Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• keep ideas of power, energy, charge and current separate
• connect the calculations to everyday concerns
• emphasise differences between current and voltage measurements

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:

• use the idea of voltage, rather than getting stuck on explaining the idea
• be clear and consistent about your use of prepositions
• relate calculations back to physical changes in loops

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.

Everyday knowledge re-purposed, so start with familiar appliances

Thinking about the learning

Many pupils will have already come across the unit of power, the watt, outside school. This may have been buying light bulbs at the supermarket, choosing an amplifier for a music system, or switching to the correct power setting for a microwave oven when heating up a snack.

These everyday experiences are likely to fit in with the science idea that the power output of an electrical device is a measure of the amount of energy it shifts each second. There's more to measure in a circuit than electrical current.

For example, many pupils will be familiar with the fact that light bulbs come in all shapes and sizes and are sold according to their wattage.

Thus, their bed-side light may use a 40 watt bulb and provide a relatively subdued light (dissipating 40 joule of energy per second). In comparison, the main light in their room might use a 100 watt bulb and be much brighter in comparison (dissipating 100 joule of energy per second).

Making such links to familiar domestic appliances can help pupils to come to understand the usefulness of electrical power, and serve as a motivator for introducing the idea of voltage.

Thinking about the teaching

Start with familiar electrical appliances. To introduce the idea of electrical power, you might demonstrate various electrical appliances with different power outputs and explain that the amount of energy each device gives out per second is called its electrical power.

A desk lamp radiates 100 joule of energy per second.

A microwave oven shifts 850 joule of energy every second as it cooks food.

A kettle shifts 2500 joule of energy every second as it warms up water.

By making comparisons between the appliances, the important idea to get over is that, for example, the kettle shifts energy 25 times more quickly than the desk lamp (2500 to 100).

The important ideas to develop are:

• The energy store is being emptied 25 times more quickly with the kettle.
• The household electricity supply meter spins around 25 times more quickly.
• The costs accumulate 25 times more quickly.

Thank goodness it only takes a matter of minutes to boil a kettle!

Linking numbers to effects

It is a very useful exercise for pupils to investigate the power outputs of electrical appliances in and around the home. By collecting the figures and grouping them according to size, pupils can find out that appliances with the biggest power outputs are those which have some kind of heating function.

For example an electric fan heater might have a power output of 2000 watt or 2 kilowatt (2 kilowatt). The heater shifts 2000 J of energy per second.

Microwave ovens often have high and low power output settings:

Microwave low power 650 watt

Microwave high power 750 watt

The directions on the microwave food packet provide details for cooking times. For example, for a bolognese sauce:

• A microwave with a power output of 650 watt cooks the contents in 4.5 minutes
• A microwave with a power output of 750 watt cooks the contents in 3.5 minutes

Use sets of figures such as these to help pupils grasp the idea that high power electrical devices can shift a lot of energy in a shorter period of time:

Teacher: Just look at these figures on the packet. What can you say about the different cooking times compared with the high and low microwave power?

Janice: On higher power the cooking time is shorter.

Teacher: Exactly right! Why does that make sense?

Esme: Because on higher power you're putting more energy in.

Teacher: That's right. On higher power the microwave is shifting more joules of energy each second.

Making instructive connections, and finding out what you pay for

It is also interesting and instructive to talk about the relative costs involved in running different electrical appliances. The first thing to establish here is what it is that you are actually paying the electricity board for. The straight answer is dissipating energy.

For example, a two bar electric fire operates at 2 kilowatt and shifts:

2000 joule of energy each second

20,000 joule of energy every 10 second

200,000 joule of energy every 100 second

As soon as the fire is switched on, the electricity meter starts spinning around more quickly as the fire heats up the surroundings. The meter keeps a record of the total amount of energy shifted by all of the electrical appliances in the house.

It is instructive to make some direct comparisons between the costs of using different electrical appliances. It's not too difficult to bring these matters close to the pupils' own interests!

Teacher: I remember when I was a young lad (!), I used to play my hi-fi record player all of the time. My mother would get fed up with this, and when the electricity bill came would blame me for the size of the bill, saying, Look at this bill! No wonder we have to pay so much for electricity with you listening to that record player all the time. Now, my mother didn't know too much about science. Was she right about the electricity bill? Do you think I was really to blame? Has anybody here had a similar sort of experience?

The bill from your electricity company is not set out in terms of joules of energy shifted. As you can see from the example of the two bar electric fire, this would very quickly give rise to some rather big numbers!

Instead the unit of energy is taken as the kilowatt hour.

