make sense of electric circuits, their understanding might be thrown by the teacher referring to a 2 ampere bulb, which seems to contradict the message that the electric current is a dependent variable (it depends on the cell potential difference and component resistance). Careless talk can therefore be confusing. We would suggest addressing the matter head-on and having the conversation with your students, following the leading question:

Teacher: How can we make sense of a 2 ampere marking on a bulb?

Use two terms interchangeably

You might try using the term loop interchangeably with circuit.

Thus:

Teacher: Connect the components into a complete loop.

in addition to

Teacher: Connect the components into a complete circuit.

This helps to emphasise the simple, closed geometry of electric circuits. It also fits nicely with talking about the rope loop model for the electric circuit.

You might even explicitly move between discussing the mechanical loop (the rope loop) and the electrical loop (the circuit on the benchtop).

Teacher Tip: Consider renaming at least part of the entire topic electrical loops rather than electric circuits.

Link the phenomena to the theory

Electric circuits provide lots of learning challenges for students as they come to understand how these circuits work. Furthermore, all of the concepts that we use to describe and explain circuit behaviour are theoretical in nature: it's not possible, for example, to see an electric current, and to count how much charge passes, or how many charge particles pass, each second.

With this in mind, we strongly advise that your teaching takes the students explicitly back and forth between the reality of bulbs and wires and the world of theory.

For example, in returning to this work on electric circuits after quite a gap in time from dealing with electricity topics in 11–14 studies, make sure that you have the practical apparatus to hand as you talk through the ideas:

Teacher: So, here we have the power supply, a lamp and some connectors. We can set the power supply… there… to 12 volt… it's fixed. Connect up the bulb to the supply. There's nothing to adjust with the bulb… it's just a resistor. Switch on and the current here [teacher points] depends on the voltage and the bulb resistance. I can select a supply voltage or a different kind of bulb, but I can't directly select a current.

Ensure that the models you choose can be reasoned with

The rope loop teaching analogy was introduced in the SPT: Electric circuits topic (in the episode Developing an electric circuit model). We're clear that there is much to be gained from the systematic and consistent use of analogies, so we advise that if the rope loop has been used lower down the school, then you and your students should return to it now: rather like renewing acquaintance with an old and trusted friend.

An essential competence in the use of analogies is to be able to move fluently between the target (in this case the electric circuit) and the analogy (in this case the rope loop). If you and your students are revisiting the rope loop model after a break of some time, it's worth carefully talking through the mapping between the target and the analogy:

Teacher Tip: Target: electrical circuit  →  Analogy: rope loop. The cell  →  The person providing pull on rope. The potential difference  →  The size of the pull. The resistor  →  The person gripping the rope. The resistance  →  The slipping force applied by the person. The electric current  →  The rate at which the rope moves

This episode expects that children will come to understand the idea of potential difference rather well, and the mapping above shows that there is a reasonable chance of using this to develop the idea of potential difference (in fact the mathematics of the rope loop and of an electrical loop have identical patterns, which is one reason to believe that such a route is fruitful. ( Here a good place to start is P = F × v and P = V × I).

Here is a simple model of a loop in which you can vary the forces:

And here is a similar electrical loop, with similarly variable quantites. We hope you can see how well the source and target domains are matched, and so how well reasoning about the (tangible) rope can support predictions about the (somewhat less tangible) electrical loop.

(The choice of resistor is not implemented in these models, but it should not be too hard to see how to do so.)

Approaches which might not be so fuitful

We'd suggest that approaches based on hills are not so fuitful and might tilt the children's thinking back towards the idea that charges in circuits in some sense carry energy.

Similarly teaching ideas such as colouring circuits to identify potential differences may be heuristically helpful, but emphasising analogies between being uphill (gravitational potential) and electrical potential are not so fruitful until a rather richer understanding of potential is available, usually attepoted in post-16 studies).

Reasoning and representing

A fuitful question is to ask what you expect childeren to be able to do with the models or analogies that you develop. How far can they be developed?

