Regarding what you called resistive adder/subtractor, I'm currently considering to use a potentiometer (ok - the digitally controllable variant) to adjust the gain of an OpAmp: regarding the inverting amplifier, a potentiometer with the wiper connected to the OpAmp's input allows fine adjustment of the gain.

Nice application where you can change the amp gain from infinity (open loop) up to zero (100% negative feedback). So, the potentiometer acts here as a device with digitally controlled resistance ratio (1). Accordingly, the conventional potentiometer can be considered as a device with mechanically controlled resistance ratio (2). Since it seems quite such devices based on the potentiometer to be "invented", I offer to number them, e.g., in brackets. Thus, at the end of the discussion, we may publish a booklet entitled "101 potentiometer circuits ":)

And really, in the circuit of an inverting amplifier, this device is an adder/subtractor with weighted inputs that sums two voltages with opposite polarities - the input voltage and the op-amp output voltage. The result of this subtraction shows if the system has reached the equilibrium (virtual ground)... and as it is applied to the inverting input, it forces the system to reach it.

Starting to talk about this legendary device, maybe we should first explain what "potentiometer" means. A voltmeter measures voltage, an ammeter measures electricity... but what does a potentiometer measure? And how is it possible the simple resistor to be a meter?

OK - let's go on thin ice :)

'Potentiometer' would imply this is a meter that measures 'potential' (difference). But INHO this is misleading, because the potentiometer is no classical 'meter' at all as it gives nothing useful unless powered. And the values always depend on how it is connected.

A functional description could be 'dual way (angle) to resistance converter with opposing characteristics'. So it is converting an angle or a way to some resistance.

Hmmm... the discussion started gaining speed like an avalanche starting from a humble resistor:)

I think they really began to call this device "potentiometer" when they began to use it as a component of an arrangement for voltage measurement (I suppose it was in the middle of 19th century). It is interesting that nowadays the op-amp non-inverting amplifer exploits the same idea.

But this is only one of many other possible applications of this device where we can name it with various names according to the specific application. So, in my opinion, we should devise a "neutral" initial name for the "pure" resistive device and then to name it depending upon the particular application.

Are you agree? If so, I suggest to name the bare unconnected "potentiometer" with the neutral name "3-terminal variable resistor" (3).

Hmm, "3-terminal ..." does not fully describe it. I was already considering something like "ratiometer" (no typo - nothing to do with radiometer). Corresponding measurement setups are called "ratio metric" in my current field of work (automotive).

Let me add my share here. Even though the potentiometer is a device whose resistance can be controlled, usually there is no easy way to know what the resistance is unless you disconnect it and measure it. So when do you use a potentiometer?

1. When you want to smoothly change the voltage drop on another device;

2. When you want to demonstrate what happens when there is no impedance match.

Right now my students use potentiometers only in the Transmission lines lab (as part of the Theory of electrical engineering classes). It is used to demonstrate the change in the amplitude and the sign of the reflected wave when the load does not match the characteristic impedance of the line.

I hope I am not redundant  when I say : 

Easy resistor changing (dreadful was Rheostat )

Variable load (may be application) 

Gain variations (using pot) - like a divider !!

In series (Rs) helps control current (Ohm's law)

Bridge circuit to estimate (or fine tune value ) unknown R

maximum power transfer (DC analysis) 

Thevenin and Norton (I know slightly off beat)

flip side - noise source ...

U. Dreher, your "ratiometer" is a more sophisticated device... and maybe we will include it later in our "101 potentiometer circuits"?

Boris, note the question is not only about the bare  potentiometer but about the circuit concepts that can be presented by a potentiometer. Indeed the output of a potentiometer is not precisely determined but this is usually done by connecting it in the negative feedback loop (including a human being). Usually, moving the potentiometer slider, we set some other value (voltage, volume, etc.) without being interested in the exact values of the resistances inside it.

Aparna, thanks for the responsiveness and benevolence as well as original answers; they always help me to build what I planned on. IMO your suggestions can be summarized as follows: variable resistor (4), particularly variable load (5) and controlling element (6) when connected in series to a load, analog voltage divider (7) as a  feedback network.