1 kilowatt hour is the amount of energy shifted when a

1 kilowatt device is left running for 1 hour.

The electricity companies refer to 1 kilowatt hour as a unit of energy, and charge you for the accumulated energy shifted, measuring your accumulation in these units. (The kilowatt hour (kW h) is a unit of energy, just like the joule.)

For example:

A 2 kilowatt electric fire left running for 3 hours shifts 6 kilowatt hour of energy (or 6 units of energy).

A 100 watt light bulb (0.1 kilowatt) left on for 60 hours shifts 6 kilowatt hour hours of energy (or 6 units of energy).

Introducing the kilowatt hour offers useful extension work for some pupils.

A puzzling quantity

Thinking about the learning

Thinking about voltage either in terms of size of push or in terms of a second factor (as well as the current) that sets the power switched by an element in a circuit (see Physics Narrative) is likely to make intuitive good sense to pupils at this stage in the teaching. Batteries of greater voltage provide a bigger push, which leads to more power dissipated in the circuits that they're a part of.

Thinking about the teaching

Why are voltage measurements important? What kind of information do they provide? What do voltage measurements tell us that is different from measurements of current?

These are important questions to be addressed in teaching. The short answer to all of them is that voltage measurements provide an energy picture of the electric circuit. Whilst current measurements tell us about the flow of charge (coulomb per second), voltage measurements provide information about power being dissipated by that charge (watt per ampere) in different parts of the circuit.

We do think that it's important not to try and go too far with younger children. Voltage is a hard idea.

We do think the use of the rope loop can help here. This is because pupils can act out what is happening in the circuit with the rope. As the rope passes through their hands, so their hands warm up, and this neatly models the shifting of energy to a thermal store by electrical working. The power dissipated is a function of two factors: the flow of the rope (current) and how hard you grip (voltage).

The more firmly the pupils grasp the rope, the warmer their hands become for each metre of rope that passes through their hands. The voltage is a similar signal, albeit electrical. It functions in a similar way to the firmness of the pupils' grasp: the larger the voltage, the more power for each ampere. (More precisely, the frictional force impeding the flow of rope is an exact analogue of the voltage.)

Because what pupils do with their hands enables them to predict where the energy will end up being shifted in the rope loop, we call this a teaching model. It's a model because it has a predictive power. The structure of this model is the same as the electric circuit model – that's why it's such a powerful heuristic tool.

Different treatments of the voltage/current and energy/power story

It is possible to introduce the idea of voltage at different levels of difficulty that can be used with pupils of different age and ability. Going into the idea in any detail is probably best done through thinking about power. This is the approach taken in the SPT: Electricity and energy topic.

At the phenomenological level, the battery voltage sets the power for each ampere. A larger battery results in brighter bulbs, because:

• There is more current in each bulb.
• There is more voltage across each bulb.

The accumulation of all this electrical working is that energy is shifted to and from stores.

The voltage compares the change of energy in different stores, predicting or measuring the comparative quantities of energy shifted by different parts of the circuit. But of course these changes accumulate over time – the longer the time for which the circuit runs, the greater the energy change. The power remains constant, so long as the circuit is functioning.

At a more advanced level, the battery voltage is taken as a measure of the number of joules of energy shifted for each passing coulomb of charge. The voltage across a bulb or some other circuit resistance is taken as a measure of the number of joules of energy shifted by each coulomb of charge as that much charge passes through that component.

Use terms interchangeably

As these new ideas about voltage are first introduced, it is helpful if sometimes you refer to volt and sometimes joule per coulomb, or volt and sometimes watt per ampere. By using the terms interchangeably in this way, the underlying meaning of voltage is continually made explicit:

Teacher: OK, so the reading on the voltmeter is 1.4 volt, it's 1.4 joule / coulomb.

Teacher: OK, so the reading on the voltmeter is 1.4 volt, it's 1.4 watt / ampere.

A story that can be varied

You might use a variation on this story:

My next door neighbour is a man called Don. Don can get a bit impatient with things at times. A couple of weeks ago he was vacuum cleaning the carpet in the front room. He switched on the vacuum cleaner and it worked OK for a minute or so but then stopped. Don bent down to see what was the matter and the vacuum cleaner just started up again.

Don resumed with his job, but just as quickly the vacuum cleaner stopped again. After this had happened no fewer than four times, stopping and starting, the cleaner seemed to die altogether. Don was getting mightily irritated by all of this and decided that there must be a bad connection in the plug. He spotted a pair of scissors lying on the chair, picked them up and cut off the plug. Unfortunately for Don, this was at the very moment when the vacuum cleaner started up again. There was a huge bang and a flash.

