Talk:Circuit Idea/Walking along the Resistive Film

A dedication to my students
''I dedicate this exciting story to my students from Faculty of Computer Systems, Technical University of Sofia, spring 2008, that have inspired me to carry out this incredible experiment on the laboratory and to tell about it on Circuit idea wikibook. Cyril''



I have been teaching analog circuitry for more than 24 years. During this period, my students and I have been carrying out many and many times this attractive computer-based experiment (it is my favorite experiment): visualizing the voltage distribution along a linear resistive film that is supplied by two voltage sources connected to the two sides of the resistor. For this purpose, we use all kinds of "resistors", some of them quite odd: resistive wires, pencil graphites, conductive foam and rubber, and of course, opened potentiometers and the good old rheostats. By sliding on the resistive surface and varying consecutively the two supply voltages, we "invent" various legendary resistive devices: movement sensors, voltage dividers, resistive summers, subtractors, Wheatstone bridge, op-amp inverting, non-inverting and differential amplifier, etc.

In addition, this marvelous experiment presents in an attractive non-traditional way the famous Ohm's law, virtual ground concept, negative resistance phenomenon, etc. to curious students. It even shows directly in a "geometrical" way classical relations between the electrical quantities (I = V/R, UOUT/VIN = -R2/R1, etc.) Furthermore, this experiment establishes a connection between the elementary passive resistive circuits (voltage divider, resistive summer, etc.) and the more sophisticated electronic op-amp circuits (non-inverting amplifier, inverting amplifier, etc.)

I have been having responsive, clever, curious and capable students that have been helping and inspiring me in my pursuit of revealing the truth about resistive circuits through these years. That is why, I have decided to place this experiment first on my site of circuit-fantasia.com and then on this wikibook.

Students


During this term I teach basic circuitry (both lectures and laboratory exercises) to 150 students from Faculty of Computer Systems, Technical University of Sofia. They are divided into five groups (64, 65, 66, 67, 68), each of them containing 30 students. Further, for the purposes of the laboratory exercises, these groups are divided into sub-groups of 15 students. Each laboratory cycle lasts two weeks: the first five sub-groups (64a, 65a, 66a, 67a, 68a) conduct laboratory exercises during every even week; the other five sub-groups (64b, 65b, 66b, 67b, 68b) conduct laboratory exercises during every odd week. My general idea is to carry out the same experiment in the laboratory consecutively with all the student groups during the present cycle (March 17 - 29, 2008).

Organization
Preparation. First, in the beginning of the week, I started this story on Circuit idea. For this purpose, I outlined briefly (about 25%) the future page: I traced out the contents by inserting the main subtitles; then, I placed semi-drawn pictures and a little explanatory text. By the way, it was very hard for me to refrain from making the whole page...

In the laboratory, I prepared all kinds of resistive elements (wires, pencil's graphites, conductive foam, etc.), power supplies, movements, VOM's, holders, etc. and arranged the laboratory equipment according to the future experiment's purposes.

I also prepared all kinds of recording equipment - a small solid state recorder (for quite a while I have recording my lessons, classes and laboratory exercises), camera and mobile phone. Maybe, next year I have to use a web camera:)?

I have also begun thinking who of famous web writers (mainly, university and college teachers) to invite to join this educational web initiative. For now, I have in mind Tony Kuphaldt (Lessons in electric circuits), Tom Hayes (Student manual for the art of electronics - great book!), William Beauty (Science hobbyist] - great site!)...

Announcement. Then, in the lecture hall, I announced my intention to conduct such a web experiment to students and showed them how can we carry out it. I told them what is the great Wiki idea and how they can join the wikibook Circuit Idea. I suggested to students to choose meaningful user names consisting of student name and group number (thus I can observe their web achievements and add more credits to the rating).

A chronology of the laboratory exercises
In this part of the talk page, my students and I describe step-by-step how the laboratory exercises have passed. The great mass of the written is extracted from the records but there is also some fragments that is written directly to this page in the laboratory during the excercises. Note that students make their reports in real time at the laboratory; I make also my "report" on the white board (ten times during the cycle!), snap it from time to time and write it on this page. Students and I make a lot of photos during the exercises; they show drafts on the whiteboard, screen shots, laboratory setups and, of course, the very students.

