Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 12 2015, 04:50PM

I dont get quite what you mean.

in any such circuit through which there is a changing magnetic flux

i assume you mean: "externally changed flux". That would be a transformer then.. and its true, that the equivalent circuit of a transformer has a voltage controlled voltage source in it (its actually an ideal transformer).

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

To help you out of this, please think about what makes the inductor-current rise so slow instead of behaving purely resistive.
If you apply a voltage, the changing magnetic field inducts a voltage oppositve to the source voltage (Thats Lenz, and that opposite voltage is where your Minus-confusion comes from) The selfinduced voltage compensates the applied voltage completely and therefore there is no changing magnetic field anymore. However without chaging magnetic field the external voltage issnt compensated anymore.. so the indurctor finds its way to deal with the situation and lets the current rise slowly.
Its simplified, but thats the explaination why the inductor counteracts currentchanges...

So... at the end: there is a negative voltage selfinduced. However this voltage is not seen outside of the inductor, so dont care about it. Lenz only tells you why the inductor behaves the inductive way.. not more.

Outside of the inductor Kirchhoff holds.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 12 2015, 06:19PM


First, in your quote, you imply that "without changing magnetic field"..."the inductor current rises slowly".
This is NOT true. Because--'without a changing inductor magnetic field'--there is ZERO current change, --ALWAYS-- (not even "slow current rise" as you state).

I see you need more information--I will look for a video link that explains this phenomenon and post--the primary thing here is dealing with conservative vs non-conservative fields. And a changing flux around an inductor constitutes a NON-conservative force--HERE is where Kirchhoff does not apply, but the general Faraday law does.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 12 2015, 06:43PM

Of coruse i described a paradox situation.

-> Apply voltage -> current flows -> field changes -> countervoltage (Lenz) compensates applied voltage -> no current flows -> no magnetic field -> no countervoltage -> but then voltage is applied -> current flows.. -> ........

If you do these steps discrete of course thats a stupid thing. But this describes why the inductor lets the current only change slowly...
None of these steps happen consecutive.. its all at once. and the inductor solves that situation to allow the current to change slowly. The bigger the inductor, the more effective it slows the current change.

What it needs to show you that there is a voltage within that process which has a negative sign.. but that is not externally visible outside the inductor and therefore does not matter for Kirchhoff.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 12 2015, 08:07PM


Yes you did...

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 12 2015, 08:16PM

But do you get the idea?

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 12 2015, 08:26PM


I know what you meant
BTW, The voltage is NOT external (no power sources inline) it is the initial capacitor voltage, Vo, that supplies the initial circuit current, Io, like in a CG (in which case a critically damped current is significant). But here, an exponentially decaying sine wave of many resonant cycles is also considered. It has been somewhat of a nuisance that the, slightly, damped 'sine' peaks (even in an IDEAL slowly exponentially decaying sine wave) are, I think, individually distorted, and non-symmetrical.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Uspring, Fri Jun 12 2015, 08:27PM

Signification wrote:

So everyone should be applying the rule: ** The closed loop integral of E 'dot' dl around a circuit = -"L di/dt" **, not "0"

Yes, certainly. Often you can neglect this, when L or dI/dt is small. In microwave circuits even short PCB traces can have significant voltage drops.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
klugesmith, Fri Jun 12 2015, 08:50PM

Who dropped the proper citation and qualification of Kirchhoff's voltage law,
as a rule for lumped-element models of electrical circuits?
"The directed sum of the voltages around any closed network is zero."

As others have said, magnetic induction effects are internal to the lumped-element models of inductors and transformers.

When dealing with external magnetic fields (Kirchhoff's laws have no place for fields),
for example a printed circuit's sensitivity to electromagnetic interference,
we can model the dΦ/dt term as a voltage source element in series.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 12 2015, 08:57PM

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

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 12 2015, 09:10PM


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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 12 2015, 09:16PM

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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
BigBad, Fri Jun 12 2015, 10:58PM

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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
..., Sat Jun 13 2015, 06:47AM

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'.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Dr. Slack, Sat Jun 13 2015, 08:29AM

You've only got consider the loop round a betatron (wikipedia) ( they did consider calling it a " Außerordentlichhochgeschwindigkeitelektronenentwi 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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Uspring, Sat Jun 13 2015, 09:29AM

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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Ash Small, Sun Jun 14 2015, 01:25PM

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."

