Greg, may I add one thing. What you said "they didn't have the luxury" ... this is a very important concept. When you give one much less LUXURY, they are forced to learn a lot better. This always puzzles me. I feel like we are SPOILED :) Maxwell, Gauss, these people had wires, and magnetic coils from which they could make something. That's it. So, a lot of what they invented was due to not having the luxury, and being able to go right down to the deepest levels of what things mean like "charge," " electric field".

They could FEEL the electrons in their bones :) Ok, I am getting carried away :) :) :) We are simply teaching V=IR to our students, which has a 100 year history behind it. All they have to do is simply divide two numbers. BOOM. done. ! This is sad ! We pat them in their back and never force them to even understand what "V" means !

It is not until the end of my MS degree that, I started asking myself what "V" means ??? Our education system needs a complete overhaul I

Hi Cyril, I have to bring two terms up : SINGLE ENDED VOLTAGE, vs. DIFFERENTIAL VOLTAGE. There are two kind of ADC's that measure single-ended voltage (when you know that, the other END is GND), and DIFFERENTIAL VOLTAGE, i.e., floating, where none of the nodes are connected to GND.

DIFFERENTIAL VOLTAGE, for example, is perfect when you have a HIGH SIDE CURRENT SENSOR, whereas, when you are doing LOW SIDE CURRENT SENSING, you only need to measure one pin, since the other pin is GND.

In your circuit, DIODE is connected to the LOWSIDE. However, if you connect the diode to HIGHSIDE, i.e., flip the R and D, your question becomes a little more relevant ... Makes sense ?

I believe Voltage and Voltage drop are two terms that have only grammatical differences and not physical differences. Though the second, voltage drop, is effectively slang or is used when discussing what happens across a specific element in a specific direction. Keep in mind that any voltage, by definition, is a difference in electric potential energy between two points. So while we may say that a voltage source has a voltage of 1.5V, we are actually saying that the voltage between the negative and positive polarities of the voltage source is 1.5V. Set ground at the Positive termina and now the "Voltage" or better "Node voltage" at the negative terminal is -1.5V but nothing physically changed. Examples that I would consider proper usage are

"What is the voltage Vr across resistor R." In this case Vr would need to be labeled on the schematic including the polarities. From a calculation/measurement perspective, there is nothing that forces the polarities to be one way or the other. The value with polarities in one direction is simply the negative of the value with the polarities in the opposite direction.

"What is the voltage dropped across resistor R." In this case, one would need to be given or assume a direction of current flow which would then dictate the polarities. If the direction given/assumed was incorrect, the "voltage drop" would simply be negative which is still mathematically correct.

Notice: “the postings on this site are my own and don’t represent Navy/Marine Corps’ positions or opinions.”

Ok. This should clarify it all:

VOLTAGE : is the single-ended (i.e., GND referenced) potential of a node

VOLTAGE of a FLOATING CIRCUIT ELEMENT: since neither node is GND-referenced, this is really the difference of the voltages of nodes a, b, where the circuit element is connected, i.e., Va-Vb.

VOLTAGE DROP: is usually referring to an undesirable feature of a circuit element. In the case of a diode, FORWARD VOLTAGE DROP is undesirable, so, VOLTAGE DROP has a negative connotation ... unless you are using that drop for something useful, like, creating a non-precise 0.6V voltage reference, which is done all the time.

Tolga and Robert, thanks for the quick responses! You have made me think more deeply on this...

Interesting interpretation, Tolga... But don't you think that the "differential voltage" is something quite strange - a "difference between two differences"? Or, if we remember that the very voltage is a potential difference, it seems the "differential voltage" is a "differential difference"?

BTW the voltage drop can be desirable when we want to decrease a voltage. Popular examples are the voltage drop across the series resistor of an old-fashioned movement voltmeter, the voltage drop across the upper resistor of a voltage divider, the voltage drop across the base resistor of a transistor switch, etc.

A simpler statement might be that the voltage is measured relative to a reference point, which usually is called "ground". Current flows from the voltage source, through the circuit, to ground. As the current flows, it passes through circuit elements. The voltage drop across one of those circuit elements is the difference in voltage from one terminal of the element to another. This is true for two-terminal devices, such as resistors, and also for more sophisticated elements, such as transistors, that have more terminals.