The idea is first to write up here chronologically what is done in the laboratory; then to systematize and polish these raw materials and place them in the main story. We will use here (and why not in the main page?) a quite informal style. I will mark student's insertions by italic to distinguish them from my teacher's text. Well, let's start!

Group 65a (Tuesday, March 18, 2008, 10.30 h)
The genuine Ohm's experiment

History. What did Ohm carry out in 1826? Do you know? Students: No... Please, let's someone write in the Google's window "Ohm's experiment" or "Ohm's law" to see what is written about the topic. Thank you ......... (insert your name here and make comments to obtain credits); please, make a folder in "Favorites" named "Ohm's law" and put there the most remarkable links.

Let's first consider his genuine experiment and then reproduce it here, in this laboratory, almost three centuries later. This is the first of all the ten exercises of this cycle; so, let's try to reproduce it in the most original form. So, what do we need to carry out it? Silence...

Building the laboratory setup. As far as I know, Ohm has discovered the local voltages along a copper wire that was supplied by a strong voltage source. So, we need a wire, a power supply, a voltmeter and an ammeter. But what kind of wire we need? Bare or insulated? Copper, silver, iron, or other? Student: Silver will work excellent...  We haven't a silver wire, let's try with a copper one:) Oh, it has welded!?! It is so well that the power supply has a current limitiing circuit (2.5 A)! That is why Ohm made a strong voltage source by applying the just invented by Seebek thermoelectric effect! Now, it is clear we need a resistive wire (nitinol, NiChrome, etc.); so, let's unwind a piece of wire (about 50 cm) from a heater. ...... (insert your name here), please, meausure its resistance. The resistance is 10 Ω, so we have 0.2Ω/cm.

Experiment 1. Now, fix the two ends of the wire in porcelain insulated terminals (holders) and apply a voltage (for instance, 10 V) first to the left end of the wire. What can we investigate now in this arrangement? What do we measure with the voltmeter? The usual viewpoint is to think of a resistor as a point, as a something that has not dimensions, as a two-terminal element that has only a property of resistance. But here we have the unique chance to peep inside the "resistor"! What will you "see" along the wire? What will the voltmeter show when we slide it from right to left? What are the local voltages along a resistor, if there is no current? Student 1: Zero... Student 2: 10 V... What is the voltage at the right? Zero... And what is it at the middle? Zero...



Well, let's try. Just touch the wire by the voltmeter probe and move it along the wire to measure all the voltage drops (for now, regarding to the ground)! If you are tired, stick a crocodile clips on the probe, "bite" the wire and move this "slider" along it! The result: everywhere local voltages are 10 V!

Experiment 2. Now, ground the right end of the wire. Oh! The wire is hot! Have I instructed you about all the dangers in the laboratory:)? Include this one: do not touch a hot wire! See the ammeter - it shows 1 A; so, the power is P = V.I = V2/R = I2.R = 10 W. By the way, are these calculations right (has the resistance a constant value)? We see, it is too hard for this thin wire to dissipate the power to the ehviroment and it is heating.

Now, move again the "crocodile slider" along the wire and measure the local voltage drops. As far as I know, Ohm did exactly the same. He moved the probe from one position to other, measured the corresponding potentials, made the difference between them and calculated the ratio (V2 - V1)/(L2 - L1) = (V2 - V1)/(r2 - r1) = dV/dR = I. Thus he has established that this ratio (it was the current I) is constant along the wire; so, Ohm has concluded that V/R = I.

We can see that moving the "crocodile slider" the voltage drops decrease gradully from 10 to 0 volts. What is the input and what is the output quantity here? Eureka! Using the "slider" movement as an input and measuring the voltage drop as an output we have "invented" the legendary (but misnamed) potentiometer, movement-to-voltage converter, sensor... Is it a linear converter? Why? A hint: the resistance is distributed linearly along the wire.