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Mon Jun 15 2015, 11:29PM


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 dΦ/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 (Φ) rate of change:

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

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

This changing flux (dΦ/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, dΦ/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 (dΦ/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, dΦ/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 dΦ/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.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Tue Jun 16 2015, 11:03AM

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 (dΦ/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 (dΦ/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?

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Tue Jun 16 2015, 02:55PM

@ 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 dΦ/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 E•dl = 0 (it is actually -L di/dt) and that the integration E•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 = -dΦ/dt = -Ldi/dt (since Φ=Li) = -d/dt open surface integral of B•dA = closed loop integral of E•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 (dΦ/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!

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Tue Jun 16 2015, 03:27PM

My problem is currently, that with Kirchhoff i can clearly describe a RLC circuit, its eigenfrequency and its amplitude decay over time given a certain starting condition by solving the differential equations.. And all this can be measured and validated with an oscilloscope..
And you actually tell me that Kirchhoff is wrong in the RLC case... thats hard to agree on. Kirchhoff is used regularly in circuits with inductive components and it allways works.

by assuming that the closed path integral E•dl = 0 (it is actually -L di/dt) and that the integration E•dl along only the inductor is -L di/dt (it is actually zero).

How? Who? Where? What?

Could you please make a proper cicuit diagram, and apply kirchhoff and tell me what you think along the way?

What would be specially interesting is when you write all the equations like
Vr = I*R
VL = L*dI/dt
Vc = I/C*dt
for Kirchhoff at the individual components, where your ring- and area-integrals come into mind...
(i honestly dont see why: Kirchhoff is circuit analysis, your integrals over E and B and stuff is NOT circuit-level)

And this is really not about disagreement. I actually can not follow your mixup like the E- and B-field in relation to a circuit. In a circuit an inductor is just an impedance where VL = L*dI/dt holds. Like the capacitor is an impedance where Vc=I/C*dt applies.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Tue Jun 16 2015, 06:53PM

...like I said DerAlbi, I don't know what else to say to you. You are simply mis-applying Kirchhoff's law You can find a "good" physics text, study what I have said as many ways as I know how, or find a youtube video that properly applies Faraday's law to a circuit containing an inductor. Since you can't seem to accept anything I send, I spent ten minutes and found this:

I have bent over backward for you on this subject--I write what I know, how I know. You are just running me in circles here--and I don't have time for that. So, I just hope someone will chime in and do better.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Uspring, Tue Jun 16 2015, 07:10PM

Signification has a point, but a minor one. If you consider a circuit of say a 10mH inductance a 10uF capacitance and 1kohm in series, arranged in a loop of say 10cm diameter and driven e.g. by a sine generator, the loop made out of these components will itself have an inductance of a few 100nH. To calculate the circuits correct behaviour, one would have to replace the 10mH by 10.0003mH.

There are many textbooks out there explaining Newtonian mechanics. Newtonian mechanics is wrong, as known since Einstein. The point is, that Newtonian mechanics works very well in many cases, but is much more simple.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Tue Jun 16 2015, 08:51PM

Uspring, thats exactly what i say but that does not satisfy signifiaction.
I tell him, if the loop is an inductor you have to put that (coupled) inductor in the schematic but thats somehow not enough. Hes fine with adding ESR, parasitic capacitances, and he can even consider ESL of capacitors and stuff.. but the parasitic inductance in the circuit seems a no-go to add.
This is perfecly my short circuited resistor above. if the short circuit wire is considered a loop and there is coupling happening, then the resistor needs to be short circuited by a transformer, not a simple wire anymoe - the model/circuit would be wrong. But somehow this seems wrong for signification...
I really do not know what we can add to this...

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Tue Jun 16 2015, 09:16PM


Of course! It would be ridiculous to do this in any other way for "everyday" applications. However, I have found it just as easy in most "everyday" circuit problems like we are discussing to use Faraday as opposed to Kirchhoff, even where Kirchhoff holds true. Since I learned the proper use and "respect the way", I tended to not use an "invalid" analysis, even though this established 'incorrect' method does give the proper answer--at the expense of thinking wrongly. Strangely, for Kirchhoff, this has become (or was always) accepted, even in the texts. I am noticing, recently, that the proper method and its realization are slowly emerging. Of course it would be insane to use relativistic-corrected equations in an classical application of the motion equations.

IMHO, a full understanding of the Faraday / Kirchhoff laws is very valuable in the E&M fields

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Tue Jun 16 2015, 09:39PM

...and that youtube video... what is your problem with it? I dont see where Kirchhoff does not apply.
In the end (the RL-circuit) he actually comes to the statement that the voltages add up to 0.

