The ‘all-in-a-row’ circuit diagram convention for series and parallel circuits

Circuit diagrams can be seen either as pictures or abstractions but it is clear that pupils often find it hard to recognise the circuits in the practical situation of real equipment. Moreover, Caillot found that students retain from their work with diagrams strong images rather than the principles they are intended to establish. The topological arrangement of a diagram or a drawing presents problems for pupils which are easily overlooked. It seems that pupils’ spatial abilities affect their use of circuit diagrams: they sometimes do not regard as identical several circuits, which, though identical, have been rotated so as to have a different spatial arrangement. […] Niedderer found that pupils, when asked whether a circuit diagram would ‘work’ in practice, more often judged symmetrical diagrams to be functioning than non-symmetric ones.

Driver et al. (1994): 124 [Emphases added]

For the reasons outlined by Driver and others above, I think it’s a good idea to vary the way that we present circuit diagrams to students when teaching electric circuits. If students always see circuit diagrams presented so that (say) the cell is at the ‘top’ and ‘facing’ a certain way; or that they are drawn so that they are symmetrical (which is an aesthetic rather that a scientific choice), then they may well incorrectly infer that these and other ‘accidental’ features of our circuit diagrams are the essential aspects that they should pay the most attention to.

One ‘shake it up’ strategy is to redraw a circuit diagram using the ‘all-in-a-row’ convention.

If you arrange the real components in the ‘all-in-a-row’ arrangement, then a standard digital voltmeter has, what is in my opinion a regrettably underused functionality, that will show:

  • ‘positive’ potential differences: that is to say, the energy added to the coulombs as they pass through a cell or the electromotive force; and
  • ‘negative’ potential differences: that is to say, the energy removed from each coulomb as they pass through a resistor; these can be usefully referred to as ‘potential drops’

This can be shown on circuit diagrams as shown below/

In other words, the difference between the potential difference across the cell (energy being transferred into the circuit from the chemical energy store of the cell) is explicitly distinguished from the potential difference across the resistor (energy being transferred from the resistor into the thermal energy store of the surroundings). The all-in-a-row convention neatly sidesteps a common misconception that the potential difference across a cell is equal to the potential difference across a resistor: they are not. While they may be numerically equal, they are different in sign, as a consequence of Kirchoff’s Second Law. As I have suggested before, I think that this misconception is due to the ‘hidden rotation‘ built into standard circuit diagrams.

Potential divider circuits and the all-in-a-row convention

Although I am normally a strong proponent of the ‘parallel first heresy‘, I’ll go with the flow of ‘series circuit first’ in this post.

Diagrams 2 and 3 in the sequence show that the energy supplied to the coulombs (+1.5 V or 1.5 joules per coulomb) by the cell is transferred from the coulombs as they pass through the double resistor combination. Assuming that R1 = R2 then, as diagram 4 shows, 0.75 joules will be transferred out of each coulomb as they pass through R1; as diagram 5 shows, 0.75 joules will be transferred out of each coulomb as they pass through R2.

Parallel circuits and the all-in-a-row convention

I’ve written about using the all-in-a-row convention to help explain current flow in parallel circuits here, so I will focus on understanding potential difference in parallel circuit in this post.

Again, diagrams 2 and 3 in the sequence show that the positive 3.0 V potential difference supplied by the cell is numerically equal (but opposite in sign) to the negative 3.0 V potential drop across the double resistor combination. It is worth bearing in mind that each coulomb passing through the cell gains 3.0 joules of energy from the chemical energy store of the cell. Diagrams 4 and 5 show that each coulomb passing through either R1 or R1 loses its entire 3.0 joules of energy as it passes through that resistor. The all-in-a-row convention is useful, I think, for showing that each coulomb passes through just one resistor as it makes a single journey around the circuit.

Acknowledgements

Circuit simulations from the excellent https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html

Circuit diagrams drawn using https://www.circuit-diagram.org/editor/

Reference

Driver, R., Squires, A., Rushworth, P., & Wood-Robinson, V. (1994). Making sense of secondary science: Research into children’s ideas. Routledge.

Electromagnetic induction — using the LEFT hand rule…?

They do observe I grow to infinite purchase,
The left hand way;

John Webster, The Duchess of Malfi

Electromagnetic induction — the fact that moving a conductor inside a magnetic field in a certain direction will generate (or induce) a potential difference across its ends — is one of those rare-in-everyday-life phenomena that students very likely will never have come across before. In their experience, potential differences have heretofore been produced by chemical cells or by power supply units that have to be plugged into the mains supply. Because of this, many of them struggle to integrate electromagnetic induction (EMI) into their physical schema. It just seems such a random, free floating and unconnected fact.

