Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• avoid cluttering up learners with inappropriate ideas
• avoid unhelpful experiences
• avoid drowning in a sea of algebra or arithmetic
• keeping ideas of power, energy, charge and current separate

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:

• avoid using the unhelpful term electrical energy
• introduce the idea of continuing (electrical) working whilst the loop is complete
• distinguish clearly between energy in stores (joule) and power in pathways (watt)
• consistently model series and parallel connections

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.

Whole electrical loops and energy stores

This episode takes us beyond ideas of charge and current by focusing on energy in simple electrical loops, with a special focus on the rate at which energy is shifted.

We extend the stores and pathways approach developed in the SPT: Energy topic as we know this provides a consistent framework for qualitative and semi-quantitative descriptions.

Existing approaches to teaching about energy typically involve lots of different kinds of energy: heat energy, electrical energy, light energy, sound energy and so on. This is rather different from the approach taken in the SPT: Energy topic, where energy is looked for in different kinds of stores: chemical stores, thermal stores, kinetic stores and so on. Here we think carefully about what is happening in simple electrical loops in terms of this approach to thinking about energy.

Electrical energy is an unhelpful phrase

Wrong Track: When the bulb is lit in the circuit, chemical energy from the cell is transferred to electrical energy in the wires, which is then transferred to heat and light energy in the bulb and surroundings.

Right Lines: When the bulb is lit in the circuit, energy is shifted from the chemical store associated with the cell to the thermal store of the surroundings.

How to be more helpful

Thinking about the learning

There are significant differences between these two ways of talking and thinking about simple electrical loops:

The right lines approach does not refer to different kinds of energy: chemical energy, electrical energy, heat and light energy. Here, energy is energy, and it's associated with different kinds of energy store.

The right lines approach has no place for electrical energy. Whereas energy can be stored in a cell (a chemical store of energy), it is difficult to see in what sense energy can be stored in the connecting wires of a circuit.

While the electrical circuit is clearly not a store of energy, it does provide the pathway along which energy is shifted by cell and bulb.

Taking the right lines approach, we therefore refer to electrical pathways but not to electrical stores.

Similarly, the right lines approach has no place for light energy. Light is taken to provide a pathway along which energy can be shifted but does not itself constitute an energy store. Taking the right lines approach, we therefore refer to light pathways but not to light stores.

Thinking about the teaching

We are clear that the right lines approach makes much more sense than the existing schemes, which refer to different kinds of energy including electrical energy and light energy. At the same time we recognise that changing to this approach involves the big challenge of changing familiar routines for both students and teachers.

The story of the circuit loop that we're moving towards is based on chemical and thermal stores and two linked pathways (electrical and heating), which operate simultaneously:

When the circuit loop is complete, a current circulates and the bulb glows.

When the bulb is glowing, energy is being shifted along an electrical pathway from the chemical store associated with the cell to the thermal store associated with the bulb (only whilst the bulb is first warming up) and to the thermal store associated with the surroundings. The circuit elements associated with the electrical pathway consist of the cell (providing a potential difference), connecting wires and bulb (offering resistance).

Electrical working occurs as charge passes through the resistance of the bulb, and energy is shifted with the chemical store being depleted and the thermal store associated with the bulb being filled.

The glowing bulb heats the surroundings through thermal conduction, convection and radiation.

The glowing bulb shifts energy to the surroundings along two pathways: heating by particles (through conduction and convection) and heating by radiation (both through emitted light and non-visible radiations).

Overall the energy level of the chemical store of the cell goes down as the energy level of the thermal store of the surroundings goes up. The power in the pathways into and out of the bulb is the same.

Revisiting the idea of remote working – it's nearly instantaneous

Wrong Track: Look! The bulb is a long way from the cell so it's obvious that it will take time for the energy to arrive and for the bulb to light. The current comes from the cell. It has to go through the cell to collect the energy and it will take time to get to the bulb.

Right Lines: No! When the circuit is completed the bulb lights immediately because the current is (almost) immediately the same in all parts of the circuit.

Avoiding unhelpful models

Thinking about the learning

The wrong track thinking shown here involves two common (mistaken) ideas:

• The current originates in the cell.
• The charges must collect energy from the cell before that energy can be shifted in the bulb.

Neither of these ideas is correct. The charge that constitutes the current is already present in all parts of the circuit and, as soon as the circuit is completed, the charged particles start flowing and energy is shifted by the bulb.

Thinking about the teaching

The teaching challenge here is to emphasise the immediate-all-at-once nature of the charge flow in an electric circuit. Without doubt this is best addressed with the rope loop analogy. In fact, if you think that your students might have lingering problems in this area, it would be worth going back to the big circuit and rope loop combination of activities first introduced in the SPT: Electric circuits topic.

Set up the big circuit in the lab and invite students to predict whether or not the bulb will light straight away when the circuit is completed. The bulb lights immediately. Now invite the students to use the rope loop analogy to explain why this is the case.

As one 13-year-old girl explained:

Jill: It's obvious! As soon as the battery starts the rope moving, the bulb heats up as the rope passes through. There's no delay because the rope all starts moving together.

