It is a common practice to consider the voltage divider as a voltage source, e.g. to say, "the circuit is supplied with a constant voltage by a voltage divider". Also widespread is the resistor to be considered as a current source, e.g. to say "the circuit is supplied with a constant current through a resistor".
IMO it is obvious that the voltage divider and the resistor are not sources; they are only components of composed sources containing additional voltage sources. Thus the composed voltage source consists of a voltage source and a voltage divider and the composed current source - of a voltage source and a resistor. In these arrangements, the voltage divider acts as a voltage-to-voltage converter and the resistor - as a voltage-to-current converter.
The explanation of this simplification is that when we say that the circuit is supplied "with a constant voltage by a voltage divider" or "with a constant current through a resistor", we implicitly assume the existence of an exciting voltage source.
What do you think about this simplification? Is it affordable? Is it misleading?
From my point of view voltage and current sources could be distinguished theoretically only if they are ideal. Ideal voltage source has zero impedance and ideal current source has zero conductivity.
When it comes to real voltage and real current sources they are pretty much the same. Depending on its output impedance the source could be closer to an ideal voltage source or closer to an ideal current source but after all we have duality - any real voltage source could be replaced with an equivalent real current source and vice versa.
This seems like an introduction to circuits question. With the voltage source, as soon as you start drawing current the voltage divider ratio changes. Also, you are wasting current running down your R2 which is a bad practise.
I have never seen such simplification. It is very misleading.
However the voltage source could work for circuits that draw very little current maybe feeding some small CMOS digital logic.
On the contrary, if you try to drive a motor like that, expect anything to happen - it might start, it may not, it may start sometimes, and fail other times. It would burn your LEDs attached to the circuit.
I would highly discourage using this such solution in teaching.
Hi Marcin,
The idea of this question is not to consider the imperfections of the simple voltage source made by a voltage divider and the current source - by a resistor; the idea is to show that the voltage divider and the resistor are only components... constituent parts of the simplest voltage/current sources...
The question is, where would you like to use this simplification and what purpose would it serve?
You cannot depict it as a voltage source if the voltage drops significantly on inserting load. The voltage between your leads could be anything from Vout to almost 0 and you cant tell whats gonna happen unless you know the implementation (resistor values).
If you just call it a Voltage source, then you cant tell what is the voltage it supplies. Consequently, you can never call it "a constant voltage from a voltage divider".
Voltage regulators are cheap small components. I dont know why would anybody risk to ruin a design with the voltage divider as a source.
Research needs to be repeatable for verification. If you omit the voltage divider implementation you are effectively preventing somebody from checking your results.
The simplest depiction of a voltage source would be one using a zener diode. Or still simple, zener diode+transistor or opamp+transistor. Or just a black box voltage regulator that you can buy.
Marcin, thank you for the profound explanations and for the smart remarks... I agree with you that the perfect modern solution, if you need a constant voltage source, is to buy a "black box voltage regulator" from the nearby shop for electronic components. But, as you have noted ("zener diode+transistor or opamp+transistor"), if you "uncover" the chip, you will see inside some kind of a voltage divider again...
I am a teacher whose vocation is to open "black boxes", to uncover the hidden (by producers) circuit secrets... Once you want to discuss this topic, let's do it in a separate question specifically dedicated to it:
https://www.researchgate.net/post/How_can_we_convert_the_imperfect_voltage_divider_source_into_a_perfect_voltage_source
Cyril, there is a difference between a VOLTAGE SOURCE and a VOLTAGE REFERENCE. Voltage sources can provide from mA ranges up to many A. On the other hand, voltage references are designed to provide a very precise voltage, with the idea that, the load on them will be very small (10mA, 20mA). There are many voltage reference ICs that are only capable of 10mA etc ... But, these ICs have other favorable characteristics, such as temperature dependence (measured in ppm). An example is Microchip MCP1525, which is a 2.5V voltage reference, capable only of 20mA or so.