Now Don isn't small by any means. He probably weighs over 15 stone. Even so he was lifted off his feet as the scissors cut through the live cable. He was lucky to be thrown free because he showed me the blades of the scissors afterwards and they were melted into a crazy shape.

The mains supply provides 240 volt, or 240 joule of energy per coulomb of charge. If you have lots of coulombs of charge arriving in a big current with this amount of energy, the effect can be exceptionally dangerous. Just ask Don!

Emphasising the differences between current and voltage measurements

Thinking about the learning

Introducing the idea of voltage and voltage measurement with a voltmeter can create confusions for pupils who tend to mix them up with existing ideas about electric current. The fact that ammeters and voltmeters look just the same can add to this confusion.

Teacher Tip: Emphasise the different functions that voltage and current fulfil in the electric circuit model.

Thinking about the teaching

It is a good idea to explicitly refer to the two stories which can be drawn upon in thinking and talking about electric circuits. These two stories are:

• The charge/electric current story.
• The power/voltage story.

Referring to the two sets of ideas in this way can help pupils to see the difference between them.

Insist… and gain

Insist at all times on describing:

Teacher: current in Something

Teacher: voltage across Something

It just does not make sense to talk about the current across the bulb or the voltage through the bulb.

If pupils get these the wrong way around, the chances are that they do not understand the underlying ideas.

Teacher Tip: There's value in being careful and consistent about describing things we cannot see – it's a real aid to the pupils as they try to imagine the world of currents and voltages.

Insist… and gain

Teacher Tip: The word voltage is more approachable than the phrase potential difference so is probably enough for 11–14 year old children. A more sophisticated development that justifies the term potential difference is probably not appropriate for a class of 11–14 year-olds. Voltage drops and gains, later referred to as potential drops and rises, by analogy with gravitational potential difference, might also best be excised from the classroom for now. Indeed, the whole idea of potential difference is one that is hard for post-16 students. We'd suggest leaving the hills analogy to then. There may be a case for introducing it subtly in 14–16 teaching. But you should beware of the difficulties, as the electrical hills are only there when there is a loop with current in the circuit elements. It's not much like a circular route in the fells, where the hills are there, whether or not there is a flow of walkers along the path. You always need to take care not to lead pupils off along the wrong tracks by injecting a half-developed analogy.

Teacher Tip: Relating voltage to power, as what is happening now in the circuit, may be a more profitable approach. Introduce it as the second factor that determines the brightness of a bulb: you'll need to specify both the voltage and the current.

Sum of component voltages is equal to the battery voltage

Thinking about the learning

Pupils will be familiar with the idea that when a second identical bulb is added in series to a circuit the two bulbs become equally dim. In episode 02, the point was made that the current in both bulbs was identical. The power dissipated in each bulb is also identical (you can see that – they're equally bright). We now have a way of accounting for this by noticing that the voltage supplied by the battery is shared between the two bulbs – equally if the bulbs are identical.

Thinking about the teaching

Having introduced voltage as a measure of power in the circuit and emphasised the point that energy must be conserved:

Teacher: So, the battery is rated at 6 volt. What does this tell us?

Wyn: The amount of energy it can supply.

Teacher: That's nearly right. It supplies 6 joule of energy every second (a power of 6 watt) for while there is a current of one ampere in the battery. You need to know both the current and the voltage to find the power.

Now it should not be too big a step to establish that the sum of the bulb voltages (when connected in series) is the battery voltage.

The simplest approach is for pupils to make their own predictions and measurements of voltage values, starting with simple battery/bulb circuits and moving on to circuits with extra bulbs in series. Pupils will be able to reason with a rope loop in order to be able to make semi-quantitative predictions, which should be enough here.

Voltages across equal and unequal resistances

Thinking about the learning

The idea to get over here is that if two resistors are connected in series to a battery, the greater share of the battery voltage is dropped across the bigger resistance. A full understanding of the circuit involves recognising that:

• The sum of the voltage drops across the two resistors must equal the battery voltage.
• More volts are dropped across the bigger resistance.
• The current is the same through both resistances.

Thinking about the teaching

This is an interesting problem, which might be set as a practical extension exercise for some pupils. Encourage active modelling of the situation, with two pupils gripping the rope to model the two resistors.

Here is a place where the loop model really does come into its own. It's very simple to model series connections. Simply grasp the rope with two hands rather than one to model two resistors instead of one. If you grasp equally firmly with both hands, you'd expect both hands to warm equally – what else could they do? It wouldn't even matter if you reversed the direction in which the rope was pulled.