Thank you Prof Mechkov for the kind words...

Okay, let's before continue with the unveiling of the secrets of the humble potentiometer check in Google if it is of interest to people:

https://www.google.bg/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=potentiometer

Oh my God... more than 10 million pages! It turns out  this is a very hot topic!

If so, then we can afford to go deeper into its philosophy...

hi Cyril,

we can use potentiometer as current limiter,current scaler,voltage devider, and current/voltage sensor.Basically only this ,but these properties makes it as a versatile device to use it in various technical applications.

Dear Kumar,

The potentiometer is usually considered as a voltage device but you have shown here a few current applications. Can you say something more about them?

I like to compare the function of a potentiometer with the properties of two resistors connected in series (with an idealized piece of wire). I think, in principle, there is no difference. However, we are using different explanations for describing what happens.

(1) We say that the current through the two resistors "produces" a voltage drop across each resistor (proportional to its value according to Ohms law).

(2) While this is true also for the potentiometer, here we sometimes are using another explanation based on the electrical field strength within the whole resistive path of the potentiometer. A simple description is based on the length of both resistive portions which is proportional to the corresponding portion of the electrical field and, hence, to the corresponding voltage (drop).

(3) This equivalence raises the following question: Is it physically correct to say that a "current produces a voltage drop across a resistor"? Perhaps the usage ( the invention?) of "electrical current"  is only something like a brilliant (abstract) idea/ imagination which helps us to design or analyze such circuits?

I think, in this context it is important to recall that in reality there is nothing like a "current source". Each current needs a driving voltage - and a "current source" is nothing else than a voltage source with a sufficiently large internal resistance. And this knowledge would allow us to use the "potentiometer model" (voltage drop according to the electrical field distribution) for all kinds of circuits (without defining any currents). However, I agree - the invention of currents simplifies everything.

Can you agree to these considerations? 

Surely for a healthy discussion , Current sources are important because they have temperature dependency and once that changes so will current. Also, Ohm's law does say it is material property and flowing has its issues so it is helpful when we look at potentials (voltage drops to quantify) 

Yes Lutz, I fully agree with you that a potentiometer is nothing else than two resistors connected in series...

In this configuration, the  voltage drops Vr1 and Vr2 across the two resistors r1 and r2 as though are connected by the common current I flowing through them. As a result, we arrive at the famous equation Vr1/r1 = Vr2/r2, and accordingly, Vr2/Vr1 = r2/r1 (the two voltages relate as the belonging resistances).

So, if we change the one of the voltages, the other will change with the proportion r2/r1 (r1/r2).... and, for example, we can see this arrangement in the ubiquitous common-base amplifier and op-amp inverting amplifier:

https://www.researchgate.net/post/Is_there_any_relation_between_the_common-base_amplifier_and_op-amp_inverting_amplifier

...

...But, I continue thinking, in the classic potentiometer arrangement, we change neither the particular Vr1 nor Vr2... we change the overall voltage V across the whole resistive network... and accordingly, the common current I = Vin/(r1 + r2)... In this arrangement, V acts as an input quantity Vin.

But still, if we want, we can change as an input quantity either Vr1 or Vr2 if we change V so that to make the according voltage drop (Vr1 or Vr2) equal to the desired input value Vin. This actually means to act as a "manual servo system" with negative feedback.

A good example of this arrangement can be the common-emitter amplifier with an emitter degeneration (e.g., a phase splitter) where the transistor adjusts the voltage drop Ve across the emitter resistor Re (almost) equal to the input voltage Vin. Due to the "current connection", the voltage drop across the collector resistor Rc is proportional (Rc/Re) to the emitter voltage Ve and, accordingly, to the input voltage Vin...

Another (already perfect) example of this idea can be the ubiquitous inverting amplifier where the op-amp makes the voltage across the input resistor R1 equal to the input voltage Vin by changing the overall voltage across the entire resistive network R1-R2.

But let's return to the "mere mortal" 19-th century potentiometer...

