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All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?

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LAN_403

Signification

Fri Jun 12 2015, 09:10PM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

DerAlbi wrote ...

Could you please elaborate how this is possible?
A CLOSED LOOP integrals start and endpoint are equal. Any added voltage along the path MUST be substacted somewhere else... or one single point (the start/stop point) has two different potentials....

Thats like redrawing a circuit diagramm, connecting a resistor from ground to ground and say that there is a voltage drop.

You are assuming a conservative field!!
NOW you know how it feels to be caught in the trap of the great non-intuitive nature of properly analyzing a series circuit in which the field is non-conservative. HERE THE CLOSED LOOP INTEGRAL IS NOT ZERO!!
---YES, VERY ODD INDEED.

DerAlbi

Fri Jun 12 2015, 09:16PM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

How can a potential-field be non conservative... now matter what path i take going from 'x' Votls to 'y' volts, you allways endup with the same integral.

BigBad

Fri Jun 12 2015, 10:58PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Basically, if there's an dphi/dt from anything other than self inductance, then you've drawn the circuit wrong; either you should have drawn a transformer, or as klugesmith has already stated, a voltage source. Either way, the RLC circuit is not incorrect.

The thing to remember is that RLC circuits are an abstraction of the real world- there's ALWAYS things that happen that aren't on that circuit diagram, such as EM radiation, and non linearities.

...

Sat Jun 13 2015, 06:47AM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

I think the crux of this 'issue' is that many people mis-interpret Kirchoff's laws. I personally have never read his works (I am pretty sure they are written in German so it wouldn't help even if I had), so I am not sure if he stated them in a way which was easy to mis-interpret, or if people just like to interpret them incorrectly, but Kirchhoff voltage law is not a path integral and it is misleading or even inaccurate to write it as such (as Signification pointed out in the first post).

One correct way to state so called Kirchhoff voltage law is 'The directed sum of the electrical potential differences (voltage) around any closed network is zero'. In this formulation you should apply it by first breaking your circuit in a number of distinct lumped elements (each with a potential difference across them, which you calculate using whatever method is appropriate for the lumped device). After you have done this, then you can say (based on the simple conservation of energy argument that Kirchhoff makes) the sum of all of these potentials must be zero. For further discussion on this point, see the wikipedia page in Kirchoff's laws

describes this more clearly than I care to.

You can, if you so desire, break the circuit into an infinite number of discrete elements (which is, to the best of my understanding, the argument that is used to convert the sum to the path integral form), however you still need to consider the fact that each of the infinitesimal lumped circuits still have a potential across them that you need to solve for using external methods.

Or perhaps you are arguing yet a more subtle point? In any case I am not sure who this 'famous MIT professor' is (perhaps Prof. Lewin and his lecture about the pitfalls of assuming lumped elements when you cannot), but I would be surprised that he is seriously claiming that 'all physics textbooks are in error'.

Dr. Slack

Sat Jun 13 2015, 08:29AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
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Posts: 1659

You've only got consider the loop round a betatron (wikipedia) ( they did consider calling it a " AuÃŸerordentlichhochgeschwindigkeitelektronenentwi ckelndenschwerarbeitsbeigollitron" ) to see that potential is not conserved, ie equal to zero, round a loop when there is a varying magnetic field impressed on it.

The grounding observation (that's grounding in the psychological rather than electrical sense) is to realise that important quantities like energy and momentum *are* conserved in slightly complicated things like betatrons and transformers, and to work on your models and interpretations so they are.

So in the betatron, you can consider the acceleration of the electron as perhaps absorbing energy or gaining momentum, and so assign a voltage drop to it, which lo and behold adds up backwards round the loop to equal the induction generated potential, Kirchoff restored.

Potential is not a conserved quantity, it is a defined quantity. In certain restricted situations, it can simplify the sums by summarising the work done by a moving entity that interacts with a field through that field. Gravitational potential (at least for our sub-light speeds and earthly densities where Newton is indistinguishable from GR) always 'behaves' because the field is irrotational. Electrical potential round a changing magnetic field is not, successively passing around a closed path (which the windings in a transformer approximate to) add more potential on each pass. It's up to our definition of potential, and what terms we allow into the model, that governs whether we tie ourselves in knots or not with it.

When you find a paradox, reality has got it right. Find the real variables (that is the strictly conserved quantities), make them behave, and that should bring your secondary concepts and models and simplifications into line.