What follows is a suggested teaching sequence that can help GCSE-level students accept the physical reality of EMI without outraging their physical intuition or appealing to a sketchily-explained idea of ‘cutting the field lines’.

‘Look, Ma! No electrical cell!’

I think it is immensely helpful for students to see a real example of EMI in the school laboratory, using something like the arrangement shown below.

A length of copper wire used to cut the magnetic field between two Magnadur magnets on a yoke will induce (generate) a small potential difference of about 5 millivolts. What is particularly noteworthy about doing this as a class experiment is how many students ask ‘How can there be a potential difference without a cell or a power supply?’

The point of this experiment is that in this instance the student is the power supply: the faster they plunge the wire between the magnets then the larger the potential difference that will be induced. Their kinetic energy store is being used to generate electrical power instead of the more usual chemical energy store of a cell.

But how to explain this to students?

A common option at this point is to start talking about the conductor cutting magnetic field lines: this is hugely valuable, but I recommend holding fire on this picture for now — at least for novice learners.

What I suggest is that we explain EMI in terms of a topic that students will have recently covered: the motor effect.

This has two big ‘wins’:

  • It gives a further opportunity for students to practice and apply their knowledge of the motor effect.
  • Students get the chance to explain an initially unknown phenomenon (EMI) in terms of better understood phenomenon (motor effect). The motor effect will hopefully act as the footing (to use a term from the construction industry) for their future understanding of EMI.

Explaining EMI using the motor effect

The copper conductor contains many free conduction electrons. When the conductor is moved sharply downwards, the electrons are carried downwards as well. In effect, the downward moving conductor can be thought of as a flow of charge; or, more to the point, as an electrical current. However, since electrons are negatively charged, this downward flow of negative charge is equivalent to an upward flow of positive charge. That is to say, the conventional current direction on this diagram is upwards.

Applying Fleming Left Hand Rule (FLHR) to this instance, we find that each electron experiences a small force tugging it to the left — but only while the conductor is being moved downwards.

This results in the left hand side of the conductor becoming negatively charged and the right hand side becoming positively charged: in short, a potential difference builds up across the conductor. This potential difference only happens when the conductor is moving through the magnetic field in such a way that the electrons are tugged towards one end of the conductor. (There is, of course, the Hall Effect in some other instances, but we won’t go into that here.)

As soon as the conductor stops moving, the potential difference is no longer induced as there is no ‘charge flow’ through the magnetic field and, hence, no current and no FLHR motor effect force acting on the electrons.

Faraday’s model of electromagnetic induction

Michael Faraday (1791-1867) discovered the phenomenon of electromagnetic induction in 1831 and explained it using the idea of a conductor cutting magnetic field lines. This is an immensely valuable model which not only explains EMI but can also generate quantitative predictions and, yes, it should definitely be taught to students — but perhaps the approach outlined above is better to introduce EMI to students.

The left hand rule not knowing what the right hand rule is doing . . .

We usually apply Fleming’s Right Hand Rule (FRHW) to cases of EMI, Can we replace its use with FLHR? Perhaps, if you wanted to. However, FRHR is a more direct and straightforward shortcut to predicting the direction of conventional current in this type of situation.

Explaining current flow in conductors (part two)

Do we delve deeply enough into the actual physical mechanism of current flow through electrical conductors using the concepts of charge carriers and electric fields in our treatments for GCSE and A-level Physics? I must reluctantly admit that I am increasingly of the opinion that the answer is no.

In part one we discussed two common misconceptions about the physical mechanism of current flow, namely:

  1. The all-the-electrons-in-a-conductor-repel-each-other misconception; and
  2. The electric-field-of-the-battery-makes-all-the-charge-carriers-in-the-circuit-move misconception.

What, then, does produce the internal electric field that drives charge carriers through a conductor?

Let’s begin by looking at the properties that such a field should have.

Current and electric field in an ohmic conductor

(You can see a more rigorous derivation of this result in Duffin 1980: 161.)

We can see that if we consider an ohmic conductor then for a current flow of uniform current density J we need a uniform electric field E acting in the same direction as J.

What produces the electric field inside a current-carrying conductor?

The electric field that drives charge carriers through a conductor is produced by a gradient of surface charge on the outside of the conductor.

Rings of equal charge density (and the same sign) contribute zero electric field at a location midway between the two rings, whereas rings of unequal charge density (or different sign) contribute a non-zero field at that location.

