# Gas station without pumps

## 2015 April 4

### Third lecture: resistance and voltage dividers

Filed under: Circuits course — gasstationwithoutpumps @ 20:13
Tags: , , , ,

Yesterday’s lecture was pure chalk talk, with no projector.  I took a number of somewhat random questions from students, then started on getting the class to try to define resistance. I got a number of fairly vague statements, until someone dredged up Ohm’s Law from their high school physics classes (or perhaps the reading they were supposed to have done before class), and suggested voltage divided by current, which is a good answer for this course.  I then explained to them the difference between resistance (V/I) and dynamic resistance (dV/dI) for non-linear devices, but I think that confused people more than helped them.  I should probably wait on the concept of dynamic resistance until they actually need it (perhaps with the electret mic?).

A question came up about how resistors were made, which I hadn’t planned to talk about, but was a reasonable digression, so I described wire-wound, metal-film, and carbon resistors.  We won’t use wire-wound resistors in this class, but half the class will have 1% metal-film resistors (bought last year) and half will have 5% carbon resistors (what the staff bought this year).  Maybe I’ll bring in a wire-wound power resistor to show them what they look like—the cooling fins on a 100W resistor are fairly impressive. I did tell them that they could experiment with carbon resistors by using pencil leads of different lengths, diameters, and compositions (the hardness of a pencil lead is dependent on the graphite/clay ratio, and the graphite is the carbon part of a carbon resistor).

I had the students do a simple Ohm’s Law exercise (3.3V across 1kΩ), then introduced a voltage divider with 5V across 2 1kΩ resistors in series. I had the students work out the current (after first getting them to realize that we needed to add a constraint that the current through the output is known to be 0A), and then the voltage output of the voltage divider.  I also had them work out what the effect would be if we tied the Vout node to ground, instead of having no current through it.

Throughout the class I relied on dice-assisted cold calling, so that students had to keep paying attention, lest they get called on without having thought about the question. As suggested in Teach Like a Champion, I asked the question before rolling the dice and choosing who would answer, so that (almost) all students were engaged with the question for at least a little while. I had 32 students registered in the class, so I was using D100 divided by 3 (round up) to get numbers on the class list, which is a bit slow.  I think I’ll switch to rolling a D8 and a D4, and computing 4*(D8-1)+D4 to get the numbers.

I did not get quite as far as I wanted to—we did not get to the general form of voltage dividers with all symbolic values (and I suspect that half the students are still having trouble switching from arithmetic to algebra, despite having had a couple of calculus classes and possibly more math). The material is in the book, which the students were supposed to have read before class (and probably didn’t), so they should be able to do the homework exercises for Monday’s class.

On Monday I’ll take questions about voltage dividers (I suspect that there will be some) and do a quick derivation of the Vout/Vin = R1 / (R1+R2) formula, perhaps in the form Vout/R1 = Vin/(R1+R2), since that corresponds directly to the notion of the currents being the same.  The rest of Monday’s lecture will be about temperature measurement using thermistors, RTDs, thermocouples, and diode junctions. I probably won’t have time for all of those, so I’ll concentrate on thermistors (which we’ll use in next week’s lab) and RTDs  (which are used for high-precision measurements in biological temperature ranges).  I don’t really care if we don’t cover thermocouples and diode-based temperature sensors, as neither are particularly important for bioengineers, and I have some material on them in the reading they are supposed to do by Monday..

1. No post-HS physics prerequisite?

My experience is that they do not connect calculus to anything else, including needing to do algebra or apply it in engineering or physics. This is partly because they tend to do everything with numerical coefficients (works best in the on-line HW) and only use y(x) because that is the only thing their graphing calculator can do. That last detail is why I have come to expect that they will struggle with x(t) and V(I), failing to see that dV/dI = R when V = IR. They also do not want to do symbolic algebra and then compute unless forced to learn how to do that in a physics or engineering class.

Comment by CCPhysicist — 2015 April 5 @ 10:06

• They have mostly had both Mechanics and E&M, though some are concurrently enrolled in E&M (because of scheduling difficulties with the Physics Department only offering the calculus-based E&M once a year). I’ll be hitting them with some dV/dt formulas in another week or so, when we derive complex impedance (in fact, we’ll derive I= C dV/dt from Q=CV first, and then plug in V = Re(e^(j omega t)) ).

Comment by gasstationwithoutpumps — 2015 April 5 @ 10:14

• Interesting that you use the real part (cosine voltage) rather than the imaginary part so it matches the sine that you normally get when setting up a scope. Is this done to reduce brain explosions?

Comment by CCPhysicist — 2015 April 5 @ 20:58

• When you set up the scope, you have no control of the phase (except by when you trigger), and cos and sin only differ in phase. For my own work, I never bother going back to the reals, and just work entirely with exp(j omega t).

Comment by gasstationwithoutpumps — 2015 April 5 @ 22:06

• Ditto. I only go back to sin(omega*t-phi) to relate it to a more familiar phase shift. I’ll have to think about using cosine in lecture, although that would not help them understand why the phasor plots in their textbook always put the observable on the vertical axis.

Comment by CCPhysicist — 2015 April 25 @ 10:16

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