Keeping the lived-in world and imagined world separate but connected

Drawing on the previous sections, we have seen that it's possible to develop an energy description of electric circuits at a number of different levels. For example, suppose we have a simple circuit loop consisting of a 12 volt supply and a bulb in which there is a current of 2 ampere (maybe a car headlamp bulb). It's possible to describe the loop in a number of different ways:

1. Physical description: the bulb is connected to the supply cell and lights up.
2. Shifting energy between stores: energy is shifted from the chemical store of the cell to the thermal store of the surroundings.
3. Shifting energy along pathways: energy is shifted from the chemical store of the cell to the thermal store of the surroundings, first along an electrical working pathway, then along the heating-by-particles and heating-by-radiation pathways.
4. Power and pathways: energy is shifted at the rate of 24 joule inverse second. There is a power of 24 watt in the electrical pathway and in the heating-by-particles and heating-by-radiation pathways.

A fundamental feature of any pathway is that it's possible to calculate the rate at which energy is shifted. This is the power in the pathway. In the case of the electrical pathway in this example, it's helpful for students to go back to first principles in thinking through the rate of shifting of energy along the pathway: this is the operating power of the pathway.

Teacher Tip: So: with the 12 volt cell, the potential difference across the bulb is 12 volt. This means that 12 joule of energy is shifted for each coulomb of charge passing through the resistance of the bulb. With a current of 2 ampere, 2 coulomb pass through the bulb each second.

Teacher Tip: So 24 joule of energy must be shifted each second by the bulb. 24 joule of energy is shifted each second, from cell to bulb, along the electrical working pathway, and 24 joule of energy is shifted each second from bulb to surroundings, along the heating pathways.

Reducing the power in the pathway: from one to two bulbs in series

Wrong Track: When the resistor is added in series, there is more resistance so energy will be shifted from the cell more quickly.

Right Lines: When the resistor is added in series, the extra resistance reduces the current and energy is shifted from the cell at a lower rate.

Using quantitative examples to help keep the thinking on track

Thinking about the teaching

This is the kind of question where using physical quantities (numbers and units) offers a direct way to sort out an answer. So, you might invent some figures along the following lines:

Teacher: Suppose we say that the cell is a 6 volt supply and that the resistor has a resistance of 12 ohm.

Teacher: We can then work out the current in the loop using I₁ = VR₁, in this case 6 volt12 ohm, so the current works out at 0.5 A.

Teacher: So, 6 joule for each coulomb, 0.5 coulomb arriving each second, this means that 3 joule of energy is shifted by the resistor each second.

Teacher: OK, what happens when we add a second resistor in series?

Teacher: The total resistance is now 24 ohm and 3 volt is the potential difference across each resistor.

Teacher: The current in the loop is 6 volt across 24 ohm, so 0.25 ampere. This makes sense, because doubling the resistance halves the current.

Teacher: So, 0.25 coulomb arriving each second and 3 joule shifted by each coulomb, this means that 0.75 joule of energy is shifted by each resistor every second.

Teacher: Alternatively we can say that, if each of the two bulbs is shifting energy at the rate of 0.75 joule inverse second, then the cell must be emptying at the rate of 1.5 joule inverse second.

Teacher: So, adding an equal resistor in series halves the rate at which the chemical store of the cell is depleted of energy.

The physical picture to leave the students with is one of the circulation of charge being reduced and therefore the rate of shifting energy being reduced. It's also worth emphasising that the rate of shifting energy at each resistor is reduced by a factor of 4 (from 3 joule inverse second to 0.75 joule inverse second) when the resistance of the loop is doubled since both the current through the resistor and the potential difference across the resistor are halved.

Increasing the power in a pathway – resistance is added in parallel to a simple circuit loop

Wrong Track: When the resistor is added in parallel, there is more resistance, so energy will be shifted from the cell more slowly.

Right Lines: When the resistor is added in parallel, an extra current loop is provided and energy is shifted from the cell at a greater rate.

Using quantitative examples to help keep the thinking on track

Thinking about the teaching

As with the previous challenge, using physical quantities offers a direct way to sort out an answer. So, you might invent some figures along the following lines:

Teacher: Suppose we say that the cell is a 6 volt supply and that the resistor has a resistance of 12 ohm.

Teacher: We can then work out the current in the loop using I = VR, in this case 6 volt12 ohm, so the current works out at 0.5 A.

Teacher: So, 6 joule for each coulomb, 0.5 coulomb arriving each second, this predicts that 3 joule of energy is shifted in the resistor each second

Teacher: OK, what happens when we add a second resistor in parallel?

Teacher: 6 volt is the potential difference across each resistor.

Teacher: Nothing has changed from the original circuit. The current through each resistor is:I = VR, in this case 6 volt12 ohm, so the current works out at 0.5 A.

As a result, 3 joule of energy is shifted in each resistor per second.

Teacher: Alternatively we can say that if each of the two bulbs is shifting energy at the rate of 3 joule inverse second, then the store associated with the cell must be emptying at the rate of 6 joule inverse second.

Teacher: So, adding an equal resistor in parallel doubles the rate at which the cell's store of energy is depleted.

The physical picture to leave the students with is one of there being a circulation of charge through each of the two parallel loops. The flow of charge through the cell is doubled and therefore the rate at which energy is shifted is increased.

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

Try these

• work with an awareness that the majority of experiences that most students have to guide their ideas are based on the classroom
• focus on power and not on energy
• distinguish clearly between energy in stores (joule) and power in pathways (watt)
• work in the present tense What's happening now whilst the circuit loop is complete
• use the circuit loop as a unit of explanation, prediction and analysis
• emphasise that (dissipative) electrical potential differences in a circuit depend on a complete 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

• electrical energy
• sequential analogies of the working of electric circuits
• ad-hoc algorithms for calculating and predicting
• conflating gravitational potential difference with electrical potential difference

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.