Question: may i ask what kirchhoff is for you?
For me there are 2 fundamental rules:
-At a circuit junction, the currents add up to 0A.
-In a cicuit loop, the voltages add up to 0V.

and that basic statement is actually shown in the endscreen of the video.
To proove that Kirchhoff is wrong? Sry, i still dont get it.
He adds up the voltage over the resistor, and the timedependend voltage over the inductor... and adds it up to 0. that invalidated kirchhoff how again?? *whooooooot*

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Tue Jun 16 2015, 10:15PM


The video is correct, I thought you would see that--that's why I linked it for you. Then in your reply you say--"he used magnetic field lines that don't connect". I wanted to know what you meant by that statement--but when I went right back to quote that statement you had edited it out and it -now- seems you decided to agree with the video and are asking me what MY problem was with it???????????? I am interested in straight learning and teaching, you play dirty!

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Tue Jun 16 2015, 11:04PM

I dont agree with his simplifications.. they were strange but lead to his goal somehow, thats right. i decided that my feelings about the lecturer dont matter and you allready replied, so i added a new post.

But can you now tell me how this invalidates Kirchhoff? You say that the video is correct, but you also say that i am using Kirchhoff wrong and it does not apply...

I wrote the Voltages like this:
Vr = I*R, VL = L*dI/dt, Vc = I/C*dt
And the Video used the same notations, set the sum of all voltages to zero (which implements Kirchhoff) and is correct in the end...
Is me beeing wrong just a matter of personal dislike?

Could you pleeeaase shed some light on this?

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Wed Jun 17 2015, 12:25AM

DerAlbi:
Use:
1) VL = 0 And
2)integral E•dl= -L di/dt
BTW: for the capacitor use VC = q/C, NOT Vc=I/C*dt ...I think you meant to write Vc=I*dt/C above

Now set up the equation using 1) and 2). What do you get? (post it--we can start here)


Are you sure in the video the sum of the voltages was set to zero?? and not -L di/dt ? I'll replay it

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Wed Jun 17 2015, 01:19AM

1) VL = 0

WHY should i use that? That is only true if the current is constant. Its called a steady state. And its actually expressed by VL = L*I/dt. -> if I is steady I/dt == 0. But its simply not true. The full truth is VL = L*I/dt.
If all textbooks are wrong about Kirchhoff, i would like to know any textbook that sais that the voltage over a coil is unconditionally zero....

BTW: for the capacitor use VC = q/C, NOT Vc=I/C*dt ...I think you meant to write Vc=I*dt/C above

Sry, what is the difference between Vc=I/C*dt and Vc = I*dt/C ? 1/2*3 = 1.5. 1*3/2 = 1.5 And NO, even some americans tend to read it wrong, there is not bracket implied by the notation... if i want a bracket there, then i would have written it. (I assume you read it the **** american way like Vc=I/(C*dt). There is no reason for that - multiplication and division do have the same priority (Both over + and - and below the "power-of"-operator)

VC = q/C

...and q is the integral of the current over time, right? so... q = I*dt. you get Vc=I*dt/C ....or I/C*dt for that matter

Now set up the equation using 1) and 2). What do you get? (post it--we can start here)

Sry to deny your request, i wont participate in such BS. 1) is wrong. 2) is true. Unfortunately mixing false and true adds up to false in this case.

Are you sure in the video the sum of the voltages was set to zero??

a few seconds before Endscreen.

And pleeeeas that guy is kind of a dude who should not teach..... In his last example he charges the coil to steady state current so that there is no voltage drop across the inductor and uses that VL=0 as condition for non steady state analysis.
The only thing that is true in that case is that dI/dt equals 0 which implies VL=0, but writing only Zero and neglecting the true mathmatical formula is... i can not tell you that in words. i actuallly can understand your confusion if you watch stuff like that.

Again and forever: The voltage across a coil is determined by its inductance and the rate of current change only. If the current change happens to be zero - fine, coilvoltage is then zero, BUT that is in no way the general case and should NEVER be asumed in a non-steady state.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Wed Jun 17 2015, 04:47AM

Turning the page.....

PLEASE USE SPELL-CHECK, WITH ALL THE RED ON THE SCREEN I CAN'T TELL MY BAD SPELLING FROM YOURS

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Wed Jun 17 2015, 11:14AM

Troll.
lett soneome elz hes a tri

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 19 2015, 04:14PM

Does this make sense to anyone?