The Voltage divider is a very cheap, yet, very imprecise voltage reference, unless the load is very small (Megaohm range). In the Voltage divider, the lower the resistance values are, the more accurate the voltage reference will be, since the dependence of the reference voltage on the LOAD will go down. Voltage dividers are excellent uA voltage references, and they are perfect to provide a reference to a circuit input that has many Megaohm input resistance. But, if the load is going to be high, using lower resistances will cause excessive power consumption.
As a voltage source, never use them ! unless you will use a source-follower (or emitter-follower) and improve their load capability.
Sorry, but this can't be deleted. The problem was the attachment. See next comment.Thanks.@AlDmour
Excellent answers. However, if presumably the load has to get its voltage through a resistor voltage divider simple circuit analysis can greatly qualify how efficient I can use this supply, or even in cases where the circuit is suggested for providing reference voltage, which is the the name for a power supply of low power capability, one must make sure that the reference voltage provided is stable enough.
My preference in circuits is Thevinin. Using Thevinin, the whole circuit (excluding the load itself) can be converted to the equivalent Thevinin power supply and Thevinin series load (the power supply's internal resistor). I attached a drawing of the circuit before and after thevinin analysis (simplification). Note that Rb is the original power supply internal resistance (usually small) which can be neglected or combined with R2. The presumed power supply shall have a voltage value given Vth equation in the diagram (Vth=R1/(R1+R2)*Vb and the "equivalent power supply" internal resistance shall be Rth=R1//R2. The net load (reference voltage) shall be then VL=RL/(Rth+RL).
From these equations one can determine lots of things about this power supply. For example, to maximize the voltage on load we must make R1 as big as possible (infinite) and R2 as small as possible (zero), hence we go back to square 1, simply connect the load to battery of proper value. same conclusions can be made about power and current. Of course, these are in compliance with the notes by colleagues above.
One note, the divider circuit can be used as a reference with the lower leg resistor replaced by a Zener. Such dividers are used in regulators as feedback circuit to produce a voltage proportional to output voltage or output signal level that can be compared with input or a proper reference.
Success to provide power through dividers can be done (and is usually done) using a magnetic coil with a center tap point (or multiple output points). This is successful because voltage is built using the magnetic field (EMF) and not as drop on a resistor. Thanks.@AlDmour.
Very interesting thoughts... and an excellent picture... The Thevinin theorem is great (no less great is another theorem of equivalent circuit transformations - the Miller theorem). It is a great challenge to explain such a basic truth in an intuitive manner because students do not have a clear idea about it...
I completely agree with your considerations about the values of the voltage divider elements...
Oh, one more comment : I would put the "voltage divider" in the "not-so-precise-voltage references" ... Within that category, don't forget the Zener-based and zener-based-buffered voltage references ... pictures attached ... clearly not remotely as pretty pictures as Ismat's :)
If I had to "rate" the quality of the voltage references, here is how I would rate them:
Temperature Dependence:
======================
RESDIV=GOOD(3) ... ZENER=GOOD(3) ... ZEN-BUFFERED=FAIR(2)
Load Response:
======================
RESDIV=POOR(1) ... ZENER=FAIR(2) ... ZEN-BUFFERED=GOOD(3)
Low-load Voltage accuracy:
======================
RESDIV=GOOD(3) ... ZENER=GOOD(3) ... ZEN-BUFFERED=FAIR(2)
There are other metrics, of course. But, in general, I have been answering Cyril's question in terms of "Analyzing the voltage divider as a voltage reference"
Tolga, thank you for the comprehensive comparison and for the hand-made pictures (BTW I completely switched over to colorful whiteboard drawings).
It is obvious that the voltage source made on the base of the genuine (ohmic resistor) voltage divider is a poor voltage source with regard to the loading (the main characteristic of a voltage source). Making the lower resistor dynamic solves both the problems (input voltage variations and moderate load variations) while the buffering solves only the second problem (big load variations). Combining the two techniques allows to compensate input voltage variations and big load variations...
