are kirchoff laws useless?

[EEVblog]

There are many alternatives to explicitly using Kirchhoff's laws. Examples are simulation software

Which ironically make extensive use of Kirchoff's laws to solve the circuit.

[T3sl4co1l]

Any analysis of a transmission line that is based *only* on KCL and *not* on Maxwell will be a failure. The most fundamental thing on the first day of any transmission line course is Maxwell. To say that currents flow through vacuum (without Maxwell) simply is not in any way correct.

It would be a gross corruption of my words, to think I implied Maxwell's equations do not apply.

Tim

[mrpackethead]

Trolling? I would be like to hear any circuit, no matter how simple, defies KXL or can be analyzed without KXL in any forms.

I fail.

[zapta]

...It's the 2nd thing you usually learn in DC circuit theory after ohms law.

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

[Kalvin]

...It's the 2nd thing you usually learn in DC circuit theory after ohms law.

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

This is nice video "M.I.T.-Walter Lewin- Complete Breakdown of Intuition - Part1":

[IanB]

This is nice video "M.I.T.-Walter Lewin- Complete Breakdown of Intuition - Part1":

I think he did a sneaky trick there. He failed to discuss some important things that would affect the observations.

[Kalvin]

This is nice video "M.I.T.-Walter Lewin- Complete Breakdown of Intuition - Part1":

I think he did a sneaky trick there. He failed to discuss some important things that would affect the observations.

I think it was a psychological trick, not as much a physical trick. But anyway, nice demonstration and makes one think how that is possible.

[zapta]

...It's the 2nd thing you usually learn in DC circuit theory after ohms law.

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

This is nice video "M.I.T.-Walter Lewin- Complete Breakdown of Intuition - Part1":

Does this really break Kirchoff?  I would think that once you have magnetic field that induce current in the wires, the wires not become current or voltage sources and should be modeled accordingly for Kirchoff analysis.

[onlooker]

Yes, it is a real breakdown of KVL, since the potential difference between point D and point C is no longer well defined or unique (or call it path dependent);

This, as expected,  will show real effects when one use a voltage meter to measure the voltage between D and C. Depending on whether the meter's probe cable laying on the left side or right side of the solenoid one will have different readings and I think this is the part that can't be modeled by distributed battery sources.

[T3sl4co1l]

He cheats because he's applying fields to a diagram, one which, by its definition, is agnostic of fields.

As I said before, the circuit diagram has no representation of the speed of light, nor the magnetic or electric fields that construct the EM field.

You can place two wires on a schematic, as close together as possible, and they will still have zero picofarads of capacitance, and zero nanohenries of mutual inductance!  It is only when you draw that "===" symbol between two wires, that you symbolize a capacitor, within which you get electric field, and electric field only.  Or that curly symbol to indicate inductance, wherein you get magnetic field, and magnetic field only.

The correct schematic representation requires a transformer to be drawn somewhere; if it is drawn where the battery used to be, everything is perfectly fine again.

If the schematic is not abstract, but meant as a crude mechanical drawing of a real system, then one will find the voltage measurement depends upon, not where the voltmeter probes are connected, but upon what paths the two voltmeter leads take away from those points.  The voltage drop across each resistor will of course be sensible, but the voltmeter loop itself will see a more significant amount.

There is a second fiction present, also: no real solenoid is infinite in length, and even an infinite solenoid has magnetic potential around it (if little-to-no flux density outside of it).  Performing this experiment with a finite length solenoid will subject all those paths to varying amounts of fringing flux, thus making the voltages dependent as I just said.

Tim

[bson]

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

It's not.  Ohm's law defines the abstract property of resistance as U/I.  It's abstract because nothing ever actually exists that you can point to and say "that right there is resistance".  Wherever there is voltage and current there is by definition resistance.  The current can be limited by a huge number of reasons; Ohm's law simply bundles these into the concept of resistance.

Not to be a confused with a resistor, which ideally has constant resistance.

[zapta]

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

It's not.  Ohm's law defines the abstract property of resistance as U/I.  It's abstract because nothing ever actually exists that you can point to and say "that right there is resistance".  Wherever there is voltage and current there is by definition resistance.  The current can be limited by a huge number of reasons; Ohm's law simply bundles these into the concept of resistance.

Not to be a confused with a resistor, which ideally has constant resistance.

Let's see how the abstract Ohm's law works without assuming kirchoff, let's say that we have a black box with two  leads connected in a circuit. The voltage across the box is 1V, the entering current at lead #1 is 1A and the existing current at lead #2 is 2A. Which of the two currents would you use to compute the resistance of the box using Ohms law?

Ohm's law assumes that there is a single current through the box, hence the dependency on kirchoff.