]faraday.pdf[/file]

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Hazmatt_(The Underdog), Fri Jun 19 2015, 05:11PM

I'm going to poke my head in just for a laugh here because I know it won't make a difference, but I thought I would have some fun with it.

So let's look at this guy for a moment


I grabbed this from Wikipedia. V1 + V2 + V3 + V4 = 0. And this is STEADY STATE, no instantaneous currents, and no switches thrown at t = 0+, and no phantom induced voltages from the aether or orgone fields. This is Kirchhoff's voltage law, and we know what to expect, the sum of the voltages is zero.

Let's also look at Ohm's Law for a second here, V = IR. So we have a "VOLTAGE DROP" across a resistance with a given current, just like in the example above. This we also know and have verified time and time again.

Both together also prove the sums of the currents in the loop equal zero.

Now let's also look at V = L di/dt. What does this mean? This means the Voltage across the inductor changes as the inductance times the "RATE CHANGE" of current over the "RATE CHANGE" of time. Meaning this current changes as the time changes, it is NOT time independent.

At some very large time t, the magnetic field stops changing as the current has stopped changing, as in a solenoid coil with a battery attached to form an electromagnet. We have all done this with a coil and a nail as children.

At this time, where t is very large, we can integrate, moving L outside of the integral, which gives us V = L (integral) di/dt, the INDEFINITE integral then gives us V = LI, much resembling V = IR our friend Ohm's Law, now how about that!

Now if we took out R2 and replaced it with L, Kirchhoff's summation loop would look something like this

V1 + V2 + V3 + V4 = 0

WOW! IT DIDN"T CHANGE! HOW SO! THERE MUST BE A TRICK!

No, because we replaced R2 with an inductor and TIME t = infinity.

RI (1) + LI (2) + RI (3) + V4 ( Battery) = 0

AND the sum of the currents around the loop also equal zero.

Kirchhoff's Law is restored.

Now go ahead and shoot holes through me, I already have my degree so it doesn't matter.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Fri Jun 19 2015, 06:52PM

At this time, where t is very large, we can integrate, moving L outside of the integral, which gives us V = L (integral) di/dt, the INDEFINITE integral then gives us V = LI, much resembling V = IR our friend Ohm's Law, now how about that!

Just a tiny but important hole to poke in L*I does not add up to Voltage if you consider the units. So that must be wrong

Lets consider Significations PDF (just one little part as an example)



Ok. Lets asume there is no electrical field between the inductor-leads...

Now: lets change the measurement setup.
We create a constantly changing B-Field with a 1H-Inductor (superconducting) and 1V aplied. That will make a dI/dt of 1A/s rising to infinity.
Within that B-Field we put a perfeclty coupled 1H Inductor and measure the voltage at the leads. But not with a resistive measurement. We just observe the electric field between the leads (there should be none according to the PDF)
At the leads we connect a small capacitor so store the (non existing) electric field for later measurement.

So after we disconnect the capacitor after some time, what voltage will it have?

We all know it: The capacitor will be charged upto 1V, because all we have built is a 1:1 transformer. Applying 1V at the primary side will result in 1V at the secondary side.
Since the voltage at the capacitor is constant (=1V) there is no current flowing.
However: if there is an electric field between the capacitor-plates it will be also between the capacitor leads. And heeeey the capacitor leads are actually connected to the inductor leads. so somehow there is an electric field between the inductor-leads...

Soo.... dear PDF.. explain that, MIT
Magic?

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 19 2015, 10:22PM


I think any reply here will make a difference--NO SHOOTING--I, for one, would like to really get all this straight, if possible, and welcome any opinion.
----------------------------------------- --------------
OK,
Actually, you could take L from under the integral sign ANYTIME--it is constant. It appears you are 'solving' just V =L di/dt. If you consider, the addition of a voltage source and a resistance, say, V4 and R2 from the Wiki... (let's call them V and R) and apply Faraday's law, going around the loop and encountering the circuit elements: L, then, R, then V, in that order,
the proper application of Faraday's law---which is :

the closed loop integral of E•dl = -L di/dt; yields the differential equation:

0 + IR - V = -L di/dt.

This is useful in TWO ways:

FIRST: rewriting this solution in the form: V - Ldi/dt = iR is very illustrative...this form shows how the time-dependent, Ldi/dt, after a long time period, vanishes, Leaving us with the steady state equation:

V = iR; Ohm' law, unchained.

