Loop Rule

**hidayah** · Aug19-05, 05:21 AM

Why does the Loop Rule arise as a consequence of conservation of energy?

**Tide** · Aug19-05, 12:11 PM

Kirchoff's loop rule simply states that if you traverse a loop and return to given point then the potential at that point remains the same, i.e. the electrical potential is single-valued!

**rbj** · Aug19-05, 06:07 PM

Originally Posted by Tide

Kirchoff's loop rule simply states that if you traverse a loop and return to given point then the potential at that point remains the same, i.e. the electrical potential is single-valued!

what's the deal with the terminology here?? are we talking about Kirchoff's voltage Law (KVL)?

if there is a net changing magnetic field inside the loop (of any reasonable quantity), it won't be a single electrical potential. this is why 60 Hz AC hum gets induced into audio circuits. but it should be small.

if there is no net changing magnetic field, then taking a small test charge from point "A" around the loop and back to point "A", then the electrostatic field is "conservative" and the integral or sum of all of the work done to that test charge will be zero and that is why, assigning the polarities consistently going around the loop clockwise, the sum of all of the voltages is zero.

Kirchoff's Current Law (KCL) for every node (less the "ground" node), Kirchoff's Voltage Law (KVL) for every loop (there are also redundant loops that need no separate equation), plus the volt-amp characteristics of every device connect between the nodes (that are also in the loops) are exactly the information one needs to analyze an electrical or electronic circuit.

**Tide** · Aug19-05, 07:17 PM

rbj,

I presume that's what hidayah is asking about.

I'm not sure what you mean when you say there's not a single electrical potential when an oscillating magnetic field is present. If the electrical potential is multivalued at any given point then it is unphysical. Perhaps you meant there are different frequency components?

**Nenad** · Aug19-05, 07:23 PM

Originally Posted by rbj

what's the deal with the terminology here?? are we talking about Kirchoff's voltage Law (KVL)?

if there is a net changing magnetic field inside the loop (of any reasonable quantity), it won't be a single electrical potential. this is why 60 Hz AC hum gets induced into audio circuits. but it should be small.

if there is no net changing magnetic field, then taking a small test charge from point "A" around the loop and back to point "A", then the electrostatic field is "conservative" and the integral or sum of all of the work done to that test charge will be zero and that is why, assigning the polarities consistently going around the loop clockwise, the sum of all of the voltages is zero.

Kirchoff's Current Law (KCL) for every node (less the "ground" node), Kirchoff's Voltage Law (KVL) for every loop (there are also redundant loops that need no separate equation), plus the volt-amp characteristics of every device connect between the nodes (that are also in the loops) are exactly the information one needs to analyze and electrical or electronic circuit.

Are you implying that 'loop' or 'mesh' analysis does not work for AC circuits? If you are implying this, you might want to rethink your statement.

**rbj** · Aug19-05, 10:46 PM

Originally Posted by Nenad

Are you implying that 'loop' or 'mesh' analysis does not work for AC circuits?

no, i am not. (and i am not sure what i said to be construed to mean that.)

If you are implying this, you might want to rethink your statement.

i am not sure if this is the offending concept, but one of Maxwell's Equations, expressed in integral form (i think it's Faraday's Law) says that when there is a changing magnetic field, going around that changing magnetic field in a closed loop gives you an induced potential (voltage) that is proportional to the rate of change of the magnetic field. do you agree with that? if so, then there is a deviation from Kirchoff's voltage Law, the voltages don't all add up to zero.

like the deviation of Kirchoff's Current Law (where the currents going into a node don't sum to exactly zero resulting in a charge buildup), this KVL deviation is not normal and is not what we do when we analyze circuits (using the so-called "node-voltage" or "loop-current" methods) because we model that non-zero current or voltage as an additive source (and it's some kind of noise or hum or error source).

are we on the same page? i know what i'm typing about here.

**Nenad** · Aug19-05, 11:04 PM

I still don't see how this is not saying that KVL, KCL, Loop analysis and Nodal Analysis does not work for AC circuits.

"Hum and buzz (50Hz/60Hz and it's harmonics) occur in unbalanced systems when currents flow in the cable shield connections between different pieces of equipment. Hum and buzz can also occur balanced systems even though they are generally much more"

http://www.epanorama.net/documents/groundloop/

I don't think that what you're trying to tell me is coming across correctly.

Regards,

Nenad

**Tide** · Aug19-05, 11:23 PM

rbj,

You're thinking about induction and, since it's caused by varying magnetic flux, it's not quite correct to talk about electrical potential (vector potential will do, however!). In any case, the potential is single valued so traversing a loop will get you back to the same potential when you return to your starting point. kirchoff works!

Induced fields are taken into account as the inductance (mutual and self) of the circuit or its components.

