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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, 01:51PM

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

It has been discovered that all physics textbooks are in error in using Kirchhoff's law in setting up the differential equation for any series circuit containing an inductor--or more specifically, in any such circuit through which there is a changing magnetic flux: "non-zero dÎ¦/dt". Such as an RCL series circuit. Are all physics books' E&M sections really in-accurate? According to a famous MIT professor, the answer is a "SAD and EMBARRASSING...YES" --referring to the manner in which the text books alter "-" signs to obtain the (known) proper answers.

His argument is that, in such cases, Kirchhoff's closed loop rule, which states: "The closed loop integral of E 'dot' dl around a circuit must be zero"...actually does NOT hold! Only Faraday's (general) law works, which can be stated, here as, the closed integral of E dot dl around such a circuit is not **zero**, but is ALWAYS ** -L di/dt **.

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

I am curious if anyone here who has heard of this, has an opinion.

DerAlbi

Fri Jun 12 2015, 04:50PM

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

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.

Signification

Fri Jun 12 2015, 06:19PM

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

DerAlbi wrote ...

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.

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.

DerAlbi

Fri Jun 12 2015, 06:43PM

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

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.

Signification

Fri Jun 12 2015, 08:07PM

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

DerAlbi wrote ...

Of coruse i described a paradox situation.

Yes you did...

DerAlbi

Fri Jun 12 2015, 08:16PM

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

But do you get the idea?

Signification

Fri Jun 12 2015, 08:26PM

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

DerAlbi wrote ...

But do you get the idea?

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.

Uspring

Fri Jun 12 2015, 08:27PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Posts: 711

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.

klugesmith

Fri Jun 12 2015, 08:50PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

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 dÎ¦/dt term as a voltage source element in series.

DerAlbi

Fri Jun 12 2015, 08:57PM

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

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.

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