|John and Corey plot brightness of a mini light bulb with a vernier light sensor vs. voltage of a variable power supply. They get a parabola, as they predicted.|
I'm trying to teach my freshmen to predict what a graph looks like. We are well used to using equations like V=IR and P=V2/R, identifying the constant value, and drawing arrows to show which quantities increase or decrease. Now I want them to be able to sketch graphs.
With these types of equations, we're only going to get one of about four general graph shapes. Although I don't describe them in words to my class, for you I'd call them a sloped line, a parabola, a hyperbola, or possibly a flat line. You can see these, with my very simplistic description of how to know which one we're looking for, here.
The day after I hand these out, we do an in-class circuits graphing exercise in which students are asked to predict what four different graphs would look like:
* voltage vs. current for constant resistance
* current vs. resistance for constant voltage
* brightness of a bulb vs. resistance at constant voltage
* brightness of a bulb vs. voltage at constant resistance
The beauty is, each of these experiments can be set up very easily in our laboratory. I have "decade boxes" which allow you to dial any resistance you want, from 1 ohm to 100 kilo-ohms.* I have vernier light sensors, which measure brightness in lux.
* careful... on the graphs that DON'T include the light bulb you have to use kilo-ohms rather than ohms so that the power dissipated by the resistance box doesn't exceed a quarter-watt. Twice today a student accidentally turned the resistance box to zero, causing the resistor box to smell bad because it was starting to burn off the insulation.
In order to make this a relatively quick exercise, I provided a blank and scaled graph on the back page of each handout. (Check the link above to see. You may use these in your class.) The key is, FIRST the students had to predict what the graph should look like; THEN, they had to do the experiment. And sure enough, the graph looked like we expected.