Simple effective resistance of a circuit at low voltages

[Asymptotic]

When you re-run the experiment, connect a second Fluke meter (set up for voltage) directly across the resistor leads as close to the resistor bodies as possible, and record both these voltages, and voltages read by the on-board Digilent voltmeter. As mentioned upthread, each plug-in breadboard connection introduces an additional resistance (hence, voltage drop) that affects measurements. It would be interesting to see if both voltages track well with one another.

I'm guessing the apparent resistance non-linearity was mostly due to operating beyond the Fluke ammeter's accuracy specs, and won't reoccur during this second run-through using a lower resistance load.

Nevertheless, one thing that stood out looking at the Digilent Electronics Explorer is it has several regulated power supplies and other heat-generating components which I suppose are tucked away under the breadboard itself. A thermoelectic, "Seebeck effect" junction is formed where ever two dissimilar conductors are in contact with one another (this is the basic effect used in thermocouple-based temperature measurement) and it happens within resistors, too. How much voltage offset is generated depends on the materials involved; for every degree C difference between one side of a resistor and the other it could be as high as 400 microvolt/°C for carbon composition while 20 uV/°C is typical for metal film resistors. This may be a factor if one side of the resistor were in contact with the (presumably, warmer) breadboard, while the other side was in open air.

 

[zapnthund50]

Results are in! The meter the school provides is a Fluke 175 True RMS Meter. The experiment was done with 6 100-ohm resistors, hooked up to give an an equivalent resistance of 149 ohms, this ensured that each used only a fraction of power, and eliminated the heating variable. Voltage was measured across the ends of the resistor chain (instead of relying on the round number in the computer).

I've attached a picture of the data, along with graphs generated, for all interested to see. The linear fit is excellent, supporting ohms law. The effect of resistance approaching the effective resistance as a limit is ... well, see for yourself. Thoughts?

Edit: note that the scale of the graph of R examines a small portion and is exagerated (ie. about 144-149 ohms), instead of just 0-150 ohms. Thus, the trend is almost gone, but is still clearly present.

 

[Tom.G]

I've attached a picture of the data, along with graphs generated, for all interested to see. The linear fit is excellent, supporting ohms law. The effect of resistance approaching the effective resistance as a limit is ... well, see for yourself. Thoughts?
Attached Files:

• 
  
  ohms law exp.jpg

Your datapoint 1 sure points out the rule "Don't count on that last digit!"
The readings of 0.085V and 0.59mA, when "corrected" in their last digit to 0.086V and 0.58mA yield 148.28 Ohm. In line with the other calculated resistances. Keep this in mind during your journey through Engineering.

It's not limited to just Electrical stuff, ALL measurements have this problem. With mechanical measurement, or any analog measurement for that matter, you get a similar effect with different people doing the reading. Perverse, isn't it?

It appears the meter(s) have opposite calibration issues, although minor. In this case on the low ranges the voltage reading is low and the current reading is high; the combination leading to a lower calculated resistance value. If they are separate meters it would be interesting to see what the low-value readings are if the meters are swapped.

 

[zapnthund50]

Your datapoint 1 sure points out the rule "Don't count on that last digit!"

It appears the meter(s) have opposite calibration issues, although minor..

The first datapoint may very well be iffy, good point. Is it normal for meters to be oppositely calibrated ... that is, reading low on the voltage, and high on the current? I know the effect we're looking at must be generated by the meter, and it seems tied in with the amount of current generated, since the effect was quite pronounced in the first experiment (current on the order of 0.1 milliamps), and almost gone in the second (order of 10 milliamps)... this makes me suspect that something is eating up current and giving us this effect. But how is the meter doing this? It couldn't be the shunt resistor, could it? Guess I might never know lol. Anyway, narrowing the effect down to the instrument is a great start.

 

[Tom.G]

I take it then that both the voltage and current wer taken with the same meter. It is very common for a meter to have a slightly different reading for the same input when on different ranges. The two main causes are

1. Range changing is done by selecting different resistors within the meter and resistors have a tolerance
2. The zero adjust may be off a little bit, which effectively adds or subtracts a constant from each reading. For readings near zero, this leads to a large relative error.

It looks like this particular meter has both. Not at all unusual, they aren't perfect.

 

[zapnthund50]

• Range changing is done by selecting different resistors within the meter and resistors have a tolerance

• The zero adjust may be off a little bit

Yes, it was the same meter used for measuring both current and voltage. How does range changing for an ammeter work ... are different shunt resistors selected? Would range changing or a moving zero adjust be able to produce the effect shown, though? It appears to mimic the equation A - e^-x ... thanks for your input.

 

[zapnthund50]

It occurred to me that the inner workings of the fluke need current to operate, such as powering the LCD. This might cause a tiny voltage drop in the inner workings of the meter, and if this remained uncorrected, could show up in very small readings (where we are measuring tiny voltages). Of course if the meter is able to correct for this, all bets are off.

 

[Asymptotic]

It occurred to me that the inner workings of the fluke need current to operate, such as powering the LCD. This might cause a tiny voltage drop in the inner workings of the meter, and if this remained uncorrected, could show up in very small readings (where we are measuring tiny voltages). Of course if the meter is able to correct for this, all bets are off.