It's also easy to model unequal resistances: simply grasp the rope more firmly with one hand than with the other. One hand will warm more quickly than the other. This predicts exactly what will happen in the electrical loop: the larger resistance will warm more than the smaller resistance.

The current in both resistors will be identical, just as the flow of rope through both hands is identical. It is the case that the larger resistor has a larger voltage across it, and this is the reason why it gets warmer. Similarly, the hand which grasps the rope more firmly shifts energy to the thermal store at a greater rate.

The power is largest where the current is largest and the voltage is largest.

The closer bulb gets more

Wrong Track: The bulb closer to the battery will get more from the battery as it's closer.

Right Lines: These are two separate loops, and the battery pushes charged particles through each of them quite separately. That's why each bulb glows just like it does in the simple circuit, with one bulb and one battery.

Each bulb gets the full battery voltage

Thinking about the learning

Pupils will be familiar with the idea that when a second bulb is added in parallel to a circuit, the two bulbs become equally, normally bright.

Adding a bulb in parallel sets up a second current loop in which charged particles are set in motion. The power dissipated by both bulbs is equal to the power dissipated by one bulb. As a result of the accumulation of this action, the energy shifted from the chemical store will turn up in another store when that same quantity of charge is passed through the bulb or resistor in the circuit.

This idea can be formalised by stating that the full battery voltage is dropped across each of the two bulbs. We think that dealing with each loop separately makes this more acceptable.

Thinking about the teaching

You might start by revising the physics:

Teacher: OK, so the battery is 3 volt. So it's working at 3 watt so long as there is a current of 1 ampere in it. How many watt in the bulb in this loop with the blue wire?

Dylan: 3 watt?

Teacher: Yes that's right! Each bulb is equally bright – 3 watt of power. The energy shifted each second so long as there is 1 ampere in the bulb is 3 joule, so the voltage across the bulb in the blue loop is 3 volt. What about the bulb in the loop with the green wires?

Kay: It's the same! 3 volt.

Teacher: Exactly! 3 joule of energy are shifted a second, so long as there is 1 ampere in the bulb.

It's important that pupils are able to visualise the double flow of charge through the battery, with each loop contributing the same as if it were in a simple circuit.

Two rope loops of different colours and of different lengths can be used to great effect here. Use each loop independently to model the effects of a single resistor in each loop. Alter the resistances by how firmly you grasp the rope, so altering the slip force. Then combine the two independent loops to find the resultant current in the battery – depending on the choices that you've made for each loop.

Power is determined by current and voltage

Thinking about the learning

The idea of electrical power brings together the moving charge (current) part of the electric circuit story along with the energy shifted (voltage) part. As such, pupils often find this a satisfying step to make as they draw on their knowledge of current and voltage and see how this leads to an understanding of electrical power.

Thinking about the teaching

For those pupils who are able to follow the line of argument, we would recommend, following through the working from first principles approach, which is set out in the Physics narrative(from current and voltage to power.

Start with the definitions of current as coulomb per second and voltage as joule per coulomb and move from these to power in terms of joule per second. Such an approach is made easier in the classroom by referring to a particular circuit (as we did in the narrative) and working with specific figures for current and voltage (for example: 2 ampere and 12 volt). Having developed the idea of power for a specific case, you can then introduce the general definition.

All too often, pupils know that power can be calculated by multiplying together current and voltage, but have little understanding either of why this should be the case or what the electrical power actually means in practice.

Maximum power

Wrong Track: If a car headlamp bulb has a power rating of 24 watt, this means that it always gives out 24 joule of heat and light energy each second.

Right Lines: If a car headlamp bulb has a power rating of 24 watt, this means that it is designed to shift 24 joule of energy per second at its normal operating voltage of 12 volt. However, if the voltage is reduced (say to 6 volt) then the power output will fall below 24 watt and the bulb will be dimmer than normal.

A range of power outputs

Thinking about the learning

So an electrical device such as a light bulb can have a full range of power outputs depending on the operating conditions. If the supply voltage falls, then so too will the current and the power output of the bulb will be reduced.

Household light bulbs are rated and sold in terms of their power output, but you need to bear in mind that figures of 100 watt or 60 watt apply for the normal 240 volt supply.

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

Try these

• relating the brightness of lamps to what's happening to the current and voltage in each loop
• using semi-quantitative reasoning and physical models, such as the rope loop

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

• diving straight into the sums to be done
• using ad-hoc rules to generate the sums to be done

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.