As Kirchhoff even then noticed, in this 2-resistor network, the two voltage drops are complementary (Vr1 + Vr2 = V). But what is even more interesting in the case of the potentiometer, the two resistances r1 and r2 are also complementary (r1 + r2 = R). And, as a result, what is the most interesting here, the current is constant regardless of the state of the potentiometer - the ratio r2/r1 varies but the sum r1 + r2 stays constant... and as the voltagee is constant, the current stays constant as well...

Note that we can put in practice this "complementary resistances" trick in two ways:

First, we can realize it "analytically" by connecting in series two opposite varying resistors without mandatory varying their dimensions. We can do it if somehow vary "ρ" in the famous equation R =  ρ.l/S (e.g., by using photo-, thermo- or other resistors). In electronics, all the complementary stages (e.g., CMOS) do this "magic" when operating in the active region. Another example can be the Dreher's digital potentiometer above, where binary weighted resistors are commutated...

But in the distant 19-th century, they realized "geometrically" this complementarity (varying "l" in R = ρ.l/S), in the possibly simplest and natural way.... using the well-known fact from geometry (and common sense) that an intermediate point splits the section of two complementary subsections. So, when moving a slider along the resistive layer of a "naked" resistor, the one resistance increases while the other decreases but their sum (the total resistance) stays constant... so they are complementary...

Maybe this was the first automatically operating current source? Well, think of the one partial resistance as of a load... and of the other complementary partial resistance - as of a regulating element. Then move the slider so that, for example, the "load" decreases its resistance. But the "regulating element" will increase its resistance so that the total sum, and accordingly the current, will stay constant.

Now look at the classic transistor current source and you will see that it exploits exactly the same complementary idea.

http://www.circuit-fantasia.com/circuit_stories/understanding_circuits/current_source/simple_bjt_current_source/simple_bjt_current_source.htm

Cyril - what do you think about my sentence

"This equivalence raises the following question: Is it physically correct to say that a "current produces a voltage drop across a resistor"? 

As far as my understanding/interest  is concerned THIS was the main point of my contribution. The "famous equation" Vr1/r1 = Vr2/r2 did serve only as the starting point for my further claims and questions.

Dear Lutz,

Thanks for the enthusiastic contribution that helps us to conduct a fancy discussion about the so simple but so clever device... an example of another elegant simplicity...

No, I think it is not correct to say that a "current produces a voltage drop across a resistor". I think it is more correct to say that the partial voltage drop across the resistor is lost on this resistor. This voltage drop belongs to the exciting input voltage... it is not "produced" by this resistor... it is lost...

Hi Cyril and what about capacitor or inductor dividers?

Josef

Dear 

Cyril Mechkov 

Potentiometer as a current device:As we all  know  wheatstones bridge ,instead of connecting 4 resistors connect 2 similar potentiometers like, connect extreme terminals as 2 pairs ,connect one pair to Vcc other to ground .connect an ammeter between the center terminals.At balance current through ammeter is zero,at imbalance ammeter reads a small current.

 in many measurement circuits(transducers) current is measured in terms of voltage and vice-versa

with regards

vasanth   

Josef, it would be a great idea to explain intuitively "capacitor or inductor dividers" (without complex numbers or operational calculus)... but let's first finish this "fairy tale" about the potentiometer:)

Exactly, Vasanth!

Don't you think that your bridge configuration above can explain the origin of the name "potentiometer"?

Lutz's question is really about attributing cause and effect. If we say 'current produces a voltage drop across a resistor', we attribute the role of cause to current, and the role of effect to voltage. But in some situations, we might use a descriptive phrase such as 'the voltage applied to this end of a resistor produces a current ... '.

I think these examples say more about the way we apply our imagination or intuition when describing circuit action, than it does about causal relationships as such.

David - thank you for this clarification. You hit the point.

"Is it physically correct to say that a "current produces a voltage drop across a resistor"?

I like to come back again to this question. Let me explain:

(1) Let`s imagine we have an ideal voltage source Vo - however, without any conducting connection between both poles. As a result we have a widespread  electrical field.

(2) Now we connect both poles with a resistor R. As a result, the source voltage will be the same - but the electrical field now is concentrated within the resistive body.