Voltage is a measurement of potential difference with respect to raferance (generally ground).Voltage drop is a drop of voltage when current flow from load (V=IZ).For D.C as frequency is zero Impedance (Z=R) voltage drop would be V=IR.

David, thank you for the clear explanation. But I wonder if always the voltage across a passive element is a voltage drop. See for example the elementary circuit in the attached picture and answer the question, " Is the voltage Vr a voltage drop?"

(the lenghts of the red colored bars represent the magnitudes of the corresponding voltages)

I think it is not a "drop" since this voltage is not determined by the resistance R and the current I flowing through the resistor; it is determined by the voltages (emf) V1 and V2. Actually this arrangement is a composed voltage source (V1-V2) connected to a resistor R and if you connect a voltmeter to the resistor, you will measure the voltage (emf) V1-V2 of the source... and it would be quite strange to name it "drop"...

I believe that Bhupendra addresses the question nicely: The voltage drop across two terminals of a circuit element is determined by the current flowing through the element and the impedance of the element. You measure the voltage drop across the element, not to the midpoint of the element.

I would like only to add that the voltage bar Vr in the picture above represents the voltage across the resistor R (between its terminals) although it is drawn into the center of the resistor.

With the picture above I have also seconded the Bhupendra's opinion. It seems the voltage drop is a voltage across a passive element that is determined by the very element. To make this possible, we need another passive element as in the case of a voltage divider in the attached picture below. Then we say that a part of the voltage is spent across the first passive element (R1) and the rest is applied to the second element (R2).

Tolga, I have made this picture especially for you as a response to your suggestion; it is a gift gor you:) It is an example of a voltage drop across a non-linear resistor.

Thanks :) "Voltage Drop" is referring to the undesirable property of the diode. A Schottky diode only has a 0.1-0.3V voltage drop, compared to the small signal diodes like the one you are showing (0.6V). So, Schottky is a "better" diode. A MOSFET that has a low RDSon has a lower "voltage drop," (e.g., 50 mV), so, it is better than a BJT, which has a 0.4V "voltage drop," (say, VCEsat=0.3V) ... This is the case, since voltage drops cause energy wastes ... So, they are undesirable ...

Well... undesirable ... But if you "desire" a voltage source producing 0.6 V (1.2 V)? Then Vf (2Vf) will become desirable for you:)

Voltage: defined as Electric potential energy per unit charge. Whereas,

Voltage Drop: when an electric current is pass through an element that do not supply voltage (Passive element), reduction of supplied energy is occurred, Energy is dissipated. The phenomenon is call it Voltage drop

Well, Dinsefa... I agree with you...

Now another "naive question"... If we connect an opposing voltage source Vb (a battery) between the main voltage source V and the load R, the voltage V drops with Vb (Vr = V - Vb). So the question is, "Is the voltage Vb a voltage drop?"

Maybe rather than using the term "voltage drop" the term "potential difference" would be more appropriate.

IMO "potential difference" corresponds better to "voltage"...

Not really as, as per your example the overall potential difference depends upon the manner in which the individual sources are actually connected. Two 10v sources may realise a potential difference of either 20V or 0V . If one did a Thevenin equivalent one cannot distinguish whether single or multiple sources are, simply what potential difference exists at the terminals.

KVL says the sum of the "voltages" (or overall potential difference") around any closed circuit is zero. The reference point may be anywhere in the circuit.

"Voltage drop" is generally understood as being akin to the power dissipated within the circuit element.

And yet, is the voltage Vb in the picture above a voltage drop?

And then, is the voltage Vc in the attached picture below a voltage drop?

voltage is source of supply which will change in R L C elements due to there dissipation capacity in elements that dissipated change is called voltage drop.

Cyril, allow me first to say that though this question looks dam naive it is on the other hand very critical and touches an issue that can preclude understanding by students in their initial circuits study. I still remember that I myself puzzled for some time as some circuit diagrams used E (or emf) while others used V whenever it comes to sources.