************* + DerAlbi ***************** (YES, I agree units must check--In my option they can often be more important than magnitudes)

SECOND: We can see how the IMPROPER application of Faraday's law gives the RIGHT answer---how most books do it.

They wrongly assume Faraday's law is:

1) "The closed loop integral of E•dl = 0" (This is the special case of Faraday, called Kirchhoff that is valid when there is no changing flux)
2) the component of the INTEGRAL of E•dl through the inductor is L di/dt

Reworking the same problem above yields the same answer...but remember the right way and the wrong way...

RIGHT WAY:
---------------------------------------------
closed integral E•dl = -L di/dt
inductor component INT E•dl = 0

WRONG WAY:
--------------------------------------------
closed integral E•dl = 0
inductor component INT E•dl = L di/dt

I prefer getting the right answer the VALID way--NOT out of a misapplication due to misunderstanding that just happens to give the right answer in this case.

@ DerAlbi:
Speaking of units revealing much information: You considered a 1H inductor (L = 1H) with 1A applied through it, and mention it 'rising to infinity' Aren't the units of a Henry (Volt-Sec/Amp)? I like to re-arrange the 'wording' of the units to a much more intuitive: One Volt per (Amp/Sec). In other words, your 1H inductor will see a rise of in potential of 1 Volt if di/dt = 1 Amp/s.
I may be missing the complete picture here, but if di/di = 1 A/s and L = 1H, with a constant 1V applied, shouldn't L reach a steady state potential rise of 1V in 1s?? What does your 'infinity' refer to? I may be looking at something wrong as I feel I need to re-read your post.
.
.
...Was there a capacitor in the PDF circuit? Anyway, the E field of the capacitor is not IN the inductor.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Sat Jun 20 2015, 12:08AM

Speaking of units revealing much information: You considered a 1H inductor (L = 1H) with 1A applied through it

Noohh 1V applied!

Aren't the units of a Henry (Volt-Sec/Amp)? I like to re-arrange the 'wording' of the units to a much more intuitive: One Volt per (Amp/Sec). In other words, your 1H inductor will see a rise of in potential of 1 Volt if di/dt = 1 Amp/s.

Its not "a rise of" it is 1V (absolute). I think thats a difference.

I may be missing the complete picture here, but if di/di = 1 A/s and L = 1H, with a constant 1V applied, shouldn't L reach a steady state potential rise of 1V in 1s??

No. Only current rises. Voltage is simply there as soon as the coil is exposed to a changing B-Field.

What does your 'infinity' refer to?

The infinitiy only refers to the fact that if you apply a constant 1V on a superconducting 1H-Coil then the current will increase to infinity in infinite time with the rate of 1A/sec.

...Was there a capacitor in the PDF circuit? Anyway, the E field of the capacitor is not IN the inductor.

No there wasnt. But thats an interesting modification!
The electric field is not only inside the capacitor! The potential difference is the same everywhere outside the capacitor. If the voltage between the plates is 1V, then the voltage between the leads is also 1V. Since those leads are connected to the coils leads, also the coils leads will have a potential difference of 1V. Therefore there will be a electric field at the coil even if there is no current flowing (cap voltage is constant 1V). That kind of contradicts the PDF in my opinion.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Ash Small, Sat Jun 20 2015, 12:16AM

I've been watching this thread, and while there seems to be some consensus regarding the 'steady state' (DC) stuff, if you apply Ohm's law to Der Albi's 'superconducting inductor', I=V/R gives infinite current, once the 'steady state' is reached, as R=0.

I don't have a degree, but I've known Ohm's law since I was a kid.

EDIT: Assuming the current source can supply infinite current.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Sat Jun 20 2015, 01:21AM

So, isn't it time to at least form a REAL circuit (even is the values are a bit unusual) then we can actually solve an
RLC circuit:
Let's suppose the capacitor, C, is the only energy *source*, similar to a (dry) coilgun circuit with Vo=1v.

So, from above we let:
L=1H
v(0) = 1v
Now, if someone will kindly suggest any old R and C please?
C=?
R=?

Then we will get an actual circuit's response.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Uspring, Sat Jun 20 2015, 12:02PM

The paragraph DerAlbi quotes, is obviously wrong. It says there, that the voltage measured by the voltmeter is not the potential drop across the inductor but instead a measure of the time rate of change of magnetic flux in the voltmeter circuit. If that would be the case, then would placing the voltmeter outside the field cause a zero reading? It would not. The electric field would be in the inductor, even if there is no voltmeter present. Dr. Slacks betatron example shows, that there are fields to e.g. accelerate electrons without any coils or voltmeters picking the field up. That is a consequence of Maxwells equations and Faradays law, which is part of them.