Sherwood and Chabay (1999): 9

These rings of surface charge produce not only an internal field Enet as shown, but also external fields than can, under the right circumstances, be detected.

Relationship between surface charge densities and the internal electric field

Picture a large capacity parallel plate capacitor discharging through a length of high resistance wire of uniform cross section so that the capacitor takes a long time to discharge. We will consider a significant period of time (a small fraction of RC) when the circuit is in a quasi-steady state with a current density of constant magnitude J. Since E = J / σ then the internal electric field Enet produced by the rings of surface charge must be as shown below.

Schematic diagram showing the relationship between the surface charge density and the internal electric field

In essence, the electric field of the battery polarises the conducting material of the circuit producing a non-uniform arrangement of surface charges. The pattern of surface charges produces an electric field of constant magnitude Enet which drives a current density of constant magnitude J through the circuit.

As Duffin (1980: 167) puts it:

Granted that the currents flowing in wires containing no electromotances [EMFs] are produced by electric fields due to charges, how is it that such a field can follow the tortuous meanderings of typical networks? […] Figure 6.19 shows diagrammatically (1) how a charge density which decreases slowly along the surface of a wire produces an internal E-field along the wire and (2) how a slight excess charge on one side can bend the field into the new direction. Rosser (1970) has shown that no more than an odd electron is needed to bend E around a ninety degree corner in a typical wire.

Rosser suggests that for a current of one amp flowing in a copper wire of cross sectional area of one square millimetre the required charge distribution for a 90 degree turn is 6 x 10-3 positive ions per cm3 which they call a “minute charge distribution”.

Observing the internal and external electric fields of a current carrying conductor

Jefimenko (1962) commented that at the time

no generally known methods for demonstrating the structure of the electric field of the current-carrying conductors appear to exist, and the diagrams of these fields can usually be found only in the highly specialized literature. This […] frequently causes the student to remain virtually ignorant of the structure and properties of the electric field inside and, especially, outside the current-carrying conductors of even the simplest geometry.

Jefimenko developed a technique involving transparent conductive ink on glass plates and grass seeds (similar to the classic linear Nuffield A-level Physics electrostatic practical!) to show the internal and external electric field lines associated with current-carrying conductors. Dry grass seeds “line up” with electric field lines in a manner analogous to iron filings and magnetic field lines.

Photograph from Jefimenko (1962: 20). Annotations added

Next post

In part 3, we will analyse the transient processes by which these surface charge distributions are set up.

References

Duffin, W. J. (1980). Electricity and magnetism (3rd ed.). McGraw Hill Book Co.

Jefimenko, O. (1962). Demonstration of the electric fields of current-carrying conductorsAmerican Journal of Physics30(1), 19-21.

Rosser, W. G. V. (1970). Magnitudes of surface charge distributions associated with electric current flow. American Journal of Physics38(2), 265-266.

Sherwood, B. A., & Chabay, R. W. (1999). A unified treatment of electrostatics and circuits. URL http://cil. andrew. cmu. edu/emi. (Note: this article is dated as 2009 on Google Scholar but the text is internally dated as 1999)

Speed of sound using Phyphox

You can get encouragingly accurate values for the speed of sound in the school laboratory using a tape measure and two smartphones (or tablets) running the Phyphox app.

Phyphox (pronounced FEE-fox) is an award-winning free app that was developed by physicists at Aachen University who wanted to give users direct access to the many sensors (e.g. accelerometers and magnetometers) which are standard features on many smartphones. In effect, it turns even the humblest smartphone or tablet into a multifunctional measuring instrument comparable to one of Star Trek’s famous ‘tricorders’.

Star Trek Tricorder (not Phyphox)

To measure the speed of sound, we need two smartphones or tablets running Phyphox. We will be using the ‘Acoustic Stopwatch’ which measures the time between two acoustic events.

Phyphox main screen

Step 1: Place two devices a measured distance s apart. Typically about 2 or 3 m should be OK otherwise the sound made by A will not be loud enough to control stopwatch B — this can be established through trial and error and depends on many factors including the background noise level.

Step 2: Person A makes a loud sound (a clap or a single syllable shout like ‘Hey!’ is good).

Step 3: Person B and stopwatch B wait for sound created by A to reach them.
Step 4: The sound reaches stopwatch B and starts it running and B hears the sound.

Step 5: B makes a loud sound in response.