First, let me first differentiate the three terms: EMF, voltage and voltage drop as they are used typically in circuits noting that the three of them are measured in volts:

1* EMF; the electromotive force, is the source of all activities. It is some force that is there produced by some chemical (a battery), magnetic induction (a generator/ a transformer), static ( a charged capacitor) ...etc. EMF, is a polarized force which can cause charged electrons to flow in a certain direction (toward the positive pole of the EMF) whenever the circuit is closed; i.e. some load and a connection.

2* Voltage drop: is that same source EMF (or part of it) received by the load (in Cyril terms, the load is "spending" the source EMF in the form of a voltage drop). A source of EMF=12V connected to a load.of 12ohms will create a voltage drop of 12V on the load. (this is assuming the source has no internal resistance-load- inside it and the load and the source are connected with zero resistance connections).

3* Voltage (or Potential): is the "voltage drop" between two points (on any load or part of the circuit) with one of the two points known implicitly; i.e the reference point which can be any point, the battery negative, a common substrate or chassis,...etc. This simplifies the analysis (as we don't have to mention the two points of a load whenever we calculate voltage drop).

One important thing when coming to sources is that some time we consider the source as EMF source and sometimes we consider it as V (voltage) source. To differentiate, EMF is the voltage drop across the source terminals at no load; i.e. whenever no current is drawn out of the source. Whenever the source is loaded, part of the source EMF is spent internally causing the actual force (voltage) of the source to drop by that value. Some times, the mix-up in circuit analysis comes because we convert sources (e.g. a reducing the battery emf and part of the circuit using Thevinin equivalent circuit of a voltage source and a series load). In this case, we use V_thevinin as the net emf while the effect of the reduced circuit is taken as the Thevinin resistance as seen by the load..

My traditional method of explaining the difference between an EMF and the voltage drop is that I make an analogy between the water pumping cycle and the electric circuit. The pump corresponds to EMF, electric current to water flow and voltage drop across a load to pressure spent on over some part of the water cycle (e.g. a water driven dentist excavator tool), so the pumping pressure is spent in the load as drilling action same as the emf of the battery spent as voltage drop across the resistor. Thanks. @AlDmour.

Brilliant explanation, Ismat... that I have never seen! I woul like to vote them a few times but the RG software dos not allow me (I am sure that other contributors will help me by voting them)!

I am also very sorry for the character E; I was widely using it in the past. See for example one of my drafts from 90's dedicated to the great "voltage compensation" (Miller) idea. To understand me Wikipedia readers, I had to explain in the translation below the picture what this E is ("think of E as of V"):

https://en.wikipedia.org/wiki/Talk:Miller_theorem#Some_history

It is so clear, as you have noted, to have a "pure" internal voltage E (emf), an effective external voltage V across the source terminals and a "loss of voltage" (voltage drop) Vr across the passive element...

Thank you again for the excellent contribution about the simple but complex things in circuitry:) Cyril

Now, for the two controversy circuits that Cyril posted above asking whether the drops are voltage drops or voltages (emf's). I liked the first circuit of two opposing batteries. It reminds me at times when we used to refresh dead batteries (especially when the battery model is not readily available around by connecting them through a resistor to control the current to a low value. Please don't try it or be cautious as the battery (dry battery) may explode. Basically, this is what is used to charge Lead acid batteries of cars and other chargeable batteries. My point is that the battery remains a battery but its internal chemical ingredients will react to build up permanent charges, hence yes, the opposing battery emf will continue to be an emf (though gradually rising if the other one is higher-charging state) and a voltage drop will be dropped internally in the (chemicals of) opposing battery (which tends to build permanent store of charges). This is same story for the first battery, the charging one which surely will have a voltage drop on its internal (chemicals) causing a drop of a voltge below emf and gradual decrease of emf itself.

for the second circuit above with capacitor, and as one colleague in above commented, it is a terminology wise. Hence, let us simply call the voltage measured across the capacitor as "voltage drop" as long as it is not generated by the capacitor itself like any other load. Thanks. @AlDmour.

Interesting things happen when we make batteries oppose... The voltage drop across the internal resistance of the main (higher voltage) battery B1 is subtracted from its E1 (emf) while the voltage drop across the internal resistance of the additional opposing (lower voltage) battery B2 is added to its E2 (emf)... as though the voltage of the second battery is increased...

