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Understanding Resistivity Through Practical Experiments

Last month, a reader of this blog asked me a question about the possibility of measuring the resistivity of a powder mixture he created. We initiated a private conversation on the topic, and we ended up agreeing to work together to make such a measurement. He would provide me with the powder he created, and I would make the measurement for him, since he doesn’t have the lab resources for such a task.

I received the material for running the test in just a week, although coming from overseas (Belfast, Ireland). It was packaged in a double layer plastic envelop, given that it is a very light powder and can go airborne very easily. To avoid spreading it across my whole lab, I handled it wearing a mask, so that my breath would not make it fly all over the places. The mask helped also in preventing me from breathing it.

Given the consistency of this powder, I had to think at a way to easily shape it in a form that would be kept intact while I was taking the measurements on it. So I had to create a container that would also provide some sort of electrodes to electrically connect the powder to my DMM (Digital Multi Meter).

But let’s proceed in order. And let’s begin with some general information about resistivity and methods to evaluate it.

Let’s start by providing a formal definition of the electrical resistivity. That is the property of any conductive material that defines its resistance to an electric current in terms of its shape and dimensions.

https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

If we take a material in the shape of a cylinder, for example, the resistivity is the ratio between the electric field applied at the two bases of the cylinder and the resulting current density.

If you think about it, the electric field applied to the cylinder can be translated in a voltage per unit of length, while the current density is nothing else than a current per unit of area.

If we consider the ratio between the applied voltage and the resulting current, we obtain a resistance. Such resistance is a function of the length of the conductor and the area of its sectional surface. The constant that correlates the resistance with the length and the area is what is called resistivity, usually indicated with the Greek letter rho.

Experimentally, we also notice that the resistivity depends also on the temperature of the material, on the impurities in the material, and on the mechanical stress to which the material is subject.

Therefore, when making a resistivity measurement, we also have to specify such conditions, in particular the temperature and the stress.

So, how do we make such a measurement?

Of all the methods that have been used to do such a thing, the two most relevant are the 4-point method, or Kelvin method, and the Wheatstone Bridge method.

https://en.wikipedia.org/wiki/Four-terminal_sensing

https://en.wikipedia.org/wiki/Wheatstone_bridge

The first is normally used to measure the resistivity of thin films or bulk materials.

The second is normally used to measure the resistivity of a material in the form of an electrical wire of known length and cross-sectional area.


Now, because the resistivity measurement can be done with a great precision with the 4-point method, given that I do have a lab instrument capable of automatically perform such measurement and calculate the result with a 4 and a half digit precision, I decided to use this method over the Wheatstone Bridge.

Note that I will actually measure the resistance obtained by dividing the voltage by the current involved in the measurement circuit.

Once the resistance of the sample is measured, I will be able to calculate the resistivity by inverting the formula normally used to calculate the resistance.

Since I have a powder to measure, I have to use a container to hold it, which would also allow me to easily add electrodes to connect the instrumentation.

The first choice for a container was one that resembles an actual commercial resistor: a cylinder.

I actually designed two of them, thinking of using both to average the measurements.

The design consisted of a simple pipe with caps that would fit the two ends to trap the powder inside. Holes on the caps would be used to pass through the conductors attached to metal plates on the inside of the caps, to establish the contact with the powder.

I inserted a screw on each hole from the inside, after fitting on each a couple of metallic washers with the function of conductive metal plate. On the outside, I added extra wiring connectors to make it easy to connect my digital multimeter.

After installing a cap on one end of the first cylinder, I started filling it with the mix of graphite and ash. That, actually, wasn’t an easy task, since the powder tended to remain attached all over the places, rather than going into the pipe.

But I did it, and finally closed the pipe with the second cap. While doing that, the pressure of the air between the cap and the pipe expelled some powder, so I decided to seal the cap with some tape, to stay on the safe side.

Unfortunately, that did not help, as enough dust came out of the pipe to make the powder inside loose enough to compromise the readings. But I discovered that only later.


I realized that the measurement did not work when I started tapping on the external surface of the pipe and the resistance reading started changing substantially. Only at that point I figured that while capping the pipe I lost enough powder to leave it very loose inside the pipe. The method I employed was not working!

The good thing about this first attempt is that I learned a couple of important things:

– first, I had to create a vessel that would not loose powder once I closed it

– second, I had to make a vessel in such a way that I could change the pressure of the powder inside to see how that would affect the value of resistivity.

So, I ended up using a totally different shape, the one you can see in this new design.

Besides the different shape of the cross-section, which was now squared, the major difference in this design is the position of the opening. Instead of having two openings at the two ends, I created a vessel with a single opening going through the whole length of the device. That way, a single cap could be used to close the hole and also act as a piston to compress the dust.

