# Gas station without pumps

## 2016 July 8

### Incandescent bulb I-vs-V

Filed under: Data acquisition — gasstationwithoutpumps @ 20:33
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Greg Jacobs in So what does an ohmmeter read when it’s directly connected to a non-ohmic bulb? asked for help in determining how to measure the resistance of a bulb at different low voltages, as his voltage source only goes down to 2V.

I used my FG085 function generator, a resistor, and PteroDAQ to measure the I-vs-V characteristics of a small screw-base bulb rated at 6.3V and 150mA.  One would expect a bulb with that rating to have 6.3V/150mA=42Ω resistance, but incandescent bulbs are not ohmic devices—the resistance of the filament depends on its temperature, and at 2700°K, the resistance is going to be much higher than at room temperature.

The thermal coefficient for tungsten is about 0.0045/K, so one would expect a difference of about 2400°K to make a ratio of about (1+0.0045/K 2400K)=11.8.  So, if the linear approximation of resistance vs temperature were good over that wide a temperature range, we’d expect about 3.6Ω at room temperature.  I measured about 3.8Ω with my ohmmeter, so this seems like a reasonable back-of-the-envelope approximation.

I hooked up the function generator to drive a 10Ω resistor and the bulb in series, and used PteroDAQ (with a Teensy LC board) to measure the voltage across the resistor and across the bulb. I had to play with the amplitude and offset of the function generator a bit, because the 50Ω output impedance means that the voltage across the bulb+resistor was substantially less than the values set (which are the nominal voltage to a high-impedance load).

Here is the current-vs-voltage characteristic for a slow (22-second-period) triangle wave as the excitation.

The plot above is a little hard to interpret, but one can clearly see the range of voltage and current, and that the plot has hysteresis—it follows a different curve when the voltage is increasing than when the voltage is decreasing. (One can also see the really bad digital-to-analog conversion in the FG085 function generator, with big steps and non-monotonic steps.)

Changing the plot to resistance (V/I) versus voltage makes for a clearer plot:

Now we can see that the resistance varies from about 5Ω to about 23.5Ω, again with hysteresis.

The large noise at the low end of the plot is due to the inherent problem of taking the ratio of two small numbers, each of which has noise added. We can clean up the appearance of the plot by using power (IV) on the x-axis, since if either voltage or power is close to zero, then power is also very close to 0:

The high noise for R is still here on this plot, but it is hidden by the y-axis.

Looking at the resistance as a function of time is helpful in interpreting the plots:

Note that the high noise (as the voltage and current get close to 0) occurs before the low point of the resistance—the resistance stays low until the bulb starts heating up again as the voltage rises.

The R-vs-V and R-vs-P plots should be interpreted as counter-clockwise hysteresis—the lower curve is the one followed as the filament heats up, and the higher curve is the one followed as the filament cools down.

The curve you get depends very much on how quickly you change the voltage. Using the same voltage range, but making the fluctuations be at 4Hz instead of 1/22 Hz results in a much more constant temperature, and hence a much more constant resistance:

At higher frequencies (here 4Hz), the hysteresis is still present, but resistance varies much less.

Of course, the question arises whether the standard 60Hz line frequency is high enough to get a constant filament temperature.

At 60Hz there is still hysteresis—the filament is heating and cooling. Note that I am using a DC offset here and the voltage never goes negative across the bulb, and so the power waveform has a 60Hz period.

The filament temperature is not constant, but the variation in resistance is much less. Note that with the higher frequencies, the maximum resistance (and hence maximum temperature) does not occur at the same time as peak power, but substantially later in the cycle.  If one wanted to get a really clean reading of resistance vs power, it would be best to change the voltage very slowly, so that the temperature has a chance to reach steady state.  Even with a period of 99s, I still saw fairly substantial hysteresis, so I tried a couple cycles with a period of 333s—I expect that the hysteresis will be small except for the low-power end of the curve, as cooling is slower when the temperature difference is small.

With a long (333s) period, the bulb almost reaches equilibrium temperature at each voltage, so the resistance vs. power curve is almost the same for increasing voltage as for decreasing voltage. [Note: the voltage range was not the same for this plot, as I had been playing with the function generator settings trying to do a hand-stepped plot.]

If one wanted to make hand measurements with a fixed power supply and no function generator, one could either change the current-sense resistor for each measurement (larger resistor for smaller currents) or keep the current-sense resistor and bulb constant, but add extra series resistors to reduce the voltage and current.  It would take a fair amount of patience to gather many measurements (or lots of students with identical bulbs).

Note that I was only looking at the low power range for the bulb—it should take about 945mW when at its full rating, and I stayed below 1/7th of the full rating.