Step 6: The loud sound made by B reaches stopwatch B and makes it stop. Let’s call the time displayed tB. This measures the delay between the sound from A reaching stopwatch B and B reacting to the sound and stopping the clock. It includes the time taken for the initial sound travelling from the device to B, B’s reaction time, and the time taken for the sound made by B to travel to stopwatch B. B does not have to be particularly ‘quick off the mark’ to respond to A’s sound — although the shorter the time then the less likely it is then a background noise will interrupt the experiment.

Step 7: The sound made by B travels toward stopwatch A.

Step 8: The sound made by B reaches stopwatch A and makes it stop. Let’s call the time recorded on stopwatch A tA.

If we break down the events included in tA and tB, we find that tA is always larger than tB:

If we subtract tAtB we find that this is the time it takes sound to travel a distance of 2s.

Step 9: We can therefore use this formula to find the v the speed of sound.

We have found that this method works well giving mean values of about 350 m/s for the speed of sound (which will vary with air temperature). This video models the method.

And so we have a reasonably practicable method of measuring the speed of that doesn’t involve complex equipment that is unfamiliar to most students; or a method that involves finding a large and featureless wall that produces a detectable echo when a loud sound is made from a point several metres in front of it.

I don’t know about you, but as a physics teacher, I feel cheated. If it doesn’t involve a double beam oscilloscope, a signal generator, two microphones and two power amplifiers then I simply don’t want to know about it . . .

The Rite of AshkEnte, quite simply, summons and binds Death.  Students of the occult will be aware that it can be performed with a simple incantation, three small bits of wood and 4cc of mouse blood, but no wizard worth his pointy hat would dream of doing anything so unimpressive; they knew in their hearts that if a spell didn’t involve big yellow candles, lots of rare incense, circles drawn on the floor with eight different colours of chalk and a few cauldrons around the place then it simply wasn’t worth contemplating.

Terry Pratchett, ‘Mort’ (1987)

Teaching Circuits using Kirchoff’s Laws

Gustav Robert Kirchhoff (1824 – 1887) was a pioneer in the study of the radiation given off by hot objects and was the first person to use the term ‘black body radiation’. He also made groundbreaking contributions to what was then the ‘new’ science of spectroscopy.

High school students first encounter his name when studying electric circuits. Kirchhoff developed laws which describe the behaviour of electric circuits and, rightly, these laws still bear his name.

Newton needed three laws to explain the whole of motion; Kirchhoff needed only two to explain the behaviour of all circuits.

Kirchhoff’s First Law (aka KCL or Kirchhoff’s Current Law)

This law is a consequence of the Principle of Conservation of Electric Charge.

The algebraic sum of all the currents flowing through all the wires in a network that meet at a point is zero

Oxford Dictionary of Physics (2015)

‘Algebraic sum’ means that we must take account of whether the electric currents are positive or negative; or, in other words, their direction.

This can be stated more simply as: the sum of electric currents flowing into a junction is equal to the sum of the electric currents flowing out of the junction.

Kirchhoff’s Second Law (aka KVL or Kirchhoff’s Voltage Law)

This law is a consequence of the Principle of Conservation of Energy.

The algebraic sum of the e.m.f.s within any closed circuit is equal to the sum of the products of the currents and the resistances in the various portions of the circuit.

Oxford Dictionary of Physics (2015)

This can be more directly understood as saying that in any closed loop of the circuit, the sum of the energies gained by the charge carriers as they pass through parts of the loop with a positive potential difference is equal to the sum of the energies lost by the charge carriers as they pass through parts of the circuit with electrical resistance.

In other words, the sum of the positive potential differences (e.m.f.s) is equal to the sum of the negative potential differences around any closed loop of a circuit.

Applying Kirchhoff’s Laws to a circuit problem

Find the current flowing through each resistor in this circuit

Applying Kirchhoff’s First Law

But wait — is the current I2 flowing in the right way? Surely it should be coming out of the positive terminal of the 7 V battery, no?

Perhaps. The direction of I2 is simply my semi-educated guess at its direction given the relative strength of the 27 V cell and the 7 V cell.

But the happy truth of using Kirchhoff’s First Law is that . . . it doesn’t matter. Even if we have guessed the direction wrong, after we have gone through the process all that will happen is that we will get the correct numerical value for I2 but our mistake will be revealed by the fact that it will have a negative value.

If we look at the junction highlighted in yellow, we can see that the algebriac sum of currents is: I1 – I2 – I3 = 0.

We can rewrite this as: I1 = I2 + I3.

And that’s about as far as we can get using just Kirchhoff’s First Law. We have three unknowns so somehow we need to obtain two more independent expressions of their relationships to solve this circuitous conundrum.