I would like to remember another technique for creating voltages - the Norton's idea. This means to replace the upper resistor with a constant-current non-linear element (transistor) and to take the voltage across the lower resistor as an output (the buffering is advisable). Thus we have four constant-voltage divider configurations (one linear and three non-linear):
* resistor - resistor (necessarily supplied by a constant voltage)
* resistor - diode
* transistor - resistor
* transistor - diode
Of course, the next step is to bring out the big guy ... OPAMP !
Here, since the resistor divider has pretty much zero load, you can use real high resistor values ...
Well, we are getting pretty close to designing a voltage regulator ... !
This, incidentally, answers another initial question you asked: as long as you can trust the Vin being fairly stable, and using the OPAMP as an impedance buffer, resistor divider is about the best option as a voltage reference
Don't you think that we are in a vicious circle - to obtain a constant output voltage we need a constant input voltage?
(There is a small typo in the picture above - the op-inputs are swapped)
Thank you for the op-amp circuit - there is a great idea inside it (connecting the transistor in the negative feedback loop). Here is an animation dedicated to this trick (another gift for you:)
The idea is simple - the op-amp increases its output voltage so that to compensate the Vbe voltage drop:
Tolga, you brought the issue of a voltage reference by the voltage divider and then you made comparison. Thanks. It is a nice comparison. One more important factor is the power supply variations. I think the voltage divider is not used used in practice as a reference as well because of this factor in addition to effect of the load response. To have a voltage divider as a reference, the power supply feeding it must be a reference itself as the effects of power supply variations can reflect proportionally on reference voltage on the resistor. This ends up with 2 basic reference circuits of a zener (for low loads/supply variations) to the zener buffered circuit (for moderate to high regulation).
One more thing in Cyril's question above concerning the current source through a resistor. What do you mean by that Cyril?. I think practically their are no current sources. What we can have is voltage sources with their currents controlled. You can't by 1A battery (regardless of the voltage) but you can buy 9V battery which can deliver currents from 0 (open) to maximum. Thanks.@AlDmour
Ismat, thank you for the support! Interesting discussion... Yes, you are right about the power supply...
IMO the problem is that the voltage divider is initially designed as a proportional device (attenuator). It is just a divider (multiplier) whose output voltage is proportional to the input voltage - Vout = (R1/(R1 + R2)).Vin = K.Vin, according to your picture where R1 is the lower resistor. But we have to make it constant. How do we do this magic?
The trick is simple. We have to make the product of the two variables (K and Vin) constant. So when Vin changes, K has to change equally but in the opposite direction so that the product can stay constant. So we need a dynamic K (transfer ratio) with a "negative direction coefficient":) We can do it in the three possible ways shown above - "resistor - diode", "transistor - resistor" or "transistor - diode"...
We can think of this technique as of a kind of passive compensation...
Oops. Sorry for the OPAMP swap ...
This is the problem with the voltage divider (VD) in general. You can make the voltage divider extremely accurate with 0.1% resistors (I do that all the time) . However, as a voltage reference, it is as accurate as the Vin ... like both of you brought up. So, the best thing to do is to use the voltage divider to "down scale" a voltage, and use an OPAMP to "upscale" a voltage ... notice, even to "upscale," you still need upscale resistors ... So, the upscaling is the "reverse" voltage divider.
In other words, In a voltage divider , Vout=Vin R1/(R1+R2) ... Whereas OPAMP allows you to "flip" the equation , Vout=Vin (R1+R2)/R1 ...
So, for instructive purposes, this is nice to teach ...
However, of course, you are dependent on Vin ... This is a problem if the goal is to get an accurate REFERENCE Voltage ...
Ok. Here you go., Staying true to the original question of RESISTOR DIVIDERS. Adding to the book of 10 things I love about resistor dividers :)
Voltage supply variations are gone ...