(3) Replacing R by a series combination R1+R2 will in principle not change the situation - however, now the electrical field is split into two parts depending on the resistor values: E1/E2=R1/R2.

Of course, this is equivalent to V1/V2=R1/R2 and leads to the classical voltage divider expression: V2=V*R2/(R1+R2) .

(4) As we can see, for finding V2  it was not necessary to use such a "phenomenon" like "electrical current" .

That was the background of my question:  Does such a current really exist? Does such a current "produce" the voltage V2 (as we always think) ? Or is the invention of the "electrical current" nothing else than a brilliant idea which allows us to simplify calculations?

As an example: It is possible to design a BJT amplifier in classical common-emitter configuration without using any current. However, in this case the transistor characteristics [Ic=f(Vce) and Ib=f(Vbe)] must be given in resistive terms, which is rather uncommon but possible!

An incredible discussion! Thank you Lutz, David and others for so interesting points of view! I think to discuss the 19th century potentiometer in the 21st century is no less exciting that to discuss the 21st century microcontroller in the 19th century:) Let me add more thoughts about the nature of this this unpretentious device device. Maybe they are somehow related to the profound Lutz's thoughts above and can second them...

I know it sounds incredible... but when moving the potentiometer's slider, what we do is... nothing (I mean a unloaded potentiometer)! We do not change any resistance nor current nor voltage nor anything else... We just peeking inside a "naked" constant resistor and only change our observation point... as my students were doing in 2008:

https://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film

It seems the so called "potentiometer" is nothing else than a naked constant resistor... and we only carefully grope its surface by the slider!

We do not change the resistance since we do not change the length "l" in R = ρ.l/S... it is preliminary defined. We only use a part of it... but the rest part complements it... so that the overall resistance stays constant...

And we can continue:.......and the slider allows us to divide the electrical field within the device into two portions E=E1andE2 , which are equivalent to two corresponding resistances R1 and R2.

But Lutz we need a current to flow through the resistor. The current is this "transmission" that carries the electrical energy and distributes it along the resistive layer. IMO the current is those that "divide the electrical field within the device into two portions E=E1andE2 , which are equivalent to two corresponding resistances R1 and R2".

Imagine that we have increased the resistance up to infinity (an opposite experiment to yours above)... and there is no current flowing... but our slider stays at its previous place... Will be the electrical field divided into two portions without any resistance and, accordingly, current? I have no heard about a pure "field divider"...

Dear cyril

You are really a different kind of tutor/observer/engineer even today you look at things with adiffernt

"But Lutz we need a current to flow through the resistor."

Cyril - why? Do we need a current to flow for producing an electrical field?

"Imagine that we have increased the resistance up to infinity (an opposite experiment to yours above)... and there is no current flowing... but our slider stays at its previous place... Will be the electrical field divided into two portions without any resistance and, accordingly, current? ."

Increasing the resistance to infinity means: No resistor at all across the voltage source. So - why should I ask for a slider if it does not exist? Or - is there any misconception on my side?

Lutz, IMO we need the resistance and accordingly - the current, to divide the applied electrical field into two partial fields...

According to my knowledge, it is the E-field within the resistor that allows a current to flow. That means: First E-field and then current (movement energy is given to the electrons).

Voltage is nothing else than the integral over the field along the length of the resistive material. And - integrating only over a certain portion of this length gives a corresponding portion of the voltage. For this, I do not need any current. Am I wrong?

Then what is the role of the current?

Here is how I use cause and effect relationships (existing or deliberately introduced) to build in a logical succession passive circuits at the beginning of the course in Basic circuitry.

http://www.circuit-fantasia.com/my-students/ske2004/classes/current-ske-1.htm

http://www.circuit-fantasia.com/my-students/ske2004/classes/current-ske-2.htm

http://www.circuit-fantasia.com/my-students/ske2004/classes/current-ske-3.htm

This was in the distant 2004 but I continue using this approach with my students.

So, we can present a potentiometer as a combination of a voltage-to-current converter and a current-to-voltage converter...

What is interesting here is that they are not simply cascaded but the latter is nested inside the former. That is why the transfer ratio of the simple potentiometer is R2/(R1 + R2) instead the tidy R2/R1...