Well, V2 is not a voltage drop but yet it behaves as a voltage drop. If we do not see what the second element is, we can thought of it as of a resistor with a voltage drop V2 across it... Interesting idea that can be used for creation of virtual elements...

I think voltage is analogous to potential energy in which energy is in static form but the voltage drop is analogous to kinetic energy in which energy transfer.

It is definitely an interesting answer... it now remains only the physicists to say whether this is true...

I like it since really there is a voltage drop across a passive element when there is a current flowing through it... a "movement" of electrons... something kinetic...

I continue to hold the view that to observe a voltage drop across a passive element, we need at least another passive element (no source) connected in series...

In the two circuits above containing two sources, as Diana observed, the sources can be replaced by a one composed source that is connected in parallel to the passive element (the resistor R). And yet If you want to see a voltage drop in this arrangement (a voltage source supplying a resistor), peek inside the resistor:) and you will see the voltage distribution along the resistor...

You will be able to see it if you walk along the resistive layer as my students (and perhaps Ohm in 1926:) did in 2008:

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

Тo be more interesting, now I chose a configuration with two "helping" (unidirectionally connected when travveling along the loop) sources...

...that is exactly an op-amp inverting amplifier presented in a fancy and intriguing for young curious people way...

Cyril, I have been trying to answer the "current flow" to myself in the most intuitive way. CURRENT is somehow intuitive. Since the "elementary charge" cannot be a sub-fraction of "q" (i.e., 1.6E-19 Coulombs), the CURRENT is really counting all CHARGE CARRYING PARTICLES THROUGH AN INTERSECTION PER SECOND. Each charge-carrying particle adds 1.6E-19 Amperes per second (i.e., Coulomb). Sum them up. you got your current (I=dq/dt). Charge carrying particles are electrons, photons, whatever ... So, if you have 1E19 particles passing through an intersection per second, you have 1.6 Amperes flowing through that intersection.

Now, going from here to voltage is also somehow easy. Each one of these particles is at a POTENTIAL. At every intersection, all particles will all be at the same potential. When they reach GND, they are at a zero potential. So, voltage drop is the difference between the potentials of the particles at point A minus point B.

So, this is a kind of a "discrete explanation" in contrast to the classic "analog explanation" that is more suitable for contemporary computer science students:)?

Once you have the attitude to "see" electrical quantities, let's visualize the invisible voltage (drops) by means of an interactive Flash animation. Let this fun movie to be a gift for all of you, my friends here who have the courage to think about the most elementary but great and eternal electrical phenomena... Thank you! Cyril

http://www.circuit-fantasia.com/collections/circuit-collection/circuits/old-circuits/v-to-v-sum-old.html

(click the "Exploring" button on the left side of the screen and control the animation by the arrow buttons located at the bottom)

Picking up on potential difference raised earlier and by Tolga. In the diagrams you are using you are using the single subscript notation (Vb). In general, and especially in multiple phase systems, one uses the double subscript notation Vxy which means the potential of x wrt y and I xy which means current is flowing from x to y.

In your circuit of the battery, capacitor and resistor if you separated the battery from the capacitor ands resistor and measured them in open circuit you would only measure V across the battery and 0 across the Vc and Vr ( assuming capacitor had no initial voltage on it)

When you connect them you will again measure the same voltage V across both the battery and the capacitor and resistor in series so that V = Vc + Vr. Being an ideal source one cannot tell the difference if it is a "voltage rise" or "voltage drop", save that we know what we had prior to connection. In steady state V=Vc and Vr = 0.

If you now disconnect again you will have V across the battery and also V across Vc+Vr.

As far as E and EMF goes it is normally used to represent Electro-Motive Force which is a voltage developed by moving a conductor through a magnetic field such as a generator. This is still used when modelling electrical machines where E is used to model the "back emf".

Cyril your comment about observing a voltage is correct and interesting and goes back to the old "uncertainty" principle. You are correct that in order to measure we have to disturb the system and in the case of electric circuits it is no different and has to create a potential difference.

Birds can sit quite happily on high tension lines provided they are at the same potential and nothing will happen. That is why in Electrical Engineering we generally treat everything as being live.

Diana, the double subscript notation is a very good idea (when neded)... and your thoughts are interesting...