Uspring

Sat Jun 13 2015, 09:29AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Dr. Slack got it right. Only electrostatic fields, i.e. no moving charges or currents, can be described by a potential, making the field a conservative one. In the case of a non zero magnetic field, Faradays law implies non zero voltages around loops. Basically that is the reason, why transformers work. A coil picks up voltages around a loop. If there are n turns, it will pick it up n times.

Ash Small

Sun Jun 14 2015, 01:25PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Wikipedia covers all this:- "KCL and KVL both depend on the lumped element model being applicable to the circuit in question. When the model is not applicable, the laws do not apply.

KCL, in its usual form, is dependent on the assumption that current flows only in conductors, and that whenever current flows into one end of a conductor it immediately flows out the other end. This is not a safe assumption for high-frequency AC circuits, where the lumped element model is no longer applicable.[2] It is often possible to improve the applicability of KCL by considering "parasitic capacitances" distributed along the conductors.[2] Significant violations of KCL can occur[3] even at 60Hz, which is not a very high frequency.

In other words, KCL is valid only if the total electric charge, \scriptstyle Q , remains constant in the region being considered. In practical cases this is always so when KCL is applied at a geometric point. When investigating a finite region, however, it is possible that the charge density within the region may change. Since charge is conserved, this can only come about by a flow of charge across the region boundary. This flow represents a net current, and KCL is violated.

KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for high-frequency (short-wavelength) AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.

It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.[2] These are treated as imaginary circuit elements that produce a voltage drop equal to the rate-of-change of the flux."

Signification

Mon Jun 15 2015, 11:29PM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

DerAlbi wrote ...

The RLC-Citcuit is completely covered by Kirchhoff.
Is that still about the Lenz-Issue in inductors?

If you believe this, you do not understand Faraday's law. You preach "math" is the key to understanding so consider the following:
It may be necessary to look at this from more of a physics point of view rather than that of an engineer. Kirchhoffs law does NOT hold here because of the 'effect' the inductor "L" has on the circuit. If a closed circuit contains a self inductor (even a simple RL circuit) a non-zero dÎ¦/dt exists through the "open surface" bound by the "closed loop" circuit. If you look at Faraday's law from Maxwell's point of view (I am not certain of which of Maxwell's equations this is-- 3 or 4), the circuit 'path' encloses a 'surface'. This path enclosing this area is mathematically expressed as:

1) "The closed-loop-integral of E dot dl"

this circuit path bounds an open surface (which MUST be associated with the path), mathematically expressed as:

2) "d/dt of the open-surface-integral of B dot dA"

Faraday's (and Maxwell's) law states that 1) and 2) above are equal. Of course this means that each expression must be the 'emf' of the circuit, which can be expressed mathematically as the flux (Î¦) rate of change:

3) Emf = -dÎ¦/dt, where Î¦ = Li (i being the circuit current). This also shows emf = -L * di/dt

Note that 1) equals 2) equals 3) !!

This changing flux (dÎ¦/dt) through the circuit's 'surface' causes the conductive circuits electric field (E) to be NON-CONSERVATIVE!!! and Kirchhoff is only valid for the special case of Faraday's law where the integral of E dot dl represents a conservative field, where the integral of E dot dl from, say, "X" to "Z" is independent of the path from "X" to "Z". This is the the potential difference between these limits of integration. HOWEVER in the non-conservative field (ie in an RLC-Circuit) the integral from "X" to "Z" DEPENDS ON THE PATH TAKEN and we must employ Faraday's law for the --general-- form where "the Emf or the closed loop integral of E dot dl = -L* di/dt...NOT zero" See 3) above.

The primary cause of the confusion here is in analyzing the circuit element "L", when assuming that the integral of E dot dl from one end of the inductor to the other is -Ldi/dt... NO...here, E=0! THIS IS WHERE THE PHYSICS TEXTBOOKS ARE WRONG!!

As a simple example of a non-conservative field, consider the number of windings (loops) of the circuit's self inductor (L). First, suppose there is only ONE winding in the inductor. Then there is only ONE surface in this element of the circuit that B passes through when the circuit is energized. Now suppose there is more than one turn in the inductor: suppose it's, say, five. Now each of the five turns creates a separate surface that must be penetrated by the changing flux, dÎ¦/dt. The Emf is now five times greater.

