# Circuits & Building Mental Models

I moved up my electric circuit unit this year for the senior physics class. Usually I put it after a full unit on waves, but after completing the waves unit with the IB students, I wasn't so pumped to go through it again from the beginning.

I began by having students try to generate the largest voltage they could from a set of batteries, motors, solar panels, lemons, and some other fun gadgets. That was a great way to spend a full 90 minute block. The next class, we played around with the PhET circuit simulator as I described in a previous post. The goal was to get them to have some intuition about circuits before we actually got down to analyzing it. Our conversation focused on batteries generally contributing energy to the circuit, and other circuit elements using that energy, leaving nothing behind at the negative terminal of the starting battery. Our working definitions for voltage, current, and resistance came out of the need for describing what was happening in the circuit.

This started a pretty textbook version of the modeling process. I gave students some circuits, asked them to make a prediction for voltage/current, they made the predictions, and then tested them in the simulator. As needed, they made adjustments to their mental model to make it consistent across all examples.

What interested me most about the results here was that the students put together a pretty solid mental model that centered on the voltage divider concept. This came out of their other assertion that current is the same for resistors in series.

This led to the students tackling this problem on the second day of looking at circuits this way:

In my AP Physics sequence, this is something I don't get to until Kirchoff's rules, so I was impressed with how nonchalantly they reported their answers after only a minute or so of thinking about the circuit.

On day 3, we went through an approximation of this lesson that I described in a previous post titled Starting at the end. We didn't get to the more complex circuits, but did get to the concept of parallel circuits.

On day 4, we spent a day getting our hands dirty building actual circuits, not with the simulator. The students had a good time piecing things together and seeing bulbs light up and make measurements with actual voltmeters and ammeters.

Today, on day 5, I was finally thinking I was going to teach them about equivalent resistance...but I hesitated. I was too scared that providing a formula would risk undermining all of the intuition they had developed.

The students worked through some Physics Bowl questions from a while back. Here's one:

I noted down a student's explanation of why the answer was 36 volts, and another student's addition to explain why it had to be 42 volts:

It then I threw this one at students:
I set the battery voltage to be 10 volts.

If my students had followed the sequence of physics lessons from the 2005 me, this would have been a piece of cake because they would have had the formula. Instead, they went through a nice sequence of stating what they knew and didn't know and making guesses. I suggested a spreadsheet as a way to keep track of those guesses and their reasoning in one place:

We went through the spreadsheet cell by cell and decided on formulas to put in. In the end, they figured out that the final two currents had to be the same.

I did some guessing and checking following their monitoring of the values, and eventually ended up with the 100 ohm resistor having a voltage drop of 9.923 volts.

Only at this point (which was five minutes before the end of class) did I apply an equivalent resistance formula:

It was a great moment to end on. My presentation of the equivalent resistance formula came out of a need, and for that reason, I was glad to provide it. I'm so happy I waited.