Luckily, we still have Kirchhoff Second Law to bring into play…

Applying Kirchhoff’s Second Law (Part 1 of 2)

Before starting, I find it immensely helpful to indicate which ends of the components have a positive potential and which have a negative potential. This process is part of a general maxim that I try to apply to all areas of physics problem solving: why think hard when your diagram can do the thinking for you? (See here for a similar process applied to dynamics problems.)

An example of ‘Why think hard when the diagram will do it for you?’

Going around loop L1 in the direction shown by the arrow:

  • The emf 27 V will be positive as the potential increases (as we are moving from – to +).
  • I3R3 will be negative as the potential decreases (as we are moving from + to -).
  • I1R1 will be negative as the potential decreases (as we are moving from + to -).

This gives us:

Applying Kirchhoff’s Second Law (Part 2 of 2)

Yet another example of ‘Let the diagram do the hard thinking for you!’

Going around Loop L2 we find that:

  • The emf 7 V will be positive as the potential increases (as we are moving from – to +).
  • I2R2 will be positive as the potential increases (as we are moving from – to +).
  • I3R3 will be negative as the potential decreases (as we are moving from + to -).

This gives us:

The rest is history algebra

Going through a rather involved process of using simultaneous equations for solving for I1, I2 and I3 . . .

(NB There’s probably a quicker way than the way I chose, but I got there in the end and that’s the important thing. AND I guessed the direction of I2 correctly. *Pats himself on the back*).

Conclusion

Kirchhoff’s Laws: I hope you give them a spin, whether or not you decide to use the procedure outlined above 🙂

Teaching refraction using a ripple tank

It is a truth universally acknowledged that student misconceptions about waves are legion. Why do so many students find understanding waves so difficult?

David Hammer (2000: S55) suggests that it may, in fact, be not so much a depressingly long list of ‘wrong’ ideas about waves that need to be laboriously expunged; but rather the root of students misconceptions about waves might be a simple case of miscategorisation.

Hammer (building on the work of di Sessa, Wittmann and others) suggests that students are predisposed to place waves in the category of object rather than the more productive category of event.

Thinking of a wave as an object imbues them with a notional permanence in terms of shape and location, as well as an intuitive sense of ‘weightiness’ or ‘mass’ that is permanently associated with the wave.

Looking at a wave through this p-prim or cognitive filter, students may assume that it can be understood in ways that are broadly similar to how an object is understood: one can simply look at or manipulate the ‘object’ whilst ignoring its current environment and without due consideration of its past or its future

For example, students who think that (say) flicking a slinky spring harder will produce a wave with a faster wave speed rather than the wave speed being dependent on the tension in the spring. They are using the misleading analogy of how an object such as a ball behaves when thrown harder rather than thinking correctly about the actual physics of waves.

A series of undulating events…

Hammer suggests that perhaps a more productive cognitive resource that we should seek to activate in our students when learning about waves is that of an event.

An event can be expected to have a location, a duration, a time of occurrence and a cause. Events do not necessarily possess the aspects of permanence that we typically associate with objects; that is to say, an event is expected to be a transient phenomenon that we can learn about by looking, yes, but we have to be looking at exactly the right place at the right time. We also cannot consider them independently of their environment: events have an effect on their immediate environment and are also affected by the environment.

If students think of waves as a series of events propagating through space they are less likely to imbue them with ‘permanent’ properties such as a fixed shape that can be examined at leisure rather than having to be ‘captured’ at one instant. Hammer suggests using a row of falling dominoes to introduce this idea, but you might also care to use this suggested procedure.

You can access an editable copy of the slides that follow in Google Jamboard format by clicking on this link.

Teaching Refraction Step 1: Breaking = bad waves

I like to start by anchoring the idea of changing wave speed in a context that students may be familiar with: waves on a beach. However, we should try and separate the general idea of an undulating water wave from that of a breaking wave. Begin by asking this question:

Give thirty seconds thinking time and then ask students to hold up either one or two fingers on 3-2-1-now! to show their preferred answer. (‘Finger voting’ is a great method for ensuring that every student answers without having to dig out those mini whiteboards).

The correct answer is, of course, the top diagram. This is because the bottom diagram shows a breaking wave.

Teaching Refraction Step 2: Why do waves ‘break’?

In short, because waves slow down as they hit the beach. The top part of the wave is moving faster than the bottom so the wave breaks up as it slides off the bottom part. In effect, the wave topples over because the bottom is moving more slowly than the top part.