[T3sl4co1l]

If it helps, Ohm's law for fields is E = rho * J.

J is the current density (a vector field), which necessarily has to obey KCL because of charge conservation.

This also says E and J are in the same angle and phase, which is correct.  For reactive conditions (say, permeable or dielectric material), this need not be the case.  (A metal can be represented as a dielectric with a large imaginary component to e_r.)

Tim

[onlooker]

Ohm's law assumes that there is a single current through the box, hence the dependency on kirchoff.

1st, Ohm's law was discovered 20 years before Kirchhoff's laws.  The best one can say is that  Kirchhoff's laws extended some aspects of Ohm's law.

Yes, "Ohm's law assumes that there is a single current through the box", or the "quasi-stationary current" condition. But, I do not think it is directly related to KCL.  KCL by itself is just about charge conservation.  The "quasi-stationary current" condition is an additional requirement to make KCL helpful/useful in circuit analysis. 

An example is the already mentioned transmission line.  The charge conservation law stays, but the "quasi-stationary current" condition is no longer valid. That is, one can still say KCL is valid (for any "node" if  a "node" means a cross-section of the line). But, KCL (or charge conservation) alone is not much helpful for analyzing the circuit.

[TimFox]

Ohm's law is approximate.  All resistors show some non-linearity.
Kirchoff's laws are exact (when you pay attention to the conditions).

[filssavi]

The point, if there is any, is that KCL and KVL do not fully account for electromagnetics.

I'm disagreeing with you because I think they do fully account for electromagnetics.

I think KCL expresses a general rule about conservation of charge, and KVL expresses a general rule about the conservative nature of electric fields. As such they are (when accumulation terms and propagation delays are neglected) axiomatically true. They are true in transformers, in antennas and anywhere else that you can measure currents and voltages without disturbing the circuit.

Since we seem to be disagreeing about this point it appears we need anothere expert person to arbitrate.

Since kvl and kcl for you explain all Electromagnetism why are we bothering to kill half of our brain trying to get around math formalism of Maxwell equations
Since you clearly are smarter than me Can you explain how fiber optics work (in depth not just current goes in the laser diode and gets out the detector) modes, dispersion and all with just kvl and kcl

[IanB]

Since kvl and kcl for you explain all Electromagnetism why are we bothering to kill half of our brain trying to get around math formalism of Maxwell equations
Since you clearly are smarter than me Can you explain how fiber optics work (in depth not just current goes in the laser diode and gets out the detector) modes, dispersion and all with just kvl and kcl

I have not said they explain electromagnetism. I have simply said that they are not invalidated by electromagnetism.

[IconicPCB]

We should ignore Kirchoff.. and analyse everything in terms of Maxwell's work. ( my contribution to the war)

[orolo]

...It's the 2nd thing you usually learn in DC circuit theory after ohms law.

I think that Ohm's law is also based on Kirchoff. If you can't assume that the current in both ends of the resistor are the same, then 'resistor current' is not well defined.

This is nice video "M.I.T.-Walter Lewin- Complete Breakdown of Intuition - Part1":

Does this really break Kirchoff?  I would think that once you have magnetic field that induce current in the wires, the wires not become current or voltage sources and should be modeled accordingly for Kirchoff analysis.

It's a trick, of course. It is implicit in the circuit that the two resistors are on the secondary side of a transformer: you don't have R1 in series with R2 alone, in a complete lumped description you have L2 (the secondary, one loop inductor around the magnetic field) in series with R1 and R2. KVL applies to these three elements, as usual. Tricky old professor.

[EEVblog]

Yes, it is a real breakdown of KVL, since the potential difference between point D and point C is no longer well defined or unique (or call it path dependent);
This, as expected,  will show real effects when one use a voltage meter to measure the voltage between D and C. Depending on whether the meter's probe cable laying on the left side or right side of the solenoid one will have different readings and I think this is the part that can't be modeled by distributed battery sources.

And cue the overunity crowd!

[EEVblog]

We should ignore Kirchoff.. and analyse everything in terms of Maxwell's work. ( my contribution to the war)

Basic circuit design would get pretty tedious very quickly.

[Helix70]

Ohm's law is approximate.  All resistors show some non-linearity.

I don't think so. Care to explain what you mean by this?

[T3sl4co1l]

Ohm's law is approximate.  All resistors show some non-linearity.

I don't think so. Care to explain what you mean by this?

Ohm's law really isn't, not to nearly the same degree as KxL anyway.

The only thing that can be said to be "ohmic" is space itself, but that's tricky and kind of useless.  I'll explain in a moment.