Experiment 3. But why do not we change the role of the quantites? With the same success we can stop the "crocodile slider" at the middle of the wire and then to vary the input voltage as an input and, as before, to measure the voltage drop (regarding to the ground) as an output. Eureka (again)! Now we have "invented" the legendary voltage divider (voltage-to-voltage converter)! What is the relation between the input and output voltage (the so-called "transfer ratio"? We can see directly that VOUT = VIN.L2/(L2 + L1).



Experiment 4. We are ready to do more sophisticated experiments... Are there more interesting points (different from the ubiquitous ground) to fix the negative voltage probe? Of course, we may touch any wire point! Well, let's begin with the middle point: "bite" it with the black (negative) negative "aligator" and slide the red (positive) "aligator" along the wire. Only, first change the unipolar voltmeter with a bipolar one. Why? What might we expect? The result is more than surprising: the output voltage varies from -5 V to +5 V! Eureka! We have obtained a bipolar movement-to-voltage sensor!

Experiment 5. What happens, if we move simultaneously both the voltmeter probes in the same direction? Students: The voltage will not change... Right! They name this "common mode input signal".

Experiment 6. And what happens, if we move simultaneously both the voltmeter probes in opposite direction? Students: The voltage will change... Right! It will even change more rapidly than above. They name this "differential input signal".

Experiment 7. Now stop both the "sliders" and wiggle the input voltage. This is a quite odd voltage divider with flying output. What is the relation between the input and output voltage (the transfer ratio? We can see directly that VOUT = VIN.(L2 - L1)/L.



We can measure the voltage drops along the resistive wire by using more unusual indicators, e.g. electric bulbs. What do you think, is there any problem to supply a bulb in this exotic way? If yes, when and why?



Applications. Where may we see this phenomenon in life? The answer is simple: everywhere where a current flow through bad conductors. In all these cases, a gradually decreasing voltage drop appears across the "conductor". A "car example": if you move the probe lamp along the heater of the rear window, you will see the voltage drop across the resistive wire.



Using the heritage of group 65a
Welcome to the laboratory. The picture on the whiteboard represents the laboratory setup that your colleagues from group 65a have used for reproducing the genuine Ohm's experiment. You can use the results of their laboratory experiment to introduce the next great idea named voltage diagram. It will help us to visualize the voltages that your colleagues have measured along the resistive film.

Introducing the idea of pressure diagram (an opened water circuit)


By the way, we can derive this idea from the well-known hydraulic analogy (plumbing) that we can see everywhere around us. For example, imagine a large vessel filled of water that supplies a long thin pipe; let's first the pipe to be tapped. The question is: "What is the pressure inside the pipe?" And more precisely speaking, "What are the local pressures along the pipe?"

We can get to know, if we drill small holes at equal intervals along the pipe (if we want to be more precise, we might stick vertically thin glass pipes acting as local manometers). The result is expectable for us: all the water levels (accordingly, all the local pressures along the pipe) are equal. This picture shows the pressure distribution along the pipe; we can name it "pressure diagram".



The pressure diagram of a closed water circuit


Now open the pipe; the water will begin flowing. What are the local pressures along the pipe now? At the left end the pressure is maximum; at the right end it is minimum. Our intuition suggests that the local pressures will decrease gradually from left to the right.

Really, the levels of the water bars (accordingly, the local pressures along the pipe) decrease gradually from left to the right. The envelope of the pressure diagram is a triangle.



Conveying the idea of pressure diagram to voltage one
Let's now apply this powerful idea to draw the analogous electrical voltage diagrams. The idea is obvious: if we think of voltage as a kind of pressure, we may present the local voltages by local voltage bars in exactly the same way as we have presented the local pressures along a pipe by a local water bars! As above, the lengths of the voltage bars are proportional to the magnitudes of the local voltages regarding to ground (we might set the zero voltage level at the height of the resistor and then to draw the positive voltage bars above and the negative voltage bars below the resistor's level). The set of these voltage bars forms the whole voltage diagram. We can use the envelope of the voltage diagram instead the very set of voltage bars, in order to simplify the image.