The correct answer is ‘two fingers’

It is important that students appreciate that although the wavelength of the wave does change, the frequency of the wave does not. The frequency of the wave depends on the weather patterns that produced the wave in the deep ocean many hundreds or thousand of miles away. The slope of the beach cannot produce more or fewer waves per second. In other words, the frequency of a wave depends on its history, not its current environment.

All the beach can do is change the wave speed, not the wave frequency.

Teaching Refraction Step 3: the view from above

We can check our students’ understanding by asking them to comment or annotate a diagram similar to the one below.

Some good questions to ask — before the wavelength annotations are added — are:

  • Are we viewing the waves from above or from the side? (From above.)
  • Can we tell where the crests of the waves are? (Yes, where the line of foam are.)
  • Can we tell where the troughs of the waves are? (Yes, midway between the crests.)
  • Can we measure the wavelength of the waves? (Yes, the crest to crest distance.)
  • Can we tell if the waves are speeding up or slowing down as they reach the shore? (Yes, the waves are bunching together which suggests that slow down as they reach the shore.)

Teaching Refraction Step 4: Understanding the ripple tank

Physics teachers often assume that the operation and principles of a ripple tank are self-evident to students. In my experience, they are not and it is worth spending a little time exploring and explaining how a ripple tank works.

Teaching Refraction Step 5: the view from the side

Teaching Refraction Step 6: Seeing refraction in the ripple tank (1)

It’s a good idea to first show what happens when the waves hit the boundary at right angles; in other words, when the direction of travel of the waves is parallel to the normal line.

I like to add the annotations live with the class using Google Jamboard. (The questions can be covered with a blank box until you are ready to show them to the students.)

You can access an animated, annotable version of this and the other slides in this post in Google Jamboard format by clicking on this link.

Teaching Refraction Step 7: Seeing refraction in the ripple tank (2)

The next step is to show what happens when the water waves arrive at the boundary at an angle i; in other words, the direction of travel of the waves makes an angle of i degrees with the normal line.

Again, I like to add the annotations live using Google Jamboard.


References

Hammer, D. (2000). Student resources for learning introductory physicsAmerican Journal of Physics68(S1), S52-S59.

Wittmann, M. C., Steinberg, R. N., & Redish, E. F. (1999). Making sense of how students make sense of mechanical wavesThe physics teacher37(1), 15-21.

The Burnéd Hand Teaches Best

The burned hand teaches best. After that, advice about fire goes to the heart.

J. R. R. Tolkein, The Two Towers (1954)

As is often the case in an educational context, and with all due respect to Tolkein, I think Siegfried Engelman actually said it best.

The physical environment provides continuous and usually unambiguous feedback to the learner who is trying to learn physical operations . . .

Siegfried Engelmann and Douglas Carnine, Theory of Instruction (1982)

I am going to outline a practical approach that will help students understand that black objects are good emitters and good absorbers of infrared radiation.

What I propose is a simple, inexpensive and low risk procedure (similar to this one from the IoP) that won’t actually inflict any actual “burned hands” but will, hopefully, through a clever (imho) manipulation of the physical environment, speak directly to the heart — or at least to students’ “sense of mechanism” about how the world works.

Half human and half infrared detector

Obtain tubes of matt black and white facepaint. (These are typically £5 or less.) Choose a brand that is water based for easy removal and is compliant with EU and UK regulations.

We also need a good source of infrared radiation. Some suppliers such as Nicholl and Timstar can supply a radiant heat source that is safe to use in schools. Although these can be expensive to purchase, there may already be one hiding in a cupboard in your school. If you don’t have one, use a 60W filament light bulb mounted in desk lamp (do not use a fluorescent or LED lamp — they don’t produce enough IR!). Failing that, you could use a raybox with a 24W, 12V filament lamp to act as the infrared source. [UPDATE: Paul Bushen also recommends a more economical option — an infrared heat lamp.)

Use the facepaint to make 2 cm by 2 cm squares on the back of one hand in black and in white on the other. Hold each square up to the infrared source so they are a similar distance from it.

Hold the hands still in front of the source for a set time. This could be anywhere between five seconds and a few tens of seconds, depending on the intensity of the source. You should run through this experiment ahead of time to make sure that there is minimal risk of any serious burns for the time you intend to allocate. If you are using rayboxes then you might need a separate one for each hand.

Schematic representation showing two hands with white and black paint on the back being held up to an infrared source.
The human infrared detector

The hand with the black paint becomes noticeably warmer when exposed to infrared radiation. We can deduce that this is because the colour black is better and absorbing the infrared than the white colour.