Signification wrote:

However, I have found it just as easy in most "everyday" circuit problems like we are discussing to use Faraday as opposed to Kirchhoff, even where Kirchhoff holds true. Since I learned the proper use and "respect the way", I tended to not use an "invalid" analysis, even though this established 'incorrect' method does give the proper answer--at the expense of thinking wrongly.

I tend to think of Kirchhoff to be a consequence of Faradays law. Exactly valid, if there are no changing fluxes and often a very good approximation, if there are. There are cases, where Kirchhoff is quite wrong, but there are also cases, where Faradays law has problems, e.g. in the quantum domain.
So you say, Kirchhoff is invalid, I will do this correctly using Faradays law. Then I say, Faraday is incorrect, you must use quantumelectrodynamics and I won't consider using an "invalid" analysis. We could go on debating this forever. At one point, one has to say, we are accurate enough. Argueing in terms of final validity doesn't lead anywhere.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Ash Small, Sat Jun 20 2015, 01:32PM

All mathematical models are wrong, but they can be useful approximations, sometimes, if you use the correct model.....Who was it who said 'In theory, theory is the same as practice, but in practice, it isn't'?

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Hazmatt_(The Underdog), Sat Jun 20 2015, 05:30PM

This is the justification from my Physics Book, Halliday/Resnick/Walker 6th Edition

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Sat Jun 20 2015, 06:59PM


Great!! Starting there...

We know that:
1) Emf = closed path integral of E•dl
and since, in general, the flux (Φ) in a circuit is proportional to the current (i), where the proportionality constant is the self inductance (L), we have:
2) Φ = -L di/dt (with Lenz'); So from your physics book:
3) Emf = -dΦ/dt; now, equating 1) and 2) yields:

***** Emf = closed path integral of E•dl = - L di/dt (NOT 0) ***** THIS IS THE GENERAL LAW OF FARADAY:

Why not just use this whenever an inductor is (or is not) in the loop and settle for the right answer obtained every time and in a valid way. AND, unlike several applications in other fields, where such an argument leads to non-classical techniques to get the "exact / precise / perfect" answer is impractical, here it is no more difficult.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
..., Sat Jun 20 2015, 10:51PM

You can, it is certainly not wrong on a technical level to solve the circuits presented in this thread that way. Of course if your professor tells you to correctly apply Kirchoff's laws and you solve it using Faraday's law you would still be marked down

The point of Kirchhoff laws are to make circuit analyses simpler. Sure, for this exceedingly simple case of a few components in a single loop you do not save a whole lot of time by using the simplified method proposed by Kirchhoff, but I would love to see you use Faraday's law to solve something as simple as a differential amplifier, without going through roughly the same steps Kirchhoff did to derive his laws, and then solving it as he proposes.

I do feel that a point which has been made several times (by Klugesmith, myself, Uspring, and others) needs further attention, which is that you need to be consistent with your method. If you apply Kirchhoff's voltage law just like you would Faraday's law (as has been done several times in this thread) you will get the wrong answer, because that is not the correct way to apply Kirchhoff's laws (as has been pointed out by the aforementioned people). If you are applying Kirchhoff's voltage law on a circuit which is under the influence of an external magnetic field, you need to put in a model for the coupling between the magnetic field and the wires in your circuit. If you do not do this, you are breaking the assumptions that are used to derive Kirchhoff's laws, and you will get the wrong answer, as you would expect.

Personally, I do not like to see Kirchhoff's law written as a path integral, because I find it misleading. Some physics books have an unhealthy obsession with calculus and try to re-write the usual Kirchhoff's formulation (...The directed sum of the electrical potential differences...) as a path integral, but as you have pointed out this can be confusing. I have yet to see a book written by an electrical engineer that does it this way, since the whole benefit to Kirchhoff's laws is that you can beak the circuit down into a number of abstract 'components' (resistances, voltage controlled current sources, small signal models for nonlinear components, etc) and easily manipulate the resulting system of equations to quickly extract the circuits behavior.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Antonio, Sun Jun 21 2015, 02:15AM