You can control the output voltage with the Pot ... Notice that, I used a SUPER ZENER (TL431), which creates a steady 2.5V reference at the + input of the OPAMP.
This is a very common device (it is actually an IC). It is a 3-terminal Zener. The output can be controlled with the 10K POT. 10uF is for noise clean-up ... OPAMP tries to match the (-) input to 2.5V ... Since, + and - pins are VIRTUALLY SHORTED ...
Notice that, the beauty of a passive resistor divider is that, it doesn't require a MINIMUM CURRENT to regulate ... The TL431 , just like the regular Zener, does ... It is 10uA or something ... Not bad, but, it burns power ...
Ooooooo .... so many fresh and original suggestions against the background of the widespread grayness... I like them... and I am happy that you are here, Tolga!
Do you share the view that a non-inverting amplifier is simply a reversed voltage divider?
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
It is interesting to peek inside this "super Zener" TL431 and to grasp the idea behind it...
Got it. I put this answer there:
Oh, may I also add a third variant you forgot in this question Cyril ?
you presented,
a) passive voltage divider, where k 1 (you presented it)
c) why not, an ASTIVE one like (a), with the OPAMP,
What good this would do ? Well, it is IMPEDANCE MATCHING ... In other words, it will create a voltage divider which is immune to load ...
that resistor allows SOME current to pass for regulation. Otherwise, the output voltage might get unstable when there is no load
Look at the potentiometer on the left (the network 100 k + 10 k) - is not it such a load?
Sure. This is good enough for ULP (Under-Load Protection). Sorry, it is a habit for me to draw that.
I think a separate emitter resistor would be necessary to close the DC collector path if the voltage divider was connected via a decoupling capacitor to the emitter...
Tolga, honestly, I am fascinated by your recent participations in all these discussions about the "simple but complex things" in the basic electrotechnics... Of course, we consider simple electrical elements with the idea to use them in complex electronic circuits... and your op-amp circuit above is a good example...
We may name it in a more traditional way a "buffered non-inverting amplifier". But it is extremely interesting not only from the perspective of this specific voltage regulator implementation but of a much more general point of view... so it deserves to examine it deeper... And as I know you have a sense of humor... and you (probably) will not take my story below in bad... I will allow myself to tell it in a little bit funny and unusal way...
Imagine that you want your students to listen open-mouthed you:) when explaining this interesting op-amp circuit... You have two choices to do this. The first is to use banal, dull and sterile explanations repeating verbatim written in the electronics "cookbooks" over the years (i.e., "do not seeing the forest for the trees"); then your students will listen you with wide open mouths just because they will yawn:) The second option is to reveal the basic idea behind this circuit ("tо see the forest for the trees") in an impressive and imaginative way; then your students will listen you with wide open mouths just because they will be fascinated by your explanations... Here is my suggestion how to do it.
Shortly, you may present the circuit as a "double-disturbed op-amp follower" where two "disturbing" elements (the emitter follower and the voltage divider) are consecutively connected (cascaded) in the negative feedback loop (see the attached picture); the first disturbance (the base-emitter voltage drop Vbe) is additive while the second disturbance (the attenuation K) is multiplicative. In this arrangement, the op-amp is doing everything possible to maintain zero voltage between its two inputs (to compensate both the disturbances) and we have three possible points where to take the output from.
* First, if we take the output after the second disturbance (K), the output voltage Vout3 will be equal to the input voltage (Vout3 = Vin) and the circuit will act as a voltage follower.
* Second, if we take the output before the second disturbance (K), the output voltage Vout2 will be proportional to the input voltage (Vout2 = Vin/K) and the circuit will act as an "multiplicative disturbed follower", i.e. as a voltage amplifier with a gain G = 1/K.
* Finally, if we take the output before the first disturbance, the output voltage Vout1 will be the amplified and "lifted" by Vbe input voltage (Vout1 = Vbe +Vin/k) and the circuit will act as an "additive-disturbed amplifier"...
