In Hysteresis lab too long, I planned for today’s lecture:
The groups then struggled with coming up with the right RC time constant for their oscillators. I’m probably going go over the calculation in class tomorrow, since I think everyone got a reasonable result, but not everyone was clear enough about their method to write it up well. I want to see clear explanations in the lab report, so I’ll go over it to help them smooth out the bumps in their explanations.
Some other things I want to do tomorrow:
- Talk about Carol Dweck’s work on mindset, as one of the students frequently wonders aloud whether the class is too difficult for her, and some of the other students may be thinking that they “don’t have the ability”. So far as I can tell, everyone in the class has the ability to master all the material in the class—but I need to get them out of “fixed mindset” into “growth mindset” and recognize that they can do more than they credit themselves with, if they are willing to work for it.
- Have them go over their computations of the finger-touch capacitive sensor and compare answers with each other. I want to make sure that they express their answers in standard units (like pF) and that they are careful about units (mixing mils, cm, and F/m probably confused a lot of students).
During the lab time, I had each group come up to use my micrometer to measure a double-thickness of packing tape. I must be using a different roll of tape than in previous years, because we consistently got about 1.7mil (0.043mm) with my Imperial units micrometer (that is we measured 3.4–3.5 mil for the double thickness), while last year I had 2.2mil. I should probably get a metric one, but I may be too cheap to spend $14 on a tool I use once a year in this class. Besides, this gave me an opportunity to tell students the difference between mil and mm, which most of them did not know. Since a lot of materials still come with thickness specifications in mil, they should at least be aware of the existence of the unit and the potential for confusion. (Several had done the prelab homework assuming 2.2mm, which would be very thick packing tape.)
- Assign one of the voltage-divider do-now problems from last year. Perhaps this one?
- What is the output voltage for a 3-resistor voltage divider? (I’ll draw the circuit)
- You have sensor whose resistance varies from 1kΩ to 4kΩ with the property it measures and a 5v power supply. Design a circuit whose output voltage varies from 1v (at 1kΩ) to 2v (at 4kΩ).
And that was pretty much how things went today. I started with the fixed-vs.-growth mindset message, and pointed them to my blog post on Carol Dweck’s book (not for the book or the post, but for the pointers in the post).
I then spent a fair amount of time going over one way to estimate the needed RC time constant from the design spec for the period of the oscillator. I tried to make a few points: that we were using the simplest model we could get away with, that there is no point to spending hours on theory when a couple of minutes with 5¢ components would let them adjust the parameters, and that we were re-using the same few formulas over and over again. I told them that I was not going to give them detailed instructions for any of the design tasks—I likened it to the difference between getting a Lego kit with detailed instructions of what pieces to put together, or getting a pile of Lego blocks and being asked to build a box with a particular volume. I’m going to give them bricks, not kits.
I did show them the sort of signal one might see on the oscilloscope, just sketching it by hand, and talked with them about where this big deviation from what our model predicted came from (capacitive feedback from the output to the input). I used that as a segue to talking about capacitive voltage dividers, where we derived the formula from our standard voltage divider formula and the impedance of a capacitor. I pointed out that since we had not included this phenomenon in our model, the periods would end up being much smaller than the simple RC calculation suggested. I also told them that they should try to figure out what is going on when they have unexpected results like that—where are the models wrong and does it matter?
We spent just a little time on doing the finger-touch capacitance together. I did not set anything up for them, but just asked them to explain how they had done it, writing it up on the board as we went. We ended up with estimates of the finger touch capacitance around 45pF.