Category Archives: Electricity

Teaching Electric Circuits? Climb On Board The Coulomb Train!

I’ve said it before and I’ll say it again: teaching electric circuits is hard.

Providing your students with a conceptual model can, in my opinion, be immensely helpful. In recent years, I have used what I call the Coulomb Train Model (CTM). It is essentially a variation on the “stiff chain” analogies that some researchers have argued as being particularly useful in developing students’ understanding.

One reason why I like the CTM is that it provides a physical picture to aid students’ comprehension of many of the electrical equations needed at GCSE.

Of course, any analogy or model will have its flaws, but on the whole I think the CTM has fewer than many of its rivals!

Essentially, the CTM pictures an electric circuit as a continuously moving chain of postively-charged “trucks” called coulombs that carry energy from the cell to (say) the bulb. In the diagram below, they should be pictured as moving clockwise.

The coulomb is, of course, the S.I. unit of electric charge, so rest assured that there is method in the apparent madness of naming our “trucks” with a word that would be unfamiliar to most of our students.

Charge flow = current x time

Charge flow = number of coulombs that pass a given point in time.

Current = number of coulombs that pass by in one second (i.e. current = charge flow / time).

In other words, an ammeter counts the coulombs passing by in one second. The ammeter only “sees” the coulombs and does not register how much (or how little) energy each one contains. Therefore current I1 and current I2 are equal.

The ammeters are shown as being semi-transparent in order to provide a visual cue that they are low resistance devices.

Energy transferred = charge flow x potential difference

On the CTM, potential difference can be pictured as energy being added to, or removed from, each coulomb.

For example, if one joule is removed from each coulomb as they pass through the bulb, the potential difference across the bulb is one volt. If one joule is added to each coulomb as they pass through the cell, then the potential difference (or e.m.f.) across the cell is one volt.

The total energy transferred from (say) ten coulombs passing through the bulb would be charge flow (10 coulombs) x potential difference (1 volt) = 10 joules.

The white gloves on the voltmeter are intended to be reminiscent of the white gloves of a snooker referee.

The intention is to disrupt the flow of the coulombs as little as possible and so this is a visual reminder that a voltmeter is a high resistance instrument.

To emphasise the fact that potential difference is an “energy difference”, challenge students to predict the reading on this voltmeter.

The potential difference V3 is, of course, zero since there is no transfer of energy to or from the coulombs.

Current in Series and Parallel Circuits

I think the CTM can be really effective in allowing students to a see a comprehensible physical analogue of the circuits.

For example, I3 = I4 = I5 = 0.5 amps; I6 = I11 = 2 amps; and I7 = I8 = I9 = I10 = 1 amp.

Potential difference in series and parallel circuit

Equally, I think the CTM can give a comprehensible physical picture of the situation.

In this case (assuming the the cell has a p.d. of 1 V and the bulbs are identical), V4 = V5 = 0.5 V.

In the parallel circuit, each bulb tranfers one joule of energy from each bulb, and so the potential difference across each bulb is one volt.

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Filed under Coulomb Train Model, CTM, Education, Electricity, physics

Electrifying Engelmann

It is a long-standing and melancholy truth that, despite the best efforts of many legions of Physics teachers, many students continue to not only dislike electricity, but to hate it with the white-hot intensity of a million suns.

What we have here, I think, is a classic failure to communicate.

A final fact is that samenesses and differences of examples are more obvious when the examples are juxtaposed. This fact implies that the continuous conversion of examples provides the clearest presentation of samenesses and, differences because it creates the changes that occur from one example to the next.

— Siegfried Engelmann and Douglas Carmine, Theory of Instruction (1982) p.46

Looking at my own teaching, I certainly attempt to juxtapose a number of circuits. I really want to highlight the similarities and differences between circuits in order to better develop my students’ understanding. But the problem is that both limited resources and other practical considerations mean that the juxtapositioning cannot happen by continuous conversion, except very rarely.

For example, I would set up (or ask students to set up) a circuit with a single bulb with an ammeter, then I (or we) would disassemble the circuit and rebuild it with the ammeter in a different position, or a second bulb added in series or in parallel . . .

It occurs to me that what we are relying on to thread these juxtapositions together in students’ minds is a sequence of circuit diagrams. I suppose it’s another case of the curse of knowledge writ large: experts and novices think differently.

As a beginning teacher, I remember being genuinely shocked that many students found it easier to interpret a photograph or a 3D drawing rather than the nice, clutter-free, minimalist lines of a circuit diagram.

Without a doubt, many students retain strong visual impressions of many of the circuit diagrams they encounter, but they do not parse and decode the diagrams in the same way as their teachers do.

And that, I think, is the major problem when we are introducing electric circuits.

But what to do?

— R. S. Thomas, The Cure

Can we introduce the important aspects of electrical circuits by continuous conversion of examples?

I think we can. And what is more, I think it will be more effective than the itty-bitty assembly and disassembly of circuits that I have practiced to date.

Conservation of electrical current (and current in parallel circuits) by continuous conversion

Parallel Circuit

This is introduced with a teacher demonstration of the above circuit. Students are invited to note the identical readings on both ammeters and asked to explain why they are identical. They are then asked to predict the effect of adding a second bulb in parallel. The teacher then adds the second bulb by connecting the flying lead. The process is repeated with the third and fourth bulbs, with the teacher testing students’ understanding by asking them to predict the change in current readings as bulbs are added and removed. The teacher also tests students’ understanding of the conservation of current by asking students to predict whether the reading on both ammeters will be the same or different as bulbs are added and removed.

I find it useful to include a bulb that is not identical to the other three. It should be noticeably brighter or dimmer than the other three with the same p.d. so that students do not make the incorrect inference that the current always increases or decreases in equal steps when the circuit is changed.

The teacher could also draw the original circuit on a student whiteboard and ask students to do likewise. The changes that are about to be made could be described and students could be asked could alter the picture/circuit diagram and write their prediction on their whiteboards. They could then compare their version with the teacher’s and their prediction could be quickly tested by making the proposed changes “live” in front of the students.

If resources and time permit, students could then, of course, go on to construct their own parallel circuits as a class practical. However, I think it is important that these vital, foundational ideas are introduced (or re-introduced!) via a teacher demonstration to avoid possible cognitive overload for students.

Series circuits by continuous conversion

Series Circuit

In this demonstration circuit, four of the three bulbs are short-circuited so that they are initially unlit. The teacher asks students to explain only one bulb in the circuit is lit: it is helpful if they have previously encountered parallel circuits and can explain this in terms of electrical current taking the “easier” route (assuming they have not yet encountered the concept of electrical resistance).

Again, the two ammeters allow the teacher to emphasise and test students understanding of the idea that current is conserved.

The teacher then asks students to predict the change in current reading when switch X is opened: will it increase or decrease? Why would it increase or decrease? The process is repeated with switches Y and Z and students’ understanding is tested by asking them to predict the effect on the current reading of opening or closing X, Y or Z.

As before, the teacher would amend her circuit diagram on her student whiteboard and students would do likewise. For example: “I am going to open switch Y. Change the circuit diagram. Show me. What will happen to the reading on the left hand ammeter? What will happen to the reading on the right hand ammeter? Explain why.”

Again, I recommend that at least one out of the four bulbs in not identical to the other three to help prevent students from drawing the incorrect inference that the current will always increase or decrease in identical steps.

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Filed under Direct Instruction, Education, Electricity, Physics, Siegfried Engelmann