Following this system approach, we can formulate general rules for using disturbances in negative feedback systems. If we take the output after some disturbance, the output voltage will not depend on this disturbance; if we take the output before the disturbance, the output voltage will depend on it...
Cyril, you would be amazed how fast the students lose interest if you do not explain them in interesting ways. I also lose interest in MYSELF :) when I am explaining things in a boring way. The mathematical formulas etc ... are cool, but, first you need to explain where things are coming from.
Your "disturbance theory" is good, but, :) ... the stuff above sounds cool.
Teaching is MOVIE MAKING ... You lose the viewer in the first 3 minutes ! It has to start with a dramatic event. So, I try to start my teaching with something like ...
*** Do you think V=IR ? everyone is looking at me like "DUH !" I don't know if they have this expression in Bulgaria :) Check it out !
Then, I measure it ... Well, it turns out, I=5A, R=1Ohm. However, V=4.9V ?
So, the formula they taught you is wrong !!!
Well, there is a secret ... When we teach V=IR, we never EMPHASIZE how much power consumption that means for the resistor . It is 25W !!!!! I have a little 5W resistor which is burning hot. And, its temperature dependence is 300ppm. This means that, when it gets 100 C hotter, it will be 3% off ! This is why !
After that, you can continue the story. :)
Tolga, unfortunately we do not have such a meaningful word in Bulgarian:)
About teaching... it is more art than science... and the (true) teacher is more actor than a scientist... But although it is more than obvious yet it is so hard to meet a true teacher... I have not yet met him/her around me... but I think I met a few true teachers here, in ResearchGate discussions:)
Thank you for the nice story about the "linear but non-linear" ohmic resistor:) It can be used as a very attractive explanation (demonstration) of the resistor non-linearity...
From my point of view voltage and current sources could be distinguished theoretically only if they are ideal. Ideal voltage source has zero impedance and ideal current source has zero conductivity.
When it comes to real voltage and real current sources they are pretty much the same. Depending on its output impedance the source could be closer to an ideal voltage source or closer to an ideal current source but after all we have duality - any real voltage source could be replaced with an equivalent real current source and vice versa.
Hi Boris! Nice to see you again! It is so exciting when 21-century knowledgeable young people try to reveal the humble 19-century truths:)
Your insertion is very relevant to this topic. I have always been impressed by the beauty of this duality... symmetry... in electrical circuits (voltage - current, series - parallel, Thevenin - Norton...)
So, we have two kinds of real electrical sources, and they are neither voltage nor current; they are "series" or "parallel", Thevenin or Norton... Both they contain an ideal source and internal resistance (we can emulate the resistance by connecting an external resistor). Thevenin has suggested to connect the resistor in series to an ideal voltage source while Norton - in parallel to an ideal current source. Thus these compound sources are derivatives of the ideal sources... and the role of the resistance is to modify the ideal source into the dual source... depending on the value of the internal resistance, each of them can work both as voltage and current source... So we can think of the resistor in the Thevenin compound source as a voltage-to-current converter and of the resistor in the Norton compound source as a current-to-voltage converter.
It is interesting to trace their metamorphoses when varying (mentally or really) the internal resistance from zero to infinity. As a result, both they will change in the succession of "ideal voltage source" -> "real source" -> "ideal current source" (saying "zero resistance", I mean "zero differential resistance", e.g. the diode non-linear resistance).
That is nice dear colleagues, Boris and Cyril, however, we must be careful when we talk about current sources as they don't exist in nature. Duality of Thevinin and Norton equivalency is not more than a circuit tool to simplify analysis. The analogy between water flow and current flow can help. In a closed hydraulic cycle water current flow under the pump pressure, the more the height that water must overcome in the cycle the less the flow rate of water, hence water flaw follows pressure and inversely proportional to height. Similarly in closed electric circuit current has to over come the resistance (level) and it depends on the source potential. Hence, current follows voltage. In both worlds we may create a constant flow (water/electrons) only by complex arrangement to ensure increased pressure (Potential ) of the pump(battery) whenever the height (resistance) increases to restore current flow rate and vise verse. Thanks. @AlDmour.