Energy is being transferred via light into the thermal energy store of the hand.

Schematic representation of energy being transferred into the thermal energy store of the hand via light.

We can use a black painted hand as a rudimentary detector for infrared. The hotter it gets, the more infrared is being emitted.

Enter Leslie’s cube . . .

Direct perception of the infrared output from a Leslie’s cube

Fill a Leslie’s cube with hot water from a kettle and then get students to place the hand with the black square a couple of centimetres away from the black face of the cube. After a few seconds, ask them to place the same hand by the white face of the cube. (Although, for the best contrast, you should maybe try the polished silver side). Make sure the student’s hand does not actually touch the face of the Leslie’s cube, otherwise they may end up with an actual burned hand!

The fact that the black face emits more infrared radiation is immediately directly perceivable by the “infrared detector” hand which feels distinctly warmer than when it’s placed next to the black coloured face rather than the white face.

This procedure is, I think, more convincing to many students as opposed to merely using (say) a digital infrared detector and reading off a larger number from the dark side compared to the white side.

Series and Parallel Circuits — an unhelpful dichotomy?

Anakin Skywalker and Obi Wan Kenobi discuss the possible unhelpfulness of the concept of ‘series circuits’ and ‘parallel circuits

Are physics teachers following the Way of the Sith? Are we all crossing over to the Dark Side when we talk about ‘series circuits’ and ‘parallel circuits’?

I think that, without meaning to, we may be presenting students with what amounts to a false dichotomy: that all circuits are either series circuits or parallel circuits.

Venn diagram showing the false dichotomy view of series and parallel circuits

The actual situation is more like this:

A Venn diagram showing a more nuanced and realistic view of series and parallel circuits

The confusion may stem from our usage of the word ‘circuit’: are we referring holistically to the entire assemblage of components (highlighted in red) or the individual ‘complete circuits’ (highlighted in green and blue)?

Will the actual ‘circuit’ please stand up? The red circuit is a hybrid circuit, the green circuit is a series circuit, and the blue circuit shows a single resistor in series or parallel with cell (depending on how you look at it)

How to avoid the false dichotomy

I think we should always refer to components in series or components in parallel rather than ‘series circuits’ or ‘parallel circuits’.

Teaching components in parallel using the ‘all-in-a-row’ circuit convention

I’ve written before about what I think is the confusing ‘hidden rotation’ present in normal circuit diagrams. I find redrawing circuit diagrams using the ‘all-in-a-row’ convention useful for explaining circuit behaviour. For simplicity, we’ll assume that all the resistors in the diagrams that follow have a resistance of one ohm.

This can be shown using the Coulomb Train Model like this (coulombs pictured as moving clockwise):

The reason the voltmeter across the cell reads +1.5 V is that energy is being transferred from the chemical energy store of the cell *into* the coulombs. The reason the voltmeter reads -1.5 V across the resistor is that energy is being transferred *from* the coulombs and into the thermal energy store of the resistor.

The current passing through the resistor using I = V/R = 1.5 V / 1 = 1.5 amperes.

Now let’s apply this convention when two resistors are in parallel.

This can be represented using the Coulomb Train Model like this:

I think it’s far clearer that ammeter W is measuring the total current in the circuit while X and Y are measuring the ‘part-current’ passing through R1 and R2 using this convention. (Note: we are assuming that each resistor has a resistance of one ohm.)

Each resistor has a potential difference of -1.5 V because 1.5 J of energy is being shifted from each coulomb as they pass through each resistor.

Also, it is clearer that the cell’s chemical energy store is being drained more quickly when there are two resistors in parallel: two coulombs have to be filled with 1.5 J of energy for each one coulomb in the single resistor circuit.

Thinking about current, the total current in the circuit is 3.0 amperes; so the resistance R = V / I = 1.5 / 3.0 = 0.5 ohms. So two resistors in parallel have a smaller resistance than a single resistor — this is a result that is well worth emphasising for students as so many of them find this completely counterintuitive!

Teaching components in series using the all-in-a-row convention

This circuit can be represented using the Coulomb Train Model like this:

The pattern of potential difference can be explained by looking at the orange ‘energy levels’ carried by each coulomb.

A current of one amp is one coulomb passing per second, so we can see that an ammeter reading would have the same value wherever the ammeter is placed in the circuit.

But look closely at R1: it only has 0.75 V of potential difference across. From I = V/R = 0.75 / 1 = 0.75 amperes.

This means that the total resistance of the circuit from R = V/I is, of course, 2 ohms.