Making a computer draw a "living" voltage diagram on the screen
Basic idea. But it is too hard and boring for us, human beings, to draw all the voltage diagrams when the circuit attributes (voltages and resistances) vary. Because these diagrams have to be not static, dead pictures; they have to be "living" diagrams (animations) that change accordingly to the circuit state. So, wee need a computer that "watches" closely what we do with the circuit under test and builds the according "living" voltage diagram on the screen. Then, let's build such a computer-based system and leave it to do this donkey work:). Then we will only look at the picture on the screen and think about the circuit phenomena behind it!

Components. First at all, we need some computer. It may be humble enough, if only it has some graphical possibilities (for example, the computer that is used in this laboratory to build Microlab system in 1986 is a version of the famous Apple II). Then we have only to connect to the PC buses a few analog-to-digital converters (ADC's) acting as analog inputs and a few analog-to-digital converters (ADC's) acting as analog inputs and our computer-based system Microlab is ready!



Power supply. Note that the analog-digital periphery "sucks" energy directly from the poor computer:); so, it acts not only as a computer but it supplies the periphery too. Then can we supply the very resistive object as well? Can we use the very DAC's to supply the resistor under test? This will allow the computer to control the obect! Only, the DAC's can give maximum 10 mA by their op-amp outputs. So, we can't supply the low-resistive (10 Ω) wire of group 65a!





Resistor. Do you remember the linear 4.7 kΩ varying resistor from the previous laboratory exercise? As far as I can remember, we carried out a "reverse engineering" then taking it to pieces:) What do we do now? Suggest a solution!  A student: Yes, I do... Obviously the colleague suggests to supply such a resistor by the DAC's 10 mA outputs without any problem (calculate the maximum current). Thus we can use it instead the low-resistive wire. Then we supplied only the one of the resistor's terminals. Now, let's complicate the arrangement and make it more confusing:) by supplying both the ends (we suspect it might be very interesting). Well, connect AO1 (DAC1) to the right and AO2 (DAC2) to the left end of the resistor.



Voltmeters. What do you think, wheather to connect the two old-fashioned but attractive bipolar voltmeters V1 and V2 to observe the input voltages? Or to rely only on the abstract digital VOM's and the digital meausurements on the screen? I see, you like the good old meters maybe because they are something "live", moving, geometrical, spatial, real... People trust such genuine things... But is there any problem as these "antiques" have 20 kΩ internal resistance)?

Ground. Now, let's say also some words about ground. But what is ground? We can find a possible answer in the Wikipedia article about virtual ground. Shortly, ground is a reference point, regarding to which we measure voltages. The PC power supply that we use is the so called "split supply". It consists of two 12 V supplies connected in series (- + >>> - +). The middle point serves as ground in this arrangement. The DAC's grounds are connected internally to this ground. We have also to connect the black test ends of our voltmeters to this ground.

Software. More than twenty years ago, I prepared a program that can visualize the voltage diagram on the screen as a "living" animation. For this purpose, the program make computer "interest" in the local voltages in three key points - the left end point, the slider intermideate point and the right end point. Let's then satisfy its curiosity:) by connecting, for a start, the DAC1's output to the ADC1's input and the DAC2's output to the ADC2's input.



Group 67a (Tuesday, March 18, 2008, 16.45 h)
The theme of the practical lesson is: Walking along the resistive film The first thing we did on this practical lesson was to reproduce Ohm's experiment, because Ohm's law is the base of the electronics we study. The idea of our practical and theoretical lessons in our course of electronics is to invent everything, every single element (even the resistor). So we started imagining how Ohm did his famous experiment and found the fundamental relationship between the current, voltage and resistance. He did his experiment in the beginning of the 19th century. This means only thing he could use as a power supply was the forerunner of the electrical battery, created by Alessandro Volta. Unfortunately this experiment failed, because Ohm used a wire with very low resistance so the power source was loaded. For reproducing Ohm's experiment we used a resistive wire. In the lab we used a power supply (maximum current 2.5A, maximum voltage 10V), voltmeter and ammeter. So we started the experiments.