As an illustration, again, consider just the inductor. Suppose you have the single-turn inductor with the two ends of the turn at absolute positions "X" and "Z". The changing flux (dÎ¦/dt) through this surface produces a certain Emf at "X" and "Z". Now if you added four turns (total = five) you now have 'five surfaces' in which B penetrates separately. So, dÎ¦/dt now passes through five surfaces yielding five times the Emf. Further, suppose that you place the endpoints of this five-turn loop at the SAME positions "X" and "Z" of the single loop. Now it should be clear that the Emf, which is equal to the closed loop integral of E dot dl, which is the same as dÎ¦/dt is now five times higher, and thus DEPENDENT on the path taken from "X" to "Z". Forcing the conclusion that this field is non-conservative.

DerAlbi

Tue Jun 16 2015, 11:03AM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

I really dont know what you point of agruing is. There seems to be a big misconception about modelling things. (Just a feeling, since i really cant follow you...)
I will point out some stuff thats occurs to me as "odd"...

This changing flux (dÎ¦/dt) through the circuit's 'surface' causes the conductive circuits electric field (E) to be NON-CONSERVATIVE!!!

Changing Flux. Changed by WHAT? So.. if you just short circuit a resistor, you argue that in a changing magnetic field there would be current flowing through the resistor.. is that your point? And since there is only a short circuited resistor in the schematic the math (Kirchhoff) must be wrong?
Actually the model is wrong then. If the resistor is exposed to a changing magnetic field and the parasitic effects are noticable the parasitics must be in the model/schematic too. In my case (of the resistor) that would be a transformer added in series to the resistor. (So the resistor is short circuited not with a wire, but a transformer - the transformer is made by the wire loop -> Kirchhoff holds then)

As an illustration, again, consider just the inductor. [...] The changing flux (dÎ¦/dt)....

Ok, open circuit, so no current flows. Just the inductor, but there is a changing magnetic field. Where does that come from? It must be a transformer, not an inductor.

suppose that you place the endpoints of this five-turn loop at the SAME positions "X" and "Z" of the single loop.

So two parallel inductors penetrated by the same magnetic field (flux). Thats a transformer again. (Primary and secondary connected togehter, shared flux, and a imaginary third winding that produces the changing flux, that is missing in all your models and generates all the missing terms)
See here:

..scroll down until you come across the word "mutual"

Everything you do seems to assume a changing magnetic field that induces voltage in your circuit via parasitic inductances. The voltage over that inductance is the problem you have, right? So why you dont add the propper parasitics (transformer) to the model?
Kirchhoff will hold then.

Sry if i am completely wrong.. but i dont get how a circuit can have a "surface" as you mentioned. If there is an interacting current loop with outside stimulants then it has to be modeled properly (including the stimulant, even if its not directly in your circuit). After that (transformer in your case) appears in your circuit as an element then everything is ok with Kirchhoff.

You model ESR, you model ESL, you model parasitic capacitances, but you dont model coupled inductive effects?

Signification

Tue Jun 16 2015, 02:55PM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

@ DerAlbi:
...looks like, what is needed is a 'good' college physics text (a nice thick heavy one) with a --complete-- section on electricity and magnetism that properly and thoroughly explains Faraday's law (of which Kirchhoff's rule is a special case when there is zero dÎ¦/dt).

If Kirchhoff's law is used in a circuit containing an inductor--it is in error, although, in the book. the correct answer is manipulated out of it by assuming that the closed path integral Eâ€¢dl = 0 (it is actually -L di/dt) and that the integration Eâ€¢dl along only the inductor is -L di/dt (it is actually zero).

Faraday's law, In full detail, for the engineer and physicist, may be expressed in a very versatile manner, allowing you to choose the equality that best fits your particular circumstance:

Emf = -dÎ¦/dt = -Ldi/dt (since Î¦=Li) = -d/dt open surface integral of Bâ€¢dA = closed loop integral of Eâ€¢dl

I don't know what else to tell you.

I will comment, though, on one part of your reply:
------------------------------------------------- ---------------------------------------------
SIGNIFICATION: "As an illustration, again, consider just the inductor. [...] The changing flux (dÎ¦/dt)...."
DERALBI: "Ok, open circuit, so no current flows.
------------------------------------------- -------------------------------------------------- -
Did you actually think I was refereeing to an unconnected inductor floating in space?

PS
You know...I'm actually looking forward to the day we are actually in complete agreement!

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