But still there is a way to make it R2/R1... it is interesting to see how...

"Then what is the role of the current?"

Yes - that was my basic question from the beginning:

Is it PHYSICALLY correct to say that the current would "produce" the voltages across both parts of the potentiometer?

I think, the current does exist (a) as a result of the applied voltage (resp. the corresponding E-field within the part) and (b) it is the "role" (consequence) of the current to produce heat (electrical power). 

My conclusion (perhaps wrong?): Connecting two resistors to a DC voltage source Vo enables a current I to flow - however, the voltages (V1, V2) across both resistors are not "produced" by this current but by the corresponding E-field within the resistors.

Without these fields the current could not exist (no mechanical energy transfer to the charged carriers). However, because the strength of the fields is proportional to the resistor values also the corresponding voltages are proportional to the resistor values. On the other hand: Vo=V1+V2=I*(R1+R2).

Hence, Ohms law is fulfilled and we can apply it using the relations V1=I*R1  and V2=I*R2.  That means: We may ASSUME that V1 and V2 are produced by the current I.  But this assumption - IMO - does not reflect the physical reality.

A powerful and challenging viewpoint... It now remains to see what physicists will say...

Cyril - I suppose our last contributions have crossed each other.

Of course, I cannot go through all the referenced links but one short comment to the last of the two figures given in your last text (I-V converter):  

You have assumed that a current I is the input quantity - and because a voltage V is the output (acroos the resistor R) this figure says: V is produced by I.

That is in accordance with Ohms law - and we are allowed to use this relation for calculating purposes.

However, having in mind that in reality no real current source does exist  we can replace the input quantity I by a voltage source Vo and a sufficiently large source resistor Ro. Then, this scheme would be in accordance with my above described model  (Vo connected to two resistors) and my "explanations" (based on the E-fields) could be applied again. Do you agree?

Yes Lutz, I always consider the last configuration with my students to show the imperfections of the simple "resistor current source"...

Each electric field (so also voltage = energy normalized over charge) has "somewhere charge".

Each charge was created by current (movement of electrons).

Each current has caused by some energy (of water, coal, uranium, radiation, wind, chemical reaction).

So what is the first current or voltage :-)) ?

Charge (current) is just only a "chain for transmission of energy".

"So what is the first current or voltage :-)) ?"

Josef - to me the answer is clear: No current without driving voltage.

"Each charge was created by current (movement of electrons)"

Question: Would you really say that the process of chemical charge separation  (battery) for creating a voltage can be called "current"?

Catch -22 everywhere !!

Duality is a necessity assumption ...

Butterfly effect is pertinent ??

Philosophies are necessary certainly not measurement all the time (truth of life ...)

"No current without driving voltage"... no movement without pressure... Yes, it is true...

But due to the inertness a moving body (or water or something else) can create pressure... the kinetic energy is transformed into potential energy... and this is an example of a "flow causes pressure" ("current causes voltage") phenomenon...

In superconductors we are able to store energy "without voltage" - only the current and the magnetic field :-)

Sadly , when I studied transmission lines we did look E-M fields also thought L-stores magnetic field and C -stores electric -rest is history :)

Josef, there the current, once "pushed", then can circulate along the closed circuit up to infinity?

But we can to drain the energy via magnetic coupling - transfer to a current or voltage - transformers.

"But due to the inertness a moving body (or water or something else) can create pressure... the kinetic energy is transformed into potential energy... and this is an example of a "flow causes pressure" ("current causes voltage") phenomenon..."

Cyril - you have startet your considerations with a "moving body" (analogy to "current"). But why does the body "move" (current flows)? I think there was a primary source (pressure resp. voltage).

I refer again to my thought experiment with a real current source (voltage source with a large source resistance). Together with a load resistor we have an ideal voltage source and two  resistors (voltage divider). This scheme allows us to define both voltage drops using the E-field distribution - without using the current through both resistors..

Therefore: Current causes voltage drop? No - I don`t think so. Current is the RESULT of the voltages (E-fields internal to the resitors) only.  That`s my view.

