Bulbs in parallel
Consider the two circuits above. If the reading on the left ammeter is 4A, what is the reading on the right ammeter?
One of the topics I’ve been considering for a long time is how to make it clear and explicit to students that each loop of a ‘parallel circuit’ draws its own current. When we talk about the current ‘splitting’ when components are connected in parallel, we are setting up the misconception that the reading on the right hand ammeter is going to be 2A when the second bulb is connected. In reality, the ammeter is going to remain reading 4A, but the current through the cell (and the wires prior to any branching) is now 8A (assuming my bulbs are the same).
SIDE NOTE: I’d also be very clear with students that there’s generally no such thing as a series circuit or a parallel circuit, what we should say is “components connected in series/parallel” as only the most basic circuits can be classified as uniquely series or parallel. But in this blog, I am discussing the unique examples of a truly series circuit (one cell and one bulb) and a truly parallel circuit (one cell with two bulbs connected in parallel).
THE (POSSIBLE) PROBLEM
We often start with this series circuit:
and then go on to add in our second bulb in parallel as below (I’ve chosen to use different coloured wires to try and make this second ‘loop’ explicit):
Now, if the equipment was working perfectly (which it clearly isn’t in these pictures — don’t you just love electricity practicals?) we might choose to point out that the bulbs are the same brightness and therefore discuss that the PD across them must be the same.
To my mind though, it’s not immediately obvious that each bulb in the circuit is also drawing an identical current. It seems like a magic trick. Not only is the PD identical across each bulb, but the current is identical through them too? Students are always expecting some change to happen, so surely the current or PD should have changed? Students might then start to confuse concepts of PD and current in attempting to build their own mental model of what’s going on.
This whole process isn’t helped by us often saying that the current ‘splits’ when components are connected in parallel, so students are expecting a current that’s half as big as it was before. Hopefully we’ll see below that we should probably more frequently talk about the current ‘summing’.
SIDE NOTE: We might further decide to put in some ammeters to check the current in each of the loops, and find values that aren’t the same: “Sir, 3.1A isn’t the same as 2.9A…” “Well, no, that’s right, but…”
A (POSSIBLE) SOLUTION
Firstly, ignore ammeters for now in this initial explanation phase. Or, if you do want to use them, be willing to go off on a digression about measurement and errors and loose connections etc.
Instead of adding my second bulb in a loop below the first bulb, why not add it above the cell (which I know is actually a battery, hidden in a plastic base with a cell symbol for reasons that I’ve never fully understood-who said electricity was confusing)?
Now this ‘red loop’ seems entirely disconnected from the ‘black loop’. If we were using a rope model of electricity to talk about this (Tom Norris has an excellent blog on this here) we can set this up nicely with two ropes (or bathroom chains which I like even more) and model this. It seems quite intuitive that these two loops are independent of one another.
The subtle point here is that the current running through the cell is now the sum of the current in the two loops. But I wouldn’t mention that to students just yet. I’d go through a whole lot of questioning about what’s going on making sure students are recognising what I want them too — each bulb is drawing its own current, independent of what’s going on in the other loop. We might, for instance, look at the circuit below to really ensure that students are clear that the ‘red loop’ and ‘black loop’ are independent.
Now, I want to emphasise that somewhere in the circuit, something must have changed though. And I do that by going back to the original ‘parallel circuit’ and adding in some completely superfluous blue wires from each terminal of the cell. I’d model this directly under the visualiser emphasing that I’m not changing anything important, just adding in more wire and it’s having no effect on the bulbs.
And now I explain to them what is happening with the current in the blue wire: “The current in the blue wire must be large enough so that the red loop gets its 5A and the black wire gets its 5A, so the current in the blue wire has to be 10A”. Questioning, lots of questioning, examples, lots of examples etc. etc. etc.
Finally, and one of the main reasons for using the blue wires rather than just talking about the current between the terminals of the cell, I can physically manipulate the top bulb and move it. I can move it down beneath the ‘black loop’ and arrange the wires to look exactly like the archetypal ‘parallel circuit’.
In conversation with Gethyn Jones, he mentioned how this is similar to the continuous conversion idea of Engelmann which is particularly powerful. We can then add in more and more loops — either directly at this point below the ‘red loop’ or by going back and adding loops at the East and West positions of an imaginary compass (where the ‘red loop’ was previously at North and the ‘black loop’ was previously at South).
In our conversation for the CogSciSci electricity chat, we discussed how this might be just as successful through a simulation such as PhET, but I do think there’s something very powerful about that last step — the physical manipulation of the circuit. By doing this, we’re moving from a point where our conceptual understanding of the current is strong and heading towards the point where this understanding can align with common circuit diagrams that don’t necessarily show the two loops as distinct.
I’d love to hear what you think of this little idea, I’m @TChillimamp on twitter.