Ismat, thank you for the impressive explanations! I would like only to remember that we have already discussed many times this question, "Does a true current source exist?" My underlying idea in all these discussions was that elements having a property of "inertness" (charged with kinetic energy) are true current sources. Here are some extracts from these discussions concerning the nature of current sources and your comment above.
----------------------------------------------------------
...So a current source is an extremely "bad" voltage source-:)?
...Or the current source is an "intentionally worsened voltage source"-:)?
https://www.researchgate.net/post/What_is_current_source_Are_there_true_current_sources_If_not_how_do_we_create_artificial_current_sources_How_do_we_make_them_perfect2
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Well, let's generalize all the possible techniques for creating artificial constant current sources:
- adding a large (compared with the load) resistor
- adding a dynamic resistor
- making the exciting voltage dynamic
- adding a dynamic "helping" voltage to the excitation voltage
- adding a dynamic "helping" current to the main current (caused by the excitation voltage)
https://www.researchgate.net/post/Do_current_sources_exist
----------------------------------------------------------
...But what do you explain if it is a true current source without an excitation voltage source inside (e.g., a charged inductor or a photocell)?
...Then how do we explain the situations when the bob of the pendulum rises and the inductor of an LC tank charges the capacitor?
...In accordance with the Lutz's persisting question, "But does a current source physically exist?", I am also waiting for an answer to my question, "Is the charged inductor a true current source?"
...I would like to ask the simple question, "What is a charged flywheel putting in motion a car?"
https://www.researchgate.net/post/Are_there_causal_relationships_in_Ohms_law_If_so_which_is_the_cause_and_which_is_the_effect
----------------------------------------------------------
...I have not yet got an answer to my questions, "What is a charged inductor when shorted? Is there any voltage inside it?" If not, then it is a true current source...
Analogical questions can be, "What is the pendulum bob when crossing the equilibrium position? Is there any pressure applied to it in this moment? Is there any potential energy in this moment?"
https://www.researchgate.net/post/Why_do_we_prefer_using_voltage_than_current_as_a_data_carrier_in_electronics_Why_are_most_of_electronic_devices_implemented_as_voltage_converters
----------------------------------------------------------
The attached picture (where the exciting voltage is denoted by "E" :) illustrates your hydraulic analogy: "the more the height that water must overcome in the cycle the less the flow rate of water, hence water flaw follows pressure and inversely proportional to height". It is extracted from the discussion below the question:
https://www.researchgate.net/post/How_do_we_convert_the_imperfect_passive_RC_integrator_into_an_almost_ideal_op-amp_inverting_integrator_What_does_the_op-amp_do_in_this_circuit
So finally I want to ask you a question: "Does a large volume of water flow moving by inertia behave like a current source?"
My opinion is that we charge an inductor with a voltage source (with "potential energy") but then, while it discharges, it behaves as a current source (with "kinetic energy"). So still true current sources exist?:)
Regards, Cyril
Cyril, i've also thought about the inductor thingy. If a current il is running through an inductor (coil) and the energy source of the inductor is turned off a transient process begins and for it we have il(-0)=il(+0). This means that the inductor acts as an ideal current source because it maintains it's current, even though the voltage drop on the inductor changes. But after the moment t=+0 the inductor is no longer an ideal current source and becomes a real one.
So if we keep the inductor in continuous transient process, and our load is connected in series with the inductor, you might think we have a pretty good current source. Especially if the time constant L/R is much larger than the period of turning on/off the energy source.
... But there are a couple of problems:
1. We can achieve the same (power up the load with current) without the inductor and the swithing on/off by simply using a voltage source :)
2. We use a voltage source to power up the inductor, so it's not really a current source.
3. If we apply additional voltage on the inductor, the current will change so it's not even close to an ideal current source.