I continue thinking that, in a circuit of a loaded real voltage source with internal resistance Ri, we can observe three kinds of voltages :

* an internal "electromotive voltage" E,

* an external "effective voltage" V across the source terminals,

* the internal difference between them (a voltage drop) Vri across the internal resistance Ri.

You are 100% correct. If one connects an ideal voltage source (no internal resistance), across say a diode like you mention above, there will be no "voltdrop" and the source will try to develop infinite current to maintain the source voltage. Add some "internal resistance" and the diode "voltdrop" appears.

In practice one would have a blown diode so as you correctly state a series resistance or series load is required to absorb the energy and not the diode itself.

Exactly! The internal resistance is what separates E from V; otherwise they would be the same...

I think that for the purposes of understanding it is useful for students to burn a few diodes (especially, LEDs:)

I've never been keen of the term "voltage drop". Like Tolga already mentioned, in my view, the question is about potentials. That is, in circuit theory branch voltages fulfilling Kirchoff's law are about potentials. The electromotive force is a property of "loops" (or more precisely, a map from "loops" to real numbers).

This, however, raises an interesting question of what do voltmeters measure. This device seems to create some fuzziness between what is meant by voltages and electromotive forces. Alain Bossavit has written some nice material of this, see

http://butler.cc.tut.fi/~bossavit/Slideshows/Aussois06Dias.pdf

Hi Lauri, when you say "The electromotive force is a property of "loops" (or more precisely, a map from "loops" to real numbers).". I really was not able to understand this seemingly complex statement (probably to me). Can you please put in simpler words?.

My simple understanding of EMF ( as I explained in a comment )is that it is the voltage measured between the two terminals of a source/battery at no load. It is therefore the source of all voltages and voltage drops in the circuit. Any voltage source can be modeled as an ideal voltage source (EMF) in series with (an internal) resistance (impedance for ac sources). I think Cyril and Tolga said the same thing as well: "The internal resistance is what separates E from V". Thanks.@AlDmour

Hi Ismat, electromotive force has to do with Faraday's law. For all surfaces S the time derivative of magnetic flux on surface S is (up to the sign) the same as the electromotive force around the boundary of S. And the boundary of S is what I call a "loop". Accordingly, emf is a property that is assigned to loops.

By assumption in circuit theory the electromotive is null over all loops. In this case one has potentials, and the voltages are differences in the potentials. Notice that this implies that over sources the sign of UI is negative while it is positive over resistors. The interpretation of this is, power is generated within sources and transferred to heat in resistors. (This goes back to Poynting's theorem)

I guess the confusion arises from the fact that E.dl integrals are also called voltages. For example, in this part of world one says the voltage over the AC sockets is 240V, and this is what the voltmeter shows when you measure it. This is also what Alain Bossavit's presentation explains in more details, but here's a short and simplified explanation.

The terminals of the socket are connected by wires to some power source. If one started to follow the wires towards the power source, one will find they form a loop up to the short path "in air" between the terminals of the socket. Now, Faraday's law holds "for all surfaces". Especially, it does NOT say, it holds only for surfaces bounded by wires. Consequently, the emf 240V is a property of the whole loop consisting of the wires, power source, and the short path between socket terminals. However, since the wires are made of good conductors, such as copper, the integral E.dl is nearly zero within the wires. Accordingly, the integral E.dl over the short path in air between the socket terminals must be almost 240V. For practical reasons everybody keeps talking about voltage instead of emf.

Another view on this is, if somebody shut down the power source, but somebody generated a time varying magnetic flux on the surface whose boundary is the loop I just described, one would find again an emf over the loop, and this would be called by the name "voltage" But, circuit theory per se does not have a "socket" to which this emf could be "plugged in", as it assumes the wires have no effect. (Of courese, there are ways, how to get over this, but that's another issue.) This is to say, circuit theory is not the best tool to explain what is meant by emf.

How simple and straightforward you have said it Ismat - "if there is no load connected (no consumed current), V = E"... and "it is the source of all voltages and voltage drops in the circuit"... it is the origin... perfect explanations!