## 2016 April 29

### Miswiring errors

Filed under: Circuits course — gasstationwithoutpumps @ 15:25
Tags: ,

In yesterday’s post, Revised microphone pre-amp lab too long, I wrote about problems in this week’s lab, and one of the items seems to have resonated with at least one other instructor:

a surprisingly large number connected both nodes for a resistor to the same end of a resistor, leaving the other end unconnected.  I’ve not seen that mistake before, so I don’t know what triggered it.

CCPhysicist commented

I’ve seen that error (connecting two wires to the same end of a resistor) before, more than once, but I also don’t have a clue why they do it. It is worst if the resistors are in a box where they can see the connectors but not the resistors (even when they see the resistor symbol between the connectors), but also happens with loose resistors. Now my students have the excuse that we start doing those labs before we get to DC circuits in lecture, so I assume it means they have no idea that current flows through things and that switches break a circuit, but I have no idea why they get to college without any experience related to the basic concept of electric current. Maybe whatever misconceptions they have about current are stubborn enough to survive a semester of physics.

As for why you got many instances of that error, I’d suspect “authoritative ignorance” syndrome. Others were following someone who talks a good game but doesn’t know the play. Can happen just by one person looking at what another is doing, without any actual bad mentoring taking place.

I don’t think that “authoritative ignorance” was the problem here, as the students making the error were in both sections and they made it in different places in the circuit. I responded with my best guess at what was happening:

My conjecture is that students aren’t using a misconception of current—they aren’t thinking about the function of the resistor at all. They just have the idea “connect up the resistor to A and B”. Having a wire between point A and the resistor and between point B and the resistor satisfies that objective, even though it doesn’t mean anything if the resistor is not between A and B

I discussed this with the class today, and suggested that they change their mental language and think of connecting a resistor between two nodes, rather than to two other components. I also talked about switching their thinking from “components connected by wires” to the dual graph, nodes connected by components, and assigning a color to each node.

Color coding each node makes it much easier to notice incorrect connections (two different colors connected together), though it doesn’t help with noticing missing connections.  For that, I recommend that students check each component to make sure every node is there, and every node to make sure it has the right number of components.

CCPhysicist commented

Perhaps I will work on introducing the concept that labs like most of our circuit labs are about discovering the function of everything we use (meters as well, because they are part of the circuit, and even the wires themselves), and discourage the use of words like “to” instead of “through”. After all, the two wires in your example actually do carry current “to” and “from” the resistor!

I insist in the weekly design reports that students not use “voltage through” or “current across”, but always “voltage across” and “current through” to talk about V and I for a component.  I don’t think that this help much with their understanding, though, as the misunderstandings about voltage always being a difference are still common, and students still routinely apply Ohm’s Law to voltages and currents measured in different places.

Any problem that involves a voltage, a current, and a resistance causes many of them to invoke $V=IR$, even when the voltage and current are unrelated or related in something other than a simple resistance.  (For example, when chosing a DC bias resistor for an electret microphone, we have a non-linear I-vs-V relationship for the mic, and generally have a voltage drop across the resistor that needs to be added to the voltage drop across the microphone to get the power-supply voltage, but students will take any of the voltages (the mic voltage, the voltage across the resistor, or the power-supply voltage) to get the resistance of the bias resistor, when only one of the voltages is appropriate.

My labs are not about “discovering the function of everything we use”, but about learning how to design circuits with imperfect parts. (That’s one difference between a physics lab and an engineering lab.) I’m trying to give the students tool skills: both mental tools and physical tools.  The notion of having multiple models for something and using the simplest one you can get away with is one of the skills I’m trying to get them to develop.  The extremely simple models used in intro physics courses are often not good enough for practical use and developing better models from first principles is too hard, so we do a lot of measuring and empirical fitting.  (The loudspeaker modeling lab is a good example, where we go through 4 different models of the loudspeaker: R, L+R, L+R+RLC, semi-inductor+R+RLC.  Sometimes the simple model of the loudspeaker as being 4Ω is adequate, and sometimes we’ll use the full complexity of the non-linear model.)

There are a lot of learning experiences that are generally unavailable with simulations (like the problem of measuring voltages in voltage dividers made of 4.7MΩ resistors when your meter has a 10MΩ input impedance, or the problem of clipping when using high gain in an op amp, because of input voltage offset errors).  Students are much more likely to remember to design around input offset voltages if they have observed an unexpected output voltage offset and tried to figure out what caused it, than if they are simply guided to do designs that have low gain without knowing why (or allowed to do large-gain designs without realizing that they wouldn’t work reliably, as I have often done myself, even though I theoretically know better).

## 2015 April 4

### Third lecture: resistance and voltage dividers

Filed under: Circuits course — gasstationwithoutpumps @ 20:13
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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..