Experiment N1:  The scheme we were examining is shown on fig.4 in the main module. We move the voltmeter in this way: one of its ends is connected with the ground and the other is walking on the resistive film by a crocodile clip as a slider. Apparently the measured voltage is 10V no matter where the crocodile clip is along the resistive film.

Experiment N2: The scheme we were examining is shown on fig.5 in the main module. Now we have a change in the measurement of the voltmeter. We can see change is linear.

So now is appropriate to make the hydraulic analog: the tapped pipe and the opened pipe. The illustrations are shown at the main module.

We slide the crocodile clip along the resistive film. This is equal to using a potentiometer. The potentiometer is practically a movement-to-voltage converter. According to the fact that the resistance is distributed linearly along the wire, we can conclude that this converter is linear. So there was a new idea: why don't we stop moving the crocodile slider, leaving it in a certain point on the resistive wire and start changing the input voltage?

Experiment N3: We have 2 voltage sources. One of them (the left one) varies and the other is constant. We see the results on the screen of the computer. You can see the illustration attached it the subtopic in the main module: V1 varies: a left-controlled voltage-to-voltage converter.

$$\ Vout = \frac{r2}{r1+r2}.Vin1 $$

Experiment N4: Now the right one varies and the left one is constant. We see the results on the screen of the computer. You can see the illustration attached it the subtopic in the main module: V2 varies: a right-controlled voltage-to-voltage converter.

$$\ Vout = \frac{r1}{r1+r2}.Vin2 $$

Experiment N5: Now both of the voltage sources vary. We see the results on the screen of the computer. You can see the illustration attached in the subtopic in the main module: Both V1 and V2 vary: a resistive summer.

$$\ Vout = \ \frac{r2}{r1+r2}.Vin1\ + \frac{r1}{r1+r2}.Vin2 $$

As we can see this is a summer with coefficients:

$$\ a = \frac{r2}{r1+r2} $$

$$\ b = \frac{r1}{r1+r2} $$ Since now we have seen the results only when the input voltages are positive. Now we change the polarity.

'''We can see that there is one point we can see on the screen on the computer with zero-potential. This is the famous virtual ground. This point moves on the horizontal axis. So there was a new question – can we make this moving point a fixed one? The answer is yes. There is one element that controls its output in according with the input voltage. This is the operational amplifier. This element keeps the virtual ground at point A. See the illustration: a passive resistive subtractor and of course the negative feedback game.''' Vsj 67gr (I have also placed a copy of this "web laboratory report" on my user page).


 * Virginia, what can I say after reading your excellent material? It is just wonderful! Thank you. I am so glad since my teacher's dreams about joining my students to this exciting wikibooks project are finally realized. Now, you might copy portions of this text that differ from the already written text to the main module. Please, do it until the end of the week; your colleagues from groupe 67a and I might help you. I wish you success. Circuit-fantasist (talk) 09:31, 27 March 2008 (UTC)

Group 64a (Thursday, March 20, 2008, 13.45 h)




Group 68a (Thursday, March 20, 2008, 16.45 h)








Group 64b (Thursday, March 27, 2008, 13.45 h)
Before the exercise our group is very excited to reproduce Ohm's experiments from the past.







Group 68b (Thursday, March 27, 2008, 16.45 h)
In the beginning, we had an "accident" with a $3 Chinese multimeter (VOM) - when we plugged its black test lead into the jack it just went down and disappeared. Then we decided to take advantage of this opportunity and began applying a kind of reverse engineering to it:) Tell here what you have seen inside the multimeter...





