The Sweet, Sweet Taste of Failure
This morning I managed to fail in two different – in fact, perfectly balanced opposite – ways at the same task.
That task was the evaluation of resistive circuits in ECE 101. I won’t go into the details lest anybody’s eyes glaze over, but basically there are two parts to this task: visually figuring out the interrelationships of the various bits of the circuit (seeing whether resistors are in series or parallel and in what order they should be evaluated), then doing some fairly basic calculations in order to work out the equivalent resistance of parts of the circuit and/or dope out the voltages across and currents through particular bits (which, if you have the resistances and one starting voltage, can be computed for the rest of the circuit using a nifty little bit of math called Ohm’s law, if you’ve done the analysis correctly).
The way ECE 101 works is, the week’s homework is due first thing on Friday. Upon arriving in the lecture hall, we’re expected to stack it up on the table at the front; then, just before commencing the class, Andy scoops it all up and stuffs it in his backpack, and the homework train has left the station. Then there’s usually a very quick one-question quiz about one of the topics covered in that week’s material. This is usually of the "math trap" sort, where what he actually wants to know is if you understand some basic concept, such that you can either see how it works right away or spend a bit more time than you actually have available trying to do the math the long way. I always fall into math traps, and today was no exception, but that is not actually part of the failurefest I mentioned above.
No, that came when he passed out the quiz and told us to turn it over, and lo, it was a fairly oblique little resistive circuit, for which he wanted the total equivalent resistance. I saw through the first part of the trap pretty easily: though the schematic provided had a lot of weird angles in it, it was actually a pretty simple circuit which, once redrawn in a tidy rectilinear fashion, offered itself easily to analysis. The second part, though, was that the values were set up so that a particular algebraic property of the equation for equivalent resistance was supposed to jump out at us and make it all fall into place at once. It didn’t for me, and I duly groveled through all the math – which I then, just to add insult to injury, Did Wrong in an embarrassingly basic way. I knew I’d done it wrong, too, and may – I can’t remember now if I actually did it or just thought about it – have gone so far as to note that I was pretty sure my final answer was incorrect. (Oddly, Andy’s sense of these things is so perverse that I might get a point back for recognizing and admitting that.)
Once the quiz was collected, Andy asked if anyone had any questions about the homework just turned in. One of my classmates asked if he could take us through the breakdown of the most complicated of the example circuits on the homework assignment, an arrangement of nine resistors in a slightly odd pattern and a 24V DC source with the standard instruction, "Find the voltages and currents on all components and present in table form."
Andy duly began leading the class through the preliminary breakdown of the circuit, at which point I instantly realized that, on the sheets from my notebook he’d just stuffed into his pack, I had completely misapprehended the circuit layout. I had, I knew, done all the subsequent calculations right, and so I had a comprehensive table of what the voltages and currents would have been if the circuit had been set up the way I thought it was; but it wasn’t, so I’d screwed that problem in the ear before I even started doing the math. Exactly the opposite of what I did on the quiz. Two flavors of failure, same topic, same instructor, same morning.
Not one of my finer academic performances, and this is only week 3. I’m starting to get the Fear.