Hi Lauri, thank you for the lengthy explanation removing some how the ambiguity of your term ": "emf is a map from "loops" to real numbers". You deeply presented the idea. I would like to further discuss Cyril's question using the principals you reminded us of.

One first thing is that emf is not only for Faraday's sources, it can be for any source that is capable of separating the charges. An electrochemical reaction in a battery is definitely an emf source that is capable of moving the charges inside it from the negative terminal to the positive terminal creating the battery emf in volts. Hence Emf sources exert energy to separate charges (creating the open circuited potential difference between the two terminals of the source). A 1 volt is 1 Joule per unit of charge. . Other sources of emf can be a solar cell, a photo diode, a thermocouple,...etc.

The charges separated by the source will accumulate up to the maximum it can attain be the phenomena producing it (thermionic, magnetic,...etc). Once a circuit is connected to the source, the emf action results in moving the charges across the closed path. The energy gained by the charges from the source emf action is spent as thermal ( or probably mechanical if the load is a motor). In other words, the charges on its journey around the loop are impeded by collisions in the load producing a potential difference across the load (the impediment creates a difference in charges density between the two terminals of the load which is the potential difference across the load). At the same time the energy that these charges got from the source are spent in the load in the form of heat (or mechanical) energy losses.

Another thing, Lauri, when you say the "electromotive is null over all loops" you re-created the confusion. Of course, this is absolutely true in the same way when state KVL as of "The sum of all voltages over a closed loop is zero". In both terms, yours and KVL no distinction is made between emfs(sources) and V's (voltage drops). They are all, after all , measured in 'volts'. I like to state your term alternatively by saying:" The integration of the (induced) electric field -in case of induction- across a closed loop is non-zero summing up to the total emf around the loop. As charges move around the loop (from -ve to +ve in the source and from +ve to -ve in the load) means energy exerted to move them. This energy is generated by the emf source (emf voltage difference) and dissipated by an opposing potential (voltage drop) in the external circuit when the charges move from the +ve to the -ve in the load. Hence alternatively "the integration of the induced emfs across a closed loop equals the integration of the generated potential drops around it". This alternative formulation is similar to KVL's second form which we were taught to us: " The sum of EMFs equals sum of voltage drops across a closed loop". I liked this last one of KVL more than the first one (sum=0) at school time as it usually enabled me to find out about lots of things (least is the actual current direction by summing the batteries and find whether it sums to -ve or positive...). I can find another use of this second form after this long question by Cyril in that it helps to keep the distinction between E and V. Thanks. @AlDmour.

Thanks Aldmour, got your point. In the parlance of electrical engineering terms voltage and emf are employed rather freely and typically everybody still understands correctly what is meant from the context.

The reason why I restricted the use of emf to induction is: if you have a loop and the emf is not zero around, you *must* have a change in magnetic flux (on any surface whose boundary is the loop). Consequently, in case of all other power sources, such as electrochemical reaction/battery, the emf around the loops vanishes. In other words, the notion of voltage is enough for all other power sources except induction. Within these power sources E.J < 0 and product UI is negative .

In case of plain induction one has E.J > 0 everywhere within the loop, and this is why the integral of E over a loop deserves a new name, emf, in field theory.

An EMF may be created several ways (chemical, induction etc) but regardless of how it is created it still represents a source "potential" to do work or transfer electrical energy. As Cyril says earlier one cannot determine whether such potential exists without an external load or as Lauri correctly states a closed circuit. Of course EM waves may propagate without such a closed circuit so as Lauri alludes to circuit theory too has its limitations. Students need to be made aware of such limitations such as lumped and distributed and steady state and transient for example. As Lauri correctly states one then has to resort to Field Theory. Sometimes it is harder to undo "simplification".

All the statements above are excellent but I like the most Ismat's thoughts... they seem for me like thoughts spoken (but better) by me itself... or like thoughts that I would ever say... while the Lauri's and Gregory's explanation are more physical and specific... I can not see any connection between the pure electrical quantity "voltage" and magnetic quantities especially in the case of an unloaded source when V = E (an open circuit - no current flowing, no magnetic field). In the same way, I could not see any connection between the electrical voltage and the magnetic flux in the Chua's memristor:

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

Cyril, think of a simple metal plate with eddy currents. What would you say is driving the currents in the plate? Voltage is pretty misleading in this case as there are no terminals.