I like to think that Kirchhoff's laws only work perfectly with small or slow purely resistive circuits. I the circuit happens to have a pair of conductors with large area one close to the other, electrical charges accumulate on them when the voltage between them varies, violating the current law. We then add a capacitor there and the law holds again. A long conductor, possibly coiled, presents a voltage over it when the current varies, violating the voltage law. We add then an inductor to the model and the law continues to hold. If this same conductor produces a voltage when the current in a nearby conductor varies, we add a transformer to the circuit to account for the effect.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
DerAlbi, Sun Jun 21 2015, 04:31AM

Kirchhoff works with every circuit element there is. There are no restrictions as long as you have a V-I-relationship that can be expressed as equation.
If such relation happens to be nonlinear, interpolated tables or a differential or even an integral so be it.
Best example of applied kirchhoffs law is a circuit simulator. And magically you even can simulate inductors!

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
klugesmith, Mon Jun 22 2015, 12:16AM

An Internet search just found it attributed to one Chuck Reid: In theory, there is no difference between theory and practice; In practice, there is.

The aphorism about models belongs to statistician George E. P. Box, FRS. His writings include several variants, today well covered by Wikipedia. Referring to books from 1987 and 2005,
p.74: "Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." p.424: "Essentially, all models are wrong, but some are useful". p.440: "The most that can be expected from any model is that it can supply a useful approximation to reality: All models are wrong; some models are useful".

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Mon Jun 22 2015, 01:58PM

I would like to make a brief summary of my original intentions, of a circuit involving an (L), to be looked upon:
There are four possibilities:
----------------------------------- ---------------------------------------
BTW, I like to use the following shorthand integral notation:
"INTEG" = any integral
"PATH" = line integral
"C.L." = closed loop (line integral)
"O.L." = open loop (line integral)
"C.S." = closed surface (surface integral)
"O.S." = open surface (surface integral)
---------------------------------------- ------------------------------------
"L"'s contribution to:

1) Emf of C.L. PATH of E•dl = -L di/dt.........L's contribution in transversing the loop= 0
2) Emf of C.L. PATH of E•dl = 0................L's contribution in transversing the loop = -L di/dt
3) Emf of C.L. Path of E•dl = -L di/dt.........L's contribution in transversing the loop = -L di/dt
4) Emf of C.L. PATH of E•dl = 0.................L's contribution in transversing the loop = 0

1) Is "correct"
2) Incorrect, but yields the proper answer ( identical to 1) )
3) Incorrect: would employ the "L" twice! (I have never seen this used--possibly because of the absurd answer)!
4) Incorrect: would "NEVER" consider "L" (resulting in just an RC behavior) "L" would be missing from the differential equation, and, from the obviously wrong, solution!

So, whether 1) or 2) is used, we get the same, correct, answer. 3) and 4) yield nonsense.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
..., Mon Jun 22 2015, 06:02PM

Your expressions without further justification of your assumptions used to derive them are insufficient to conclude 'correct' or 'incorrect'.

1) is correct under the usual assumptions of Faraday's law (infinitely thin conductor, not moving at relativistic speeds, no external fields acting on the circuit, yatta yatta, maybe we can all agree to use Halliday/Resnick/Walker's derivation?)
1) is incorrect under several of the usual assumptions of Kirchoff's law, mainly the assumption made in the derivation of Kirchoff's laws that the 'wires' (which refer to the abstract concept of an electrical connection between 2 components, not the physical wires in your circuit) have exactly the same voltage at all points (on a given wire) for a given time. Clearly in this circuit if we model the inductor as a coiled up 'wire' we have a contradiction.

2) is incorrect under the usual assumptions of Faraday's law, because in order to set E*dl = 0 there needs to be no flux in the circuit (neither external or internal).
2) is correct under the usual assumptions made for Kirchoff's law, where one has modeled the inductance of the physical inductor as a lumped element with inductance L, and additional 'wires' (which recall, are not representative of the physical conductors in the circuit, but rather the abstract concept of the electrical connections between the lumped components) which do not drop any voltage.

3) and 4) are wrong under either set of assumptions, but I would argue that with some creative assumptions they could be correct. In any case, they aren't particularly useful to us since they won't be modeling an inductor in this universe

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
BigBad, Mon Jun 22 2015, 08:06PM

Is it just me, or have you guys not thought about why complex numbers are used to analyse circuits?

Kirchoff's law work just fine with inductors and capacitors in the circuit if you use complex impedances; provided also that there's no significant unmodelled stray inductances or capacitances etc.

In that case, the voltages do indeed zero out around loops.