Conclusion

I regret to say that I have probably been teaching ‘series circuits’ and ‘parallel circuits’ on autopilot for much of my career; the same may even be true of some readers of this blog(!)

The Coulomb Train Model has been considered in depth in previous blogs, but I think it’s a good model to encourage students to use their physical intuition (aka ’embodied cognition’) to understand electric circuits.

Whether you agree with the suggested outlines above or not, I hope that it has given you some fruitful food for thought.

Circuit Diagrams: Lost in Rotation…?

Is there a better way of presenting circuit diagrams to our students that will aid their understanding of potential difference?

I think that, possibly, there may be.

(Note: circuit diagrams produced using the excellent — and free! — web editor at https://www.circuit-diagram.org/.)

Old ways are the best ways…? (Spoiler: not always)

This is a very typical, conventional way of showing a simple circuit.

A simple circuit as usually presented

Now let’s measure the potential difference across the cell…

Measuring the potential difference across the cell

…and across the resistor.

Measuring the potential difference across the resistor

Using a standard school laboratory digital voltmeter and assuming a cell of emf 1.5 V and negligible internal resistance we would get a value of +1.5 volts for both positions.

Let me demonstrate this using the excellent — and free! — pHET circuit simulation website.

Indeed, one might argue with some very sound justification that both measurements are actually of the same potential difference and that there is no real difference between what we chose to call ‘the potential difference across the cell’ and ‘the potential difference across the resistor’.

Try another way…

But let’s consider drawing the circuit a different (but operationally identical) way:

The same circuit drawn ‘all-in-a-row’

What would happen if we measured the potential difference across the cell and the resistor as before…

This time, we get a reading (same assumptions as before) of [positive] +1.5 volts of potential difference for the potential difference across the cell and [negative] -1.5 volts for the potential difference across the resistor.

This, at least to me, is a far more conceptually helpful result for student understanding. It implies that the charge carriers are gaining energy as they pass through the cell, but losing energy as they pass through the resistor.

Using the Coulomb Train Model of circuit behaviour, this could be shown like this:

+1.5 V of potential difference represented using the Coulomb Train Model
-1.5 V of potential difference represented using the Coulomb Train Model. (Note: for a single resistor circuit, the emerging coulomb would have zero energy.)

We can, of course, obtain a similar result for the conventional layout, but only at the cost of ‘crossing the leads’ — a sin as heinous as ‘crossing the beams’ for some students (assuming they have seen the original Ghostbusters movie).

Crossing the leads on a voltmeter

A Hidden Rotation?

The argument I am making is that the conventional way of drawing simple circuits involves an implicit and hidden rotation of 180 degrees in terms of which end of the resistor is at a more positive potential.

A hidden rotation…?

Of course, experienced physics learners and instructors take this ‘hidden rotation’ in their stride. It is an example of the ‘curse of knowledge’: because we feel that it is not confusing we fail to anticipate that novice learners could find it confusing. Wherever possible, we should seek to make whatever is implicit as explicit as we can.

Conclusion

A translation is, of course, a sliding transformation, rather than a circumrotation. Hence, I had to dispense with this post’s original title of ‘Circuit Diagrams: Lost in Translation’.

However, I do genuinely feel that some students understanding of circuits could be inadvertently ‘lost in rotation’ as argued above.

I hope my fellow physics teachers try introducing potential difference using the ‘all-in-row’ orientation shown.

The all-in=a-row orientation for circuit diagrams to help student understanding of potential difference

I would be fascinated to know if they feel its a helpful contribition to their teaching repetoire!

Misconceptions and p-prims at ResearchED 2021

Many thanks to all those who attended my talk on “Dealing with Misconceptions: the p-prim and refining raw intuitions approach” and for the stimulating discussions afterwards!

And especially huge thanks to Bill Wilkinson for his help in sorting out some tech issues!

The PowerPoint can be downloaded below.

You can watch a short summary of the talk here.

The references are below with links to freely available copies (where I’ve been able to find them).

I think Redish and Kuo (2015) is an excellent introduction to the Resources Framework.


DiSessa, A. A. (1988). Knowledge in pieces. In G. Forman & P. B. Pufall (Eds.), Constructivism in the computer age (pp. 49–70). Lawrence Erlbaum Associates, Inc.

DiSessa, A. A. (1993). Toward an epistemology of physics. Cognition and instruction10(2-3), 105-225.

Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics68(S1), S52-S59.

Nelmes, A. (2004). Putting conceptions in their place: using analogy to cue and strengthen scientifically correct conceptions.

Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education24(5), 561-590.