Next remove the metal place but let the time varying magnetic field remain; the electromotive force is still there around any loop "in air" although there are no currents. Talking of voltages in this case would be rather, if not highly, confusing.

Lauri you are correct and just like the paradox of the chicken and egg, potential and kinetic energy so too must electric and magnetic fields co-exist.

Even more interesting is Faradays paradox which defies the odds.

It is well known that external electric and magnetic fields may induce significantly more intense electric and magnetic fields in certain materials.

The Ismat's thoughts about the KVL make me deeply think what actually this law says... Maybe it is a special expression of the law about the energy conservation? So if we assume the voltage is power and the voltage drop is a (power) loss, we can "translate" its two versions as follows:

"The sum of all voltages over a closed loop is zero" - > "The sum of all powers and losses over a closed loop is zero"

" The sum of all powers equals the sum of losses across a closed loop".

So it represents the well conscious by people fact that nothing in nature is not lost?

100% correct Cyril, it is a statement about the conservation of energy (KVL) and conservation of charge (KCL).

Lauri, maybe they introduced the word "force" in the phrase "electromotive force" as a general word designating something "driving"?

From Wikepedia

The electromotive "force" is not a force, as force is measured in newtons, but a potential, or energy per unit of charge, measured in volts.

Gregory, the fact that power is proportional to the square of the voltage slightly bothers me...

Gregory, I see... the electromotive "force" is not a force just like the magnetic flux in the Chua's memristor is not magnetic:)

Why is that?

Cyril I understand charge is required to establish an (point) electric field (divergence theorem) and moving charge or current is required to establish a magnetic field (curl). Energy is stored in the EM fields which can do work and propagate EM waves and which engineers may exploit. EM fields must coexist like PE and KE.

Sophisticated thoughts...

I would say term "electromotive force" should be taken as a compound word.

Cyril, solutions of circuit equations are {U,I}-pairs, and they specify the power balance of systems following from some initial condition.

Kirchoff's voltage law is a special case of Faraday's law, i.e., the integral of E along a loop has to vanish. This follows from the energy conservation principle. Since qE is the force on a charge, the integrals of qE along any path are about work. If the work related to transporting a charge around some loop is not zero, then one would be able to come up with an electric perpetual machine: If the work is less than zero around a loop ,then by reverting the direction one would gain energy out of nothing.

Kirchoff's current law is a special case of charge continuity law div J + d rho/dt = 0 (one is not able to create or destroy charge) reducing to div J = 0: the same amount of current enter and exit a point.

More sophisticated thoughts:) ... thank you!

Actually Cyril the "thoughts " follow Maxwell's basic theory and are well over 100 years old. He, and others, did not have the luxury of any circuit theory from which to work from.

Actually Lauri' s explanation of work done around a loop being zero is possibly where the term "voltage drop" arises. One would assume a charge gains energy when it moves through or comes from a source ( "voltage rise") and then loses energy when it moves through a load hence the term "voltage drop" which is akin to a loss of energy.

Phew!! what a lot of work.

Greg, may I add one thing. What you said "they didn't have the luxury" ... this is a very important concept. When you give one much less LUXURY, they are forced to learn a lot better. This always puzzles me. I feel like we are SPOILED :) Maxwell, Gauss, these people had wires, and magnetic coils from which they could make something. That's it. So, a lot of what they invented was due to not having the luxury, and being able to go right down to the deepest levels of what things mean like "charge," " electric field".

They could FEEL the electrons in their bones :) Ok, I am getting carried away :) :) :) We are simply teaching V=IR to our students, which has a 100 year history behind it. All they have to do is simply divide two numbers. BOOM. done. ! This is sad ! We pat them in their back and never force them to even understand what "V" means !

It is not until the end of my MS degree that, I started asking myself what "V" means ??? Our education system needs a complete overhaul I

Tolga too true and you are 1000% correct.

These days if there is no iphone or PC app it does not exist!! (he he!)

However we only have ourselves to blame. That is why Cyril in asking what appears to be very simple and fundamental questions is in the end very revealing and interesting.