The ideas that Kirchoff falls apart if there's inductance, or that Faraday's law is not already part of Kirchoff are total bullshit. You just have to use complex impedances and currents and voltages.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Mon Jun 22 2015, 08:47PM

This thread shares valuable knowledge (to me...) as it progresses: I pay close attention to all replys and learn from them--I also look forward to more...

Here are two short segments of (I think, the same) MIT lecture that appeared to illustrate (with an actual demonstration circuit (at the end of part 2) this Faraday vs Kirchhoff 'phenomenon'.

part 1:


part 2:


I am still searching for that 'detailed supplement' but can't seem to find it on the MIT page. I will post it when I find it. I saw it a couple year's ago, so I know it is out there--it is convincing--certainly to the students!

BTW: at the start of part 2, when he mentions 100 and 900 "VOLT" components, he actually means "OHMS".

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Antonio, Mon Jun 22 2015, 11:57PM

Complex impedances are just an algebraic representation of what happens when the voltages and currents are all in sinusoidal steady state. Of course Kirchhoff's laws apply there, but that analysis can't be applied directly in transient waveforms, where Kirchhoff's laws also apply, as long as the assumption of a lumped circuit is valid.

In the MIT lecture the circuit is made with a loop of wire around the central solenloid interrupted by the two resistors, and the oscilloscope reads the voltages over the resistors with the ground connection between both. The outcome is perfectly correct, since the loop of wire forms a transformer with the solenoid. The "missing" voltage source is over the loop, induced by the solenoid switching. Care must be taken to route properly the connections to the oscilloscope, otherwise the coupling to the leads may be significant too.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Ash Small, Tue Jun 23 2015, 03:35AM


The results obtained are exactly what you'd expect from this circuit:





(I forgot to add the resistor values, 100 Ohm on the left, and 900 Ohm on the right, the same as in the demo.)

In the previous demonstration (the first video) the 1 volt source was across the meter as well as the 100 Ohm resistor. In the second demonstration, it's obviously not measured by either meter, as it's an induced voltage that is induced around the whole loop.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Uspring, Tue Jun 23 2015, 08:52AM

Signification wrote:

***** Emf = closed path integral of E•dl = - L di/dt (NOT 0) ***** THIS IS THE GENERAL LAW OF FARADAY:

EDIT: Not quite. Faradays law relates the E*dl path integral to the flux change dphi/dt.

Why not just use this whenever an inductor is (or is not) in the loop and settle for the right answer obtained every time and in a valid way. AND, unlike several applications in other fields, where such an argument leads to non-classical techniques to get the "exact / precise / perfect" answer is impractical, here it is no more difficult.

Actually it is more difficult to do it this way. Consider an inductor and other components wired in a loop. Applying Faradays law to all of this would require to calculate the flux inside the inductor and also inside the circuit loop. The field inside the inductor will be affected by its core and you also will need a specification of its geometry, i.e. turns, diameter etc. Also some of the inductors field will spill into the circuit loop contributing to the emf. This involves solving Maxwells equations for the whole circuit and in practice, nobody goes into the pain of doing this.

You can get a nearly accurate result by simply reading off the inductance value printed on the inductor, neglect the inductance of the circuit loop and apply Kirchhoffs law.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Tue Jun 23 2015, 10:20AM


The relation which I think is the most important (which maybe I should have written) is the one that relates the "CLOSED PATH" circuit integral with the connecting "OPEN SURFACE" B-field integral, namely:

closed loop integral of E•dl = d/dt of the open surface integral B•dA ( I think I got that right--end of a rough day / night )

Things seem to start with Oersted's: Φ proportional to i

The remainder of your msg is sort of what I have been waiting to see, an illustrating example...I intend to 'work it out' in some detail...

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
BigBad, Tue Jun 23 2015, 05:10PM

Transients are no problem. You just do Fourier analysis; and it all falls out, (at least, provided it's linear.)

If it's not linear, Kirchoff's laws still apply, as a limit case, but you have to use an iterative process, which may not necessarily entirely follow Kirchoff, but any deviations are errors in the process; variations from what the real circuit will do (provided there's no unmodelled strays).

It's only really the strays that mess up Kirchoff, it's not an incorrect model of reality per se.

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Dr. Slack, Tue Jun 23 2015, 08:20PM

??? ???

Re: All physics textbooks wrong in the setup and derivation of the RLC series circuit equation?
Signification, Fri Jun 26 2015, 01:59PM

THE END (?)