When mounting the probe terminals, this time I didn’t use washers like in the previous case. Instead, I used this coating that, once dried, leaves a layer of pure silver on the treated surface.

This has two advantages with respect of the previous solution:

– first, a thick layer can be lay down very easily and uniformly

– second, silver is the best conductor known on the face of the planet, so its interference with the precision of the measurement is really negligible.

I stopped filling the vessel once I reached a height of 5mm, then I cleaned up the top of it the best I could, and carefully covered everything with the lid.

Note that the lid is made of a very light piece of PLA, so its weight is negligible compared with the atmospheric pressure acting on it. And to prevent the lid from moving or to change the pressure inadvertently, I fixed it in place with some masking tape. The whole thing is done in such a way that there is no extra pressure applied to the dust. However, if i use my fingers to push on the lid itself, I can still manually apply some extra pressure to see how it affects the resistivity of the material.

It was time to make a new set of measurements, so I fired up my DMM, I set it up to do the 4-point resistance measurement, and connected the 4 probes to the external connectors of the vessel.

Then I took my first reading, which was of 20.9 ohms. I also shook a little bit the vessel to make sure the powder was packed but not under additional pressure, and the reading did not change. That was exactly what I wanted to see.

And with that reading I calculated the value of resistivity at the atmospheric pressure, which was 10.45 ohm mm, or 0.01045 ohm m. And of course I also noted the temperature of the room during the experiment, which was about 72F or 22 degrees Celsius. Temperature changes the value of the resistivity, so it is important to know the temperature reading during the experiment.

I then repeated the process applying pressure on the vessel lid and made a few readings at different pressure values, recording all the numbers I took.

I found that increasing the pressure would lower the resistivity, until I reached a pressure of 22.563 kPA on top of the atmospheric pressure. At that point, any increase in pressure did not produce a decrease in the resistivity.

Two words about the pressure measurements, which were an important part of the procedure.

I basically used this precision scale to measure the weight exercised by my fingers on the lid. Then, knowing the area of the lid exposed to the powder, I was able to calculate the actual pressure.

At that value of pressure, and higher, I measured a resistance of 9.20 ohm, and therefore a value of resistivity of 4.6 ohm mm, or 0.0046 ohm m.

With that value, and the previous measurements at different pressures, I was able to determine that the resistivity decreased almost linearly with the increase of the pressure, and came out with this graphic representation.

For further details, here is the video I posted on YouTube on the same topic.

A Multiple Power Supply For The Workbench


When working with a new prototype on my bench-top, I tend to use one single power supply to power it up. However, sometimes, I need to power up more circuits at once, possibly using different voltages. And it is in those cases that I am forced to use more than one power supply. There are also some cases where I need a dual power supply and, besides the case where I need a +/- 12V, I don’t have a power supply unit capable of giving me other dual voltage values. I even built a simple device, capable of converting a single dual power into a dual one, for those cases where I need it. But that converter is able to provide only a very small amount of power and that is not good when the powers involved are high.


At the end, I need a power supply unit capable of providing me with different voltages at the same time, possibly also current generators and, certainly, the possibility of having both single and dual power supply.
Units on the market capable of providing such features are very expensive, and they don’t even provide all the possible capabilities that I need while, instead, they provide other capabilities that I normally do not care about
To solve this problem, I decided to make my own power supply unit, capable of doing all the things that I find useful in my lab, and at a fraction of the cost of a professional power supply unit.
Let’s take a look at the schematic I designed.

schematic_v2Download


First, in order to be able to connect together a positive and a negative polarity, without having a short circuit, I needed to have totally separated circuits, with independent transformers, so that I could establish any point of reference on each transformer and connect together such points to obtain dual power supplies.
Because of that, I have a total of four transformers in this schematic.
The first on the top, though a single transformer, it provides two independent outputs on two independent secondaries. I used that transformer as the base for building two independent variable power supplies that could be connected together through a switch to obtain a single variable dual power supply, with the two branches independently regulated, useful in certain situations.
The next two transformers, which have exactly the same characteristics, are used to power up the two sides of a fixed dual power supply. One transformer is used for the positive output with respect to the reference point, and the other transformer is used for the negative output with respect to the reference point.
The fourth and last transformer, on the bottom left, is a very small one used solely to provide the power to move a cooling fan for the power supply case.
The two variable power supplies are each made around a buck/boost converter manually controllable, which works both as voltage and current generator and also provides a display to visualize various parameters.


Here is the user manual of this little device.

ZK-5KX_voltage-converterDownload

It has several types of protection, it can be powered with a voltage anywhere in between 6 and 36V, and it can provide a voltage output between 0.6 and 36V, with a maximum current of 5A which can also be regulated, therefore offering the capability of working as a current generator.