There are myriad examples of non-ohmic devices.  Diodes are excellent.  Even among regular metals, depending on what time and voltage scales you're talking about, you can experience:
- Long time scales: self heating (e.g. light bulb filament)
- High current density: electromigration (and similar effects like memristance, in ionic conductors)
- Extremely high current density, high voltage: breakdown, ionization, plasma (e.g., The Z Machine)

It's somewhat miraculous, and rather handy, that so many ordinary metals and compounds are ohmic at all!

In bulk materials that aren't perfectly pure metals (there's a suitable physics definition for this), you can get diode junctions between crystal grains and mating surfaces.  For example, nickel plated connectors are undesirable for sensitive RF, due to possible mixing/modulation/distortion, due to Ni-NiO-Ni junctions on the connector surfaces.

Possibly the best (read: most linear over the largest dynamic range) ohmic configuration is no material at all: ohms defined by the EM field itself.  The impedance of free space is the ratio between electric and magnetic field strengths: just as the ratio of voltage to current gets you a resistance, or the ratio of inductance to capacitance gets you a resistance [squared].  It's kind of useless, because you don't get a resistor with two terminals; a wideband antenna is the closest representation of this, but contains metal.  And anyway, the side effect is beaming EM radiation off to infinity, which might not be desirable (also, any reflections received by the antenna will change the terminal impedance).

Even this will break down at some energy density, because nothing is forever; I'm not sure what the actual intensities required are, but a particle-physics description will go something like, photon up-conversion using virtual particles as reaction mass; eventually resulting in pair production of electrons and protons (and other assorted things, at ever-higher energy levels).  The ultimate mass-energy density limit of course being a black hole, but that's truly beyond astronomical: even light-speed quasar jets aren't quite *that* intense.

In any case, EM is truly and wholly fundamental to all of physics: it gave rise to relativity, is a crucial ingredient in QED (perhaps the most accurately proven theory in history), and extends all the way to the bottom of the Standard Model (where classical fields-as-we-know-them give way to particle-like descriptions of interactions, and numerous other charges become as or more important on the smallest scales, such as quark flavor charge).

Indeed, since KxL is just another conservation law, we could say something more general: that laws of that nature are much more widespread, so that whether you're talking loop voltage, or node current, or atomic quark color, or anything else that's conserved, it's the same mathematical symmetry in the system.  Of course, we don't call all those symmetries as "Kirchoff": that's limited only to the ones in electronics.

Tim

[filssavi]

Since kvl and kcl for you explain all Electromagnetism why are we bothering to kill half of our brain trying to get around math formalism of Maxwell equations
Since you clearly are smarter than me Can you explain how fiber optics work (in depth not just current goes in the laser diode and gets out the detector) modes, dispersion and all with just kvl and kcl

I have not said they explain electromagnetism. I have simply said that they are not invalidated by electromagnetism.

Well about that, it's not true either, KVL and KCL are used in lumped model circuit analisys so if you are low frequency (or better said the considered wavelenght are longer than your circuit lenght) they are indeed valid

If you start going upin frequency (or in circuit length think distribuzione grid wise) you will start seing that wires are not ideal any more they will delay and distort your waveform

These are trasmissione line effects and here regular KVL and KCL does not apply any more, what is done usually is to considerazione a lumped model equivalente of the whole line and then you can indeed stil use kirchoff's laws bug that is only an approximation its  not the real deal and as such it has some limitations

So if Kirchoff's law are of any good depends whether  you can just treat the TL as a black box or not if you can then you can measure it's properties (or more likely S parameters) and merrily use KVL/KCL if however this is not the case and you need to know exactly what is going on in the middle of the line then you cannot use them you need to step up your game and start consider full Maxwell's equations

P.S. it might be semantics but since optics fiber are Electromagnetism and KCL/KCL are not valid in this domain then they are invalidated by Electromagnetism (EM for short) in general, now if by EM you really mean the subset of EM we all generally work in so geometrically small low frequency circuits than yes they are and not invalidated but that is only a mall subset of EM field theory not the whole thing

[photon]

I think that Lewin is doing a magic trick in this video, pulling a rabbit out of a hat just for show. It is sleight of hand and does not stand up to closer inspection.

KCL is a statement of the conservation of charge and KVL is a statement of the conservation of energy. These conservation laws are true. If Lewin thinks he has an example circuit where KVL does not apply, then he has a circuit where the conservation of energy does not apply. But the conservation of energy always applies if you consider all sources of energy.

Lewin's example:
http://videolectures.net/site/normal_dl/tag=28248/non-conservative_fields-do_not_trust_your_intuition.pdf
is magic. The sleight of hand is that he introduces an energy source (a solenoid) from outside of his example circuit. He adds energy to the circuit without adding a circuit element to account for it.

You could find an example where Maxwell's equations do not apply in the same way. Just write the equations and omit a current or magnetic source.

I say bullshit.