Dear Lutz,

We have reached this point of this discussion many times... but I will add a new thought to it...

Note that at the discussed moment there is no pushing force (pressure)... there is only a moving body. Of course, this moment is preliminery created by applying a force... but in this moment we see only a movement creating pressure.

So, first we have a pressure-to-flow conversion (voltage source), and then, after some time, we have a flow-to-pressure conversion (current source)... and we have this due to the inertness (time dependence)...

In your "instant" example there is no inertness (no time dependence)

Cyril - yes, I know what you mean and I agree. That is the reason we pretend - for practical reasons - that the current would produce the voltage across the resistor. And that is a good and working approach.

However, if we ask for the "physical truth", the answer looks different IMO.

In the resistance varies potential energy of electric field into heat (therefore thermal energy).

If at the beginning is the "fixed" charge, it is actually a discharge of a capacitor.

If available energy source that restores charge on demand, it is a current source (kept constant current) or a source of electrical voltage (kept constant voltage).

I bothered to do an initial (incomplete) list of the proposed so far possible applications, names, concepts, viewpoints... of what is called "potentiometer":

• dual way (angle) to resistance converter with opposing characteristics (1)
• device with digitally controlled resistance ratio (2)
• device with mechanically controlled resistance ratio (3)
• 3-terminal variable resistor (4)
• ratiometer (5)
• device that "smoothly changes the voltage drop on another device" (6)
• device that "demonstrates the efects caused by the reflected wave" (7)
• variable resistor (8)
• variable load (9)
• controlling element (10)
• analog voltage divider (11)
• current limiter (12)
• current scaler (13)
• voltage divider (14)
• current/voltage sensor (15)
• two resistors connected in series (16)
• Vr1->Vr2 voltage-to-voltage converter (17)
• Vr2->Vr1 voltage-to-voltage converter (18)
• common-emitter amplifier with emitter degeneration (19)
• phase splitter (20)
• automatically operating current source (21)
• transistor current source (22)
• complementary stages as CMOS (23)
• Wheatstone bridge implemented by two potentiometers (24)
• naked constant resistor (25)
• electrical field divider (26)
• cascaded voltage-to-current and current-to-voltage converters (27)
• nested voltage-to-current and current-to-voltage converters (28)
• ......................................................................................................

It remains to figure out (see) only more 73 applications of the incredible device to reach the so desired number 101:)

But what have done we? Imagine we forgot to add "potentiometer":)

Let's do it (numbering it with "0" at the top of the list)!

• potentiometer (0)
• .....................................

Cyril - I don`t understand your last contribution: A device called "potentiometer" is used as a potentiometer? What is the content of this sentence?

Lutz, I mean one of the first applications of this device as a voltage measuring instrument (with a theoretically infinite internal resistance) that gave its name:

https://en.wikipedia.org/wiki/Potentiometer_(measuring_instrument)

You can see my explanation that I (Circuit dreamer) wrote five years ago in the Wikipedia talk page below (click on the Extended content button to see more details):

https://en.wikipedia.org/wiki/Talk:Potentiometer/Archive_2#What_is_.28not.29_a_potentiometer.3F

It would be interesting for me to discuss this topic here.

OK - I see. Thank you.

I also thank you Lutz, because your comment made me seek out this material that I had not looked at since then... and now I had the pleasure to read it...

It reminded me of those dark times when my enthusiasm clashed with heartlessness of those people whom I dedicated later a special RG question:

https://www.researchgate.net/post/What_is_electronics_Wikipedia_inside_and_what_are_Wikipedians_inhabiting_this_area2

Well, if you think a potentiometer can operate in a reversed mode as a voltage-to-movement converter, let's add it to the list of applications:

• reversed potentiometer acting as a voltage-to-movement converter (29)

I would remind that there is another kind of a reversed potentiometer acting as a step-up voltage-to-voltage converter (non-inverting amplifier):

https://www.researchgate.net/post/Can_we_reverse_a_voltage_divider_by_applying_the_input_voltage_to_its_output_and_taking_the_output_voltage_from_its_input

So, we can add it to the list:

• reversed potentiometer acting as a voltage-to-voltage converter, i.e. amplifier (30)

...and why not as an amplifier?