It is also very easy to setup and use. It has a 4 wires connector. Two wires provide the input DC voltage and two wires provide the regulated output, either as voltage or current generator.

The manual goes on explaining how to use the rotary encoder and the two auxiliary buttons on the front panel, as well as the dimensions necessary to accommodate the devices on a larger panel of a bigger device.

Going back to our schematic, you can see that I used two of those regulators, represented here with the two blocks. So, each secondary of the large transformer is independently rectified and filtered by this section, to obtain a DC voltage of 34V with up to 2.5A. This two DC voltages go to the input of the power regulators and the outputs are available at the corresponding binding posts on the power supply front panel. Note also the switch that connects together the negative pole of the upper regulator with the positive pole of the lower regulator, to eventually provide a dual power supply where each branch can have and independent value of voltage or current.

The second section, with the two smaller transformers, is the one that provides the fixed voltage power supplies, very useful when working with devices like op-amps, for example, or any other device that needs to be fed with a dual power supply.

The secondary of both transformers T2 and T3 go each through a bridge rectifier and a filtering electrolytic capacitor.

From there, the positive voltage section is made of 3 separate regulators:

– an LM317, which brings down the DC voltage to a more comfortable value for the next regulators

– an LM7812, that provides a +12V to a corresponding output binding post.

– an LM7805, that provides a +5V to yet another output binding post.

Each of the 3 regulators has its own filtering capacitor, to minimize the residual ripple present to the voltage because of the rectification of the AC power provided by the transformer.

You can also see a number of diodes 1N4007, used as a protection for the solid state regulators during the power down of the whole power supply device.

The negative voltage section works exactly the same way, but uses the negative voltage regulators LM337, LM7912, and LM7905.

Another useful feature of this power supply system is the availability of two USB connectors on the front panel, used essentially to provide a 5V power supply, to power USB based devices, or to simply charge the battery of a device that has a USB power connector.

These two USB outlets are visible at the bottom left of the schematic, and it is perfectly visible that only pins 1 and 4 are used, which are those providing the 5V. The data pins 2 and 3 are not even connected.

Finally, the schematic shows also the last transformer, with its own half-wave rectifier and filtering capacitor that powers the cooling fan for the entire case. Why not, since I had laying around that little transformer for which I don’t have any other use.

And now, if you are interested in making your own power supply system, I suggest you to take a look at the video presented below, where you can found details on how to make also your own case for the device, as well as a number of useful information for its assembly.

Lights On! (part 2)


Hi there!
It is summer, and I have a number of upgrades in mind for my outdoor living areas: some involving electric upgrades, some involving gardening, some involving landscaping.
One thing I have in mind involves the night illumination of the gazebo and its surroundings. The current illumination is based on low power LED strings, powered by batteries recharged during the day by small solar panels.

However, I found that this kind of illumination has a lot of drawbacks. First of all, the lights are very dim. They are just fine when entertaining guests having conversations while enjoining the freshness of the evening air. But when it comes the time to do some table game that requires being able to look at pictures or reading stuff, often we end up going inside where we can have more light.
In addition, I need to turn on and off the lights manually, whenever I need them. If I leave them always on and let their sensors take care of the switching, they end up using the whole battery by the middle of the night and, sometimes, they take so long to recharge that by the time it is evening they don’t last that much anymore.
The solution would be to use bigger solar panes, but the batteries are still small and they also need their time to recharge. If I let them recharge too fast, they will start loosing their capability of retaining the charge too soon, and I would have to replace them relatively often. So I would trade off the usage of solar panels with more waste in exhausted batteries.

The right thigh to do, in my view, is therefore to use regular 120V lamps, obviously low power LED, but brighter than the ones I currently have. The thing is that I do like the automatism of having them turn on and off automatically from dusk to dawn. So, I thought I could design and build my own dusk to down automatic switch, which actually require just very few component and it is very cheap to make.

Schematic


Above is the schematic of my dusk-dawn automatic switch. It is a very standard design, and it requires just a few components.
The load is basically made of the LED lamps we want to control.
The 120Vac input goes directly through a protection fuse and to the series of a 50K resistor and a photo-resistor which is the sensor that will detect the daylight condition to turn the light bulbs on and off.

When there is enough daylight, the resistance of the photo-resistor is very low, in the range between 1K and 4K. When we are getting closer to dusk, the daylight starts dimming and the resistance instead increases. Once the resistance hits the 16K threshold, the voltage at its leads goes above 30Vac.

It is at this point that the DIAC starts conducting and it triggers the TRIAC. The TRIAC, in turn, will let the current flow through the load, thus turning on the lights.
Very simple right?