More discussions

 * I speak fluent German and I started looking for original works of Georg Simon Ohm -- he lived and worked in the cities where I used to live or stay. Anyway, I was trying to feel the climate where Georg Ohm worked and discovered what now seems obvious to us. Here is his main work - Die galvanische Kette] (in German). I am in the process of reading and don't want to rush thru this fine piece of art. Ohm was a very fascinating person - first, he was a striving bachelor. Suddenly, Ohm got a hold of Volta cell (really, that was a hydrogen cell, right) and established an Ohm's Law by his name with the help of a burner (some question why wasn't he using a Bunsen burner?). However, there was a something called now a Baghdad Battery http://en.wikipedia.org/wiki/Baghdad_Battery My question is: was Georg Ohm the first to notice and/or put it in writing? Ohm's law, I remember, one of my better teachers used to say that Ohms Law can explain almost everything in electronics, regretfully "I have to teach you the other stuff, too'. He was right, look at Richardson Law, how similar it is to Ohm's law or take magnetics...strictly ohm's law... MikeZ (talk) 14:36, 24 March 2008 (UTC)


 * MikeZ, thank you for the link pointing to the remarkable Ohm's work. As I can see, you speak German very well; so, can you read Ohm's publication and tell us (my students and me) what Ohm's laboratory equipment was? What was his voltmeter, ammeter, power supply, etc.? Were they really an electroscope, a magnet needle and a thermocouple? I second your teacher who used to say that Ohms Law can explain almost everything in electronics. I also try to explain almost everything in electronics by using only Ohm's and Kirchoff's laws; my students will say, if I have managed to make it:) Circuit-fantasist (talk) 17:47, 24 March 2008 (UTC)


 * I skimmed quickly thru the book of Ohm -- rather boring treatise. It appears to me that he made every effort to make the simple matters as complex as possible - his revenge on his peers who underappreciated him. It is pretty much mathematical analysis of differential debate of electrostatics around the wire. The whole 280 pages would bore anybody to death. I suspect that this is an afterthought after he came up with his famous equation. As you know most of the works from that time are boring and hard to follow - I guess they didn't have any TV yet so they spent their time writing books.


 * I went thru his other works and I noticed there was something that he wrote about Becquerel, like he was explaining that Becquerel did not do everything the way Oms thought he should have. I started digging and found that:  That is interesting because as you remember Seebeck won a dispute with Ohm later about sound theories. I can imagine Seebeck was not happy that it was Ohm who got the credit for teh 'Ohm's Law'. Also, that article mentions where Ohm got his source of electricity: from Seebeck and I thought he got it from Volta. I have a small refrigerator in my car that I use to keep the food on the way from the store to home. It uses a thermoelectric effect, pretty basic stuff. The switch determines if I want to keep the food warm or cold.


 * (page 155) is a fascinating account on she state of German Physics in the 1820s. Also page 156 confirms my impressions about Ohm's writing. Leitung der Elektricitaet mentions Becquerel working on conductivity of metals.


 * This story tells about Ohm's experiment. The apparatus used by Ohm was as follows. Current flowing through the metal bar in the center cylinder deflects a magnetized needle suspended above it. The deflection angle is proportional to the current. The source of electric potential is a thermocouple (discovered by Seebeck in 1821). The ends of the thermocouple are heated by steam and cooled by ice-water in the small containers on the tripods. The use of a thermocouple made the measurement possible; other sources of potential available in the 1820's were too unreliable." Remember, in those days they did not have $3 multimeters (good to 20A DC) and they did not have batteries. Wire insulation was silk and had to be made by the experimenter. For them concept of current and voltage was abstract, almost revealed by God himself. Not long before they stopped drowning women suspected of witchcraft (there are still in Germany gallows by the roadside left from those days and they look very functional too ;) So in those dark ages, physicists attempted to explain why there were obvious discrepancies between different wires, what was electric current and how it was related to electrostatics. Which way does the current flow anyway? The answer depends on the educational background of the person: academia has one answere and Navy technicians are of different opinion ;)


 * Nothing is cast in stone and much depends on the ability of the school which allows (tollerates) new ways of teaching and explaing. You Cyril are one of the very few teachers who dare to attempt the new. MikeZ (talk) 07:26, 25 March 2008 (UTC)