I think people have become too trusting, complacent and expectant and as you say the true value of an MSc and PhD is when one is forced to narrow ones focus and deal and confront the real or actual issues.

Mind you our curriculums have become so content driven and managerial oriented that taking time to think, rather than to just remember, has probably lost it rightful place and context.

It is interesting that people like Maxwell and many others in his day had very varied interests and diverse backgrounds.

Only if Gauss and Maxwell , and Poynting (since he is Lauri's favorite :) could come and teach us. We could make a movie out of this. :) :) :) I am also thinking about Babbage, who built a calculator out of GEARS !

Today, when I don't know something, I Google it . BOOM. 1 minute. the answer is there. I almost feel guilty. :)

Agree. Tolga it is not so much the answer but the process in arriving at it that is all important. Experience cannot be bought but must be earned the good old fashion way.

Very good way to describe it. If you know the reason behind the answer, you have the answer for a lot more of the related questions ... We build a neural network-based database in our brain, and everything is associative ... We build that database by relating things to each other ... and, hence, adding tree branches to our database ... When somebody teaches us I=dQ/dt ... we learn it, and we can calculate what I is, given Q and t ... But, if we know the reason behind this formula, then, we might not even need to know another formula, such as, Q=CV. We already have it, since we can arrive at that answer from what we know by forward-tracing the pieces ...

It was very interesting to see Lauri answering a lot of the questions by using Poynting's theorem, although it seemed distant to me at first. It is because, deep down in the knowledge tree, everything relates to each other ... Keep going down the tree, you see the NATURE ... Everything behaves according to the laws of NATURE ... The difference between these different scientists is that, their angle of approach was different (e.g., thermodynamics vs. quantum physics etc ...). But, nature is nature. You arrive at the same result ... This is why it is super important to know the reason for the formula. And, this happens with relentless ASKING ... even if it is the simplest questions ... like what is an ELECTRON ? what is VOLTAGE ?

I am shocked by the large number of comments since yesterdays comments which led in the end to educational points of view as well. Yes, in current education of engineers we overlooked the basics in the hurry toward the applications and practice. However, we have to keep going to the basics from time to time. Talking about basics gets me back to some comments above mainly by Lauri ( which were made mainly in response to earlier comments by me).

First, concerning the restriction of EMFs to induction sources. I can't really understand why you made that restriction, Lauri. You say that " in case of all other power sources, such as electrochemical reaction/battery, the emf around the loops vanishes". Why it does not vanish in a loop with induced emf?. especially that you yourself affirm in a subsequent comment that " the integral of E along a loop has to vanish" or as you said " a perpetual machine emerges" which you meant a machine that can indefinitely produces work violating basic physics.

Again, in any closed circuit basic KVL / integral of E around a closed loop amounts up to zero. This is energy conservation as we all agree. This is provided that we make no distinction between Es and Vs (sources and drops). Or else we can use the other alternative of integral (sum) of all sources around a closed loop equals integral (sum) of all voltages (drops) across all loads. Both two forms are applicable to all sources/loads types and across any loop at all instances (steady state or transient). The loop can have lumped /discrete components (sources/loads) or continuous source/load. For example, the eddy loop example Of Lauri is an example of a continuous source (emf is infinitesimally built around the loop while the load itself is as well a distributed resistance (Impedance) around it. Hence, yes, we better give the name of E to the integration of emf around any eddy loop while at the same time give the name R/Z to the integration of the load around it. Hence, modeling the loop as an E (source) and Z (Load). Iam not sure, but it might be this is how eddy currents are calculated (we have to sum/integrate over all the loops after all). If we have the magnetic field with the plate there we will have E and Z ( resulting in Eddy current of E/Z) but if we don't (just air), there will be also E (as Lauri said, electric field in the air) and Z (but now Z= infinity), hence Zero eddy currents. This is like an open source Emf. Thanks.@AlDmour.

I just have no words to express my admiration for all that wisdom above...

Ismat as I understand matters what Lauri is saying is that when a battery is used to develop an emf in a closed circuit or loop it has to be physically located or inserted in or within the loop. If the emf is generated via induction then this is not the case as the emf is developed by induction by the magnetic field passing through the loop and the rate at which this occurs, By Lentz's Law it will oppose the change responsible for it.