V2=Vo[R2/(R1+R2)]  >>>> Vo=V2[1+R1/R2]  .

Reversed potentiometer acting as a step-up voltage-to-voltage converter is the fancy name of the non-inverting amplifier:)

I have placed the list of possible potentiometer applications, viewpoints and concepts on Google Docs where everyone can edit by clicking the link below:

https://docs.google.com/document/d/1KEEN6TwsEX_4iqZv1lb6Qt9oqMiYsALYEpGkIZH_dh4/edit?usp=sharing

Seriously ! Prof Mechkov, it steps up ???

Yes Aparna, we can make it step up:) Just read the question below...

https://www.researchgate.net/post/Can_we_reverse_a_voltage_divider_by_applying_the_input_voltage_to_its_output_and_taking_the_output_voltage_from_its_input

In the left side of the attached figure, a "normal" voltage divider is drawn; in the right side - a reversed voltage divider is drawn. The reversal is implemented by the help of the op-amp.

Yessss, the right (with opamp) rings a bell ... Thank you

Meanwhile, I had to conduct today the next lab dedicated to diode circuits. Again an amazing exercise has become where we together, my students and I, managed to reveal the secret of diode limiters:

https://www.researchgate.net/post/What_is_the_secret_of_diode_limiters_Can_we_build_these_diode_circuits_in_a_logical_manner_rather_than_giving_them_as_ready-made_circuit_solutions

Perhaps it would be interesting for you?

It certainly would !! These days those non-Si based, drives me *#%)%^

Dear Aparna, would you explain what this mystic message (*#%)%^) means:)

Maybe it's time to tell you about the experiments that we - my students and I, carried out in the laboratory two months ago... when I posed this question. I will show them step-by-step, in a form of a kind of "scenario" with some comments related to our discussion.

As I have mentioned in the question, we drove the potentiometers with combinations of floating power supplies (adapters) - DC (12V/1A) and AC (24V/0.5A)... and this enabled us to all sorts of experiments...

Step 1: negative ground, positive DC variable voltage source, direct-phase AC variable voltage source.

Step 2: positive ground, negative DC variable voltage source, inverted-phase AC variable voltage source.

Step 3: middle ground, split DC variable voltage source, split-phase AC variable voltage source.

https://drive.google.com/open?id=0B45uRPpHPD9hOWU0NWpHckVXVlk

https://drive.google.com/open?id=0B45uRPpHPD9hd0c3M2U0UTlmTGs

Step 4: relative ground, bipolar DC variable voltage source, two-phase AC variable voltage source, bridge.

Step 5: common-mode signal.

Step 6: differential-mode signal.

The summer semester already ends... and also the course of Basic circuits... and it is time to say goodbye to my favorites...

But is there something more satisfying for a teacher than the success of his/her students? So I am very happy that two of them - Georgi Velev and Evgeni Sabev, participated successfully in a Space Apps Challenge 2016 of NASA with their proect Adept... and reached the final... In the laboratory we discussed the circuit of the strain gauge bridge and the instrumentation amplifier.

https://2016.spaceappschallenge.org/challenges/space-station/astrocize/projects/adept

A year ago, their team achieved the same success with the project Valkyrie. Their team leader Martin Kuvandzhiev was then my student...

https://2015.spaceappschallenge.org/project/valkyrie/

https://www.youtube.com/watch?v=qUglQecc2K0

https://www.youtube.com/watch?v=72cvLqnaD0c

How many circuit concepts can be presented by the humble potentiometer? - Before the course Basic circuits I have never thought that we are going to go through so much and new experiments for us. We have been dedicated into a lof of secrets. I and my colleagues are very pride with our worldwide success in the NASA Space Apps Challenge.

I think that such projects of devices including sensors, electromechanical actuators, electrical bridge circuits, electronic analog and digital circuits, microcontrollers, embedded software and mobile applications, are the most live and interesting for young people today...

But to continue in this direction with even greater enthusiasm, these young people need encouragement and praise for their achievements...