If we look at power sources from a physical point of view in order to have current we need an electric field. Only an electric field could make the electric charges flow in a certain direction, and this is a voltage source. You can't make the electric charges flow without creating a potential difference so the current source doesn't exist in reality. An ideal current source creates a current flow without creating a potential difference which is physically not possible. They have been introduced only to simplify the theoretical analysis.
Well Boris... Undoubtedly, all your thoughts above are true in the first phase of charging the inductor by a voltage source... But what about the second phase - the discharging? Is there a voltage then? If so, where is this voltage? Where to connect the voltmeter inside the inductor to measure it:)? Or maybe then the voltage is not an electric-field quantity but sooner a magnetic-field one... and this is a sort of a "magnetic voltage":)... like the displacement current "flowing" through the capacitor?
https://www.researchgate.net/post/Does_the_current_flow_through_a_capacitor_and_if_so_why
Here are my answers to your statements above about the "couple of problems" around the current source:
1. "We can achieve the same (power up the load with current) without the inductor and the swithing on/off by simply using a voltage source :)" There is one very important advantage of the "inductor current source" - there is no power losses in this arangement (that is why they use it in switchable supplies).
2. "We use a voltage source to power up the inductor, so it's not really a current source." Yes, we use a voltage source but only in the first step (charging).
3. "If we apply additional voltage on the inductor, the current will change so it's not even close to an ideal current source." If the inductance is big enough, the current will not change for a long enough time. So, in the first moment, it is an ideal current source.
Yes, we use a voltage source but only in the first step (charging).
-------------------------------------------------------
Cyril, there is one significant difference. When the inductor is charged and the voltage source is removed, the inductor has a potential difference between it's ends. An ideal current source is not supposed to create a potential difference so in fact the inductor is just another voltage source... or perhaps both - voltage and current source at the same time.
Boris, IMO any ideal current source behaves just like the inductor in the first moment after the disconnection - it tries to pass its current through the "load". If the load is a short connection, there is no voltage; if it has some resistance, a voltage drop V = I.R appears across it; if the resistance is too high (up to infinity), the voltage increases up to infinity as well...
Okay, You are absolutely right. Still if there is a voltage drop on the load, this means there is a voltage gain at the current source. This just proves there is no difference between voltage and current sources.
Let's get back to the theme. The only way i could see them distinguished is by their output impedance. Low output impedance - voltage source, high output impedance - current source. In order to transfer maximal power to the load, the source and the load's impedances should be complex conjugate matched.
In such case it could be said that a load with high impedance should be powered with a "current source" (power source with high impedance) and a load with low impedance should be powered with "voltage source" (power source with low impedance).
Then we could go back to your initial image. From such point of view whether the first and second circuit are current or voltage sources would depend on the values of R1, R2 and R.
Boris, it seems the two current (flow) creating phenomena - the inductance and the inertness, are not completely analogous... Although both they produce current (flow), in the case of the inductor (as you have noted above) there is a voltage while, in the case of moving by inertia body there is not a pressure... and the pressure appears only when the body encounters some resistance...
The inductor deserves a special question about how it produces a current only by opposite voltage without any internal resistance (and accordingly, losses)... Every artificial current source contains resistance (linear, non-linear, constant, variable...)...and we can observe two voltages (the internal E and the external V) separated by this resistance... while in an inductor there is only one voltage... To be honest, I would say that for a long time I was going to ask the question, "How do the inductor and capacitor oppose to the input voltage sources?" to second the Tolga's enthusiastic comments about the behavior of these reactive elements...
The problem is that from the next week I will start a series of labs about basic digital circuits with my students... and I would like to join them to our RG discussions by asking according questions... This will distract me temporarily from the basic analog circuitry (until the next term) when I have a course on analog devices...
Still, I found time to ask the question above:
https://www.researchgate.net/post/How_do_inductor_and_capacitor_oppose_input_voltage_sources_Can_we_consider_them_as_time-variable_voltage_sources
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