Here is one (a rather exhaustive account) way in which you might develop the idea of potential difference through the rope loop and then apply it to reasoning about series circuits.

Equations need to make sense

Equations, such as I = VR, are very important tools in physics. They summarise relationships in a precise and economical way and allow us to carry out simple calculations. One problem for many students in school is that they learn how to substitute values into an equation but have little sense of the story of the equation – what the equation is actually telling us.

To get round this learning challenge, whenever you're using an equation, ask the students to talk through how the equation connects the variables:

Teacher: We choose the potential difference and the resistance, and that fixes the current. Can anyone remember how these three are connected?

Teacher: Good – now what happens to the current if the potential difference drops? And if the resistance grows very large… or very small?

Teacher Tip: Talk the calculation through, don't just write it down. I = VR, so the current is xx voltyy ohm, which works out as zz ampere to 2 significant figures.

Adding resistance – in two ways

As resistance is added, the total effective resistance may increase or decrease – it all depends on the number of loops.

Think about how to emphasise the difference between these two before you go on.

Adding a second identical bulb to a simple circuit, in series

Wrong Track: The second bulb will be brighter than the first because the current gets to it first after leaving the cell and so more energy will be shifted there.

Right Lines: The two bulbs will be of equal brightness because the current is the same through both of them and the cell potential difference is shared equally.

Teaching responses

Thinking about the learning

The key insight here is that, when the second bulb is added to the loop, the current is reduced (and the charged particles move more slowly) in all parts of the circuit. This reduced current is the same in both bulbs and an identical potential difference is set up across each, with the bulbs being of equal brightness.

Thinking about the teaching

We suggest two approaches: the rope loop; and illustrate with numbers.

The rope loop model is very effective in helping to talk and think through what happens when the second bulb is added:

Instead of one person gripping the rope we now have two.

With the same pull/push from the cell, the rope circulates more slowly due to the extra resistance.

The two people gripping the rope feel the same heating effect in their hands.

This heating effect felt by each person is less than when there was just one person gripping the rope.

Supposing the cell potential difference is 12 volt.

With one bulb, the full 12 volt potential difference is across the bulb: in other words, 12 joule of energy are shifted for each coulomb of charge passing.

With two bulbs, there is a 6 volt potential difference across each bulb: in other words, 6 joule of energy are shifted for each coulomb of charge passing.

From one to two loops – adding a second identical bulb in parallel

Wrong Track: When the second bulb is added, there is extra resistance, the current goes down and the bulbs are both dimmer.

Right Lines: The two bulbs will be of equal, normal brightness because there is the same current in each loop (the same as in the original loop) and the potential difference across each lamp is equal to the potential difference across the cell.

Teaching responses to this challenge

Thinking about the learning

The key insight here is that, when the second bulb is added in parallel to the existing loop, this second loop provides an additional pathway along which charge can be set in motion and the total current in the cell is doubled.

Thinking about the teaching

We suggest two approaches: the rope loop; and illustrate with numbers.

Instead of one rope loop, we now have two, each containing a cell and a bulb.

With the same pull/push from the cell the two rope loops circulate at the same rate as each loop has the same resistance.

Each person gripping each rope loop feels the same heating effect (rope circulating at same rate, with same slip force applied).

This heating effect felt by each person is the same as when there was just one person gripping the rope.

Suppose that the cell drives a current of 2 ampere in the original loop, containing a single bulb.

A second identical loop is added, again containing a single bulb.

The cell will drive a current of 2 ampere in this loop also.

The total current in the cell is now 4 ampere.

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

Try these

• Using and sharing an effective toolkit for thinking about circuits that allows you to make predictions
• Connecting thinking about your toolkit to choices made in assembling circuits on the benchtop
• interpreting equations as relationships between physical quantities
• giving a physical interpretation to equations
• using a range of representations to relate physical quantities (diagrams, words, mathematics, apparatus)

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

• encouraging the dash to the formula
• using triangles to rearrange equations
• relying on rote substitutions into formulae
• using an incoherent set of ad-hoc rules and metaphors, each of restricted validity

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.