These effects are incorporated into the meter's basic percentage and LSD (Least Significant Digit) accuracy specification. What can be important (but doesn't appear to be involved in your case) is internal burden resistance, which changes depending on current range. For this Fluke 175 the accuracy spec is +/-1.0%, and 3 LSD for all ranges (10.00A, 6.000A, 400.0 mA, and 60.00 mA). All of your current measurements were less than 60 mA; it is likely the meter autoranged to the 60 mA scale. Note that the burden specifications for a Fluke 175 are 37 mV/A on the 6 and 10 amp range, and 2 mV/mA on the lower ranges.

A basic difference between analog and digital meters is an analog meter movement responds to current (more current = more magnetic flux = greater pointer displacement; for a Simpson 260, the movement is 50 microamps full scale) while a digital is at it's heart a voltmeter. When configured for current measurement, a DMM measures voltage dropped across an internal 'burden' resistor placed between the test leads. A burden voltage spec of 37 mV/A suggests a 0.037 ohm resistor is used on the Fluke 175's 6 and 10 amp ranges, and 2 ohm resistor for the 60 and 400 mA ranges. Voltage drop across the burden resistor is scaled as current (using Ohm's law, I=E/R), and displayed by the meter.

A Fluke 87 uses the same principle, and very nearly the same burden resistors for these ranges (they are spec'd as 0.03 V/A, and 1.8 mV/mA), but adds two microamp ranges (6000 uA, and 600.0 uA) at 100 uV/uA burden. This means a Fluke 87 uses a 100 ohm resistor when the microamp ranges are dialed in. 100 ohms may be enough added resistance to significantly affect circuit operation.

 

[Asymptotic]

Your datapoint 1 sure points out the rule "Don't count on that last digit!"
The readings of 0.085V and 0.59mA, when "corrected" in their last digit to 0.086V and 0.58mA yield 148.28 Ohm. In line with the other calculated resistances. Keep this in mind during your journey through Engineering.

It's not limited to just Electrical stuff, ALL measurements have this problem. With mechanical measurement, or any analog measurement for that matter, you get a similar effect with different people doing the reading. Perverse, isn't it?

It appears the meter(s) have opposite calibration issues, although minor. In this case on the low ranges the voltage reading is low and the current reading is high; the combination leading to a lower calculated resistance value. If they are separate meters it would be interesting to see what the low-value readings are if the meters are swapped.

This link to an article by John Gyork at Design World goes into digital meter accuracy in greater detail. It's too bad this is one of your last classes because it is an excellent introductory exercise in metrology - the science of measurement - and serves as a good jumping-off point to understanding the tangled web between precision, accuracy, resolution, repeatability, reproducibility, and uncertainty.

Extending on the rule Tom quoted, "Don't count on that last digit!", I've calculated your current measurements against Fluke 175 meter specifications.

• Calculated resistance variation is within specified current meter accuracy.
• I've used measured voltages in resistance calculations as though they are precisely dead-on, but in actuality they too have their own +/- percentage and LSD accuracy limitations, and would have to be worked out to get a more precise idea of the error budget.
  
• The first data point of 0.59 mA is only about 1% of 60 mA full scale. If this were an analog meter movement the pointer would have barely moved from zero.
  
• Take note how much more the LSD matters at lower values.
  
• 0.59 mA +/- 1% basic accuracy is between 0.584 and 0.596 mA (rounded to a resolution of 0.58 and 0.60 above), but it's the least significant digit spec of '3' added to and subtracted from them that makes a bigger difference (0.55 to 0.63 mA). Calculated resistance at 0.085 V are from 135.8 ohms to 153.4 ohms over this current range. The 147Ω test resistor value falls in between them.

 

[zapnthund50]

I've calculated your current measurements against Fluke 175 meter specifications.

View attachment 199069

You are an excellent resource, thanks for running those calculations! The fact that errors grow larger as we near the beginning of the range of the 60 mA scale is particularly interesting. I suppose my last question is, how is the error curve generated? That we may never know. It seems curious that it resembles a function in the family of A - e^-x. At any rate, I'm completely satisfied that we are seeing an error introduced by the meter. Thanks to all for your great input!

 

[Asymptotic]

Glad we've been of help.
It isn't only that instrument-derived error is greater at the extremes, but everything about low signal measurement is touchier, and makes one pay attention to even the smallest of details in order to account for observations.

Just putting this out there for future readers of this thread. There are few better ways to understand instrument capabilities and limitations that to build them, or barring that, to understand what design considerations go into the process. Joseph J. Carr wrote two excellent books on precisely this, and each are available used for under $20 (although new copies can be more than $200).

"How to Design and Build Electronic Instrumentation"
"Elements of Electronic Instrumentation and Measurements (3rd Edition)"

 

[jim hardy]

It's important to understand your test equipment lest it fool you..

Great thread, guys! Look how much came out of his seemingly simple lab experiment.
A computer simulation wouldn't have taught nearly so much.

We learn best by doing.

old jim