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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

Mon Jun 22 2015, 08:47PM

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

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".

Antonio

Mon Jun 22 2015, 11:57PM

Registered Member #834 Joined: Tue Jun 12 2007, 10:57PM
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Posts: 644

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.

Ash Small

Tue Jun 23 2015, 03:35AM

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

Signification wrote ...

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'.

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.

Uspring

Tue Jun 23 2015, 08:52AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Signification wrote:

***** Emf = closed path integral of Eâ€¢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.

Signification

Tue Jun 23 2015, 10:20AM

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

Uspring wrote ...

Signification wrote:

***** Emf = closed path integral of Eâ€¢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.

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 Eâ€¢dl = d/dt of the open surface integral Bâ€¢dA ( I think I got that right--end of a rough day / night )

Things seem to start with Oersted's: Î¦ 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...

BigBad

Tue Jun 23 2015, 05:10PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Antonio wrote ...

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.

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.

Dr. Slack

Tue Jun 23 2015, 08:20PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

???

Signification

Fri Jun 26 2015, 01:59PM

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

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