Images, Resonances, Echoes, take 2

Images

How do you draw circuits?

Circuit diagrams are amongst the most abstract representations used in elementary physics teaching. How best to support reasoning with them, and indeed, what kinds of reasoning do you want to support? Or, more succinctly, how do you prepare to answer the question "Why are we doing this, miss?" Diagrams play a significant supporting role in reasoning about circuit loops, so starting with thinking about choices made, even after deciding to use conventional symbols, may be productive.

Is there a good convention for how to orientate the drawing of a circuit (leave aside for the moment the process of introducing representations)? After all, even for a simple circuit, there are many possibilities.

I suggest a good reason for the importance of circuits is that it gives insight into switching power, which is what we use circuits at all scales for remote (electrical) working in the everyday lived-in world. You may have other reasons, which will lead you to different conclusions.

If switching power, and reasoning about power is central, then drawing the dissipative elements those where power is switched) vertically enables the representations of power to be arranged fruitfully.

Current or charge flow (as shown here) are the same everywhere in the loop, so these are not a determinant of the orientation.

Components, other than wires and switches, are best drawn vertical in introductory teaching.

That prepares the way for reasoning about where the power gets switched, and how much, in circuits with both series and parallel connections.

Reasoning about the power switched and about the depletion of the battery is well supported by the arrangement of the arrows.

Here potential difference also appears, again reasoning about the relative values benefits from the dissipative elements arranged vertically.

And how do you draw them? Freehand, using pre-made symbols in a drawing package, photocopying?

As an aside these are drawn with code, which encapsulates the complexity of the arrangement of curves to construct a simple circuit containing a bulb to:

circuitSimple("bulb")

Just as concepts in physics can be compressive, so can code. Familiarity in either case determines utility!

Perhaps you consider this worry about orientation should be binned as an example of "marginal gains ". Perhaps so, but one child's marginal gain may be another child's tripwire. And there is plenty of evidence that there are a lot of confounding patterns of reasoning about electric circuits out there. Ours not to make the learning journey any harder than necessary.

To read more:

On difficulties in teaching elementary electric circuits in the Supporting Physics Teaching topic Electric Circuits.

Resonances

Patterns of reasoning in circuits– compensations and constraints

To alter the power switched by electrical circuit elements, change the potential difference or the current. The power switched is the product P=IV. In this circuit you set values of current and pd, but the (compensating) relationship remains true. Large values of pd can compensate for small values of current, and vice versa. There is a "trade-off". Reasoning where compensation is in play has been recognised as hard at least from Piaget onwards. Perhaps support we can offer about reasoning, by way of the box display.

You might want to do a side-by-side theoretical comparison, to go alongside a laboratory demonstration.

Circuits with series and parallel connections have more complex patterns, because the changes you make in one part of the circuit affect what happens everywhere in the loops.

The electrical quantities are constrained – they cannot be varied independently. To bring this home, consider a simple circuit again. The potential difference, the resistance and the current are constrained.

Constraints and compensation, here introduced in the context of thinking about electrical loops, are useful patterns of reasoning across many topics in physics.

Compensation – every time you think about the power on a pathway or the energy in a store.(probably more on this to come, arguing for a way to smooth the path from "not getting something for nothing" to the conservation of energy.

Constraints – most relationships used in elementary physics are of this kind: and "linear causal reasoning" has often been shown to lead children's understanding astray.

To read more:

On compensation in the Supporting Physics Teaching topic Electricity and Energy

On Linear causal reasoning see Viennot, L.(2007): Reasoning in Physics: The Part of Common Sense. Springer.

Echoes

Waves and delayed mimicry

In IRE01 I suggested that you could and probably should introduce the idea of a wave using delayed mimicry as the essence, as this enabled you to capture the essence of the idea of a wave without algebra.

The next stage in the development was suggested, but not made explicit. After some suggestions that this would be welcome, here is an echo from that impact–a delayed response.

Replace the single mimic with a chain of mimics, evenly spaced. The delay for each mimic as it copies the movements of its neighbour will be identical. Therefore, each mimic will be delayed with respect to the source depending on its distance from the source. This begins to appear much like a wave.

To get the full sine wave, just vibrate the source continuously.

As longitudinal waves share this essence, small changes can make a longitudinal waves.

Probably you'd want to show non-sinusoidal waves as well, probably as transverse waves, to maximise the chances of children seeing a difference. Again, a small change is all that's needed, altering the vibrations of the source. The mimicry goes as before, unless you want to change the speed of propagation, in which case just alter the delay before a mimic copies it's neighbour.

After that you can play with the variations.

To read more

Try this short paper.