**rbj** · Aug20-05, 12:14 AM

i dunno what to say to you guys. i dunno if it's a communication problem or whatever. maybe i'm just trying too hard to dot the i's and cross the t's, but this is a real thing in real circuit design on real printed circuit boards. if you have a bunch of components laid out in a loop that is big enough in area, and in an environment where there is some 50 Hz or 60 Hz electromagnetic radiation about, this causes this hum to get into the voltage signal of those components laid out in a loop. this is precisely because of Faraday's Law and that, in fact traversing this loop will get you back to a different potential when you return to your starting point. but, what we do so we can use our normal node-voltage or loop-current analysis methods, is we model that difference in potential (that should be zero if we were more fortunate) as a "virtual" component: an additive independent voltage source. it might be a couple of microvolts.

this is not controversial among practicing electrical engineers. but it is something we don't put into the first sophmore physics and EE texts, because we don't want to confuse the hell out of students and we are able to model this added voltage as a lumped voltage source in the loop and then say all of the voltages add up to zero.

are we still in disagreement?

**Tide** · Aug20-05, 12:19 AM

rbj,

The hum is real but your explanation is not.

traversing this loop will get you back to a different potential when you return to your starting point

Please explain how the electrical potential at a point can have two different values?

**rbj** · Aug20-05, 12:20 AM

one more thing:

forget about circuits for the time being...

given just Coulomb's law and a static electric field, then you have a conservative potential field and doing a line integral of work moving a test charge around any closed loop will get you zero. always.

this is not the same thing as a having a static electric field along with a changing magnetic field.

**rbj** · Aug20-05, 12:49 AM

Originally Posted by Nenad

I still don't see how this is not saying that KVL, KCL, Loop analysis and Nodal Analysis does not work for AC circuits.

this is not directly related to the issue at hand, but, in fact, the KVL, KCL, Loop and Node analyses we do for circuits at low frequencies does not work for extremely high frequency (like microwaves and above) AC circuits. you get to go to grad school in electrical engineering and take a sh1tload of really hard classes to learn how to do that stuff.

think of an antenna. there is current at one part of the radiating element where it is driven, but no current at the ends. that sure as hell does not satisfy KCL.

edit: just to be clear KVL, KCL, Loop and Node analyses work well when the wavelength of the signal in the circuit is much longer than the dimensions of the circuit and components. when that is the case, you gotta do physics rather than just circuit analysis.

"Hum and buzz (50Hz/60Hz and it's harmonics) occur in unbalanced systems when currents flow in the cable shield connections between different pieces of equipment. Hum and buzz can also occur balanced systems even though

hum and buzz can occur inside of a single box where the power supply components are not adequately shielded from the very low voltage analog signal processing components. you get some kind of nasty large varying E and M fields and the changing M fields induce spurious voltages in loops of components strung together. when the signal going into the op-amp is only a few microvolts (say it's coming out of an un-preamped microphone), that induced 60 Hz voltage can add up to something that competes well with the desired signal. and it is precisely because the voltages are not adding to exactly zero.

what happens when you have a single circular closed loop of wire in the presence of a non-zero and changing magnetic field? what happens when you apply

$LaTeX Code: \\oint_{s} \\mathbf{E} \\cdot d\\mathbf{s} = - \\frac {d\\Phi_{\\mathbf{B}}} {dt}$ ?

that first integral, on the left hand side, is a voltage. do you get zero?

**rbj** · Aug20-05, 01:08 AM

Originally Posted by Tide

The hum is real but your explanation is not.

i'm sorry you don't like it.

Please explain how the electrical potential at a point can have two different values?

the purely electrical potential at a point does not have two different values at the same instance of time.

but KVL isn't just that. KVL says that, assigning a consistent sense of polarity going around a loop of electrical components, that the voltages of all of the components of the loop add to zero. but if there is a changing magnetic flux that this loop of components is strung around, those voltages will not add to zero.

KVL works. but sometimes to make it work (when analyzing these noisy or hummy situations) we lump that non-zero induced voltage into a single virtual voltage source in that loop. sometimes we model it as several little voltage sources in series with each component in that loop (that might be more accurate, but is often not necessary).

**Tide** · Aug20-05, 02:04 AM

The loop rules apply to an instant of time.

**rbj** · Aug20-05, 10:57 AM

Originally Posted by Tide

The loop rules apply to an instant of time.

i never implied anything different. the left hand side of

$LaTeX Code: \\oint_{s} \\mathbf{E} \\cdot d\\mathbf{s} = - \\frac {d\\Phi_{\\mathbf{B}}} {dt}$

is a line integral in space applied at a instant of time and the right hand side is an instantaneous rate of change at the same instant of time.

yet, if the right hand side is non-zero (that is my premise for the case of induced hum), then the left side is non-zero.

also, back to terminology: by "loop rules" i presume you mean Kirchoff's voltage Law. if this is not the case, then all bets are off.

**Antiphon** · Aug20-05, 12:22 PM

Rbj is right again. I have taken all those hard classes and then some.

When you analyze a circuit, it's an idealization where the
inductance, capacitance and resistance are concentrated in the components.

In reality they are distributed everywhere. So KVL works for an idealized
circuit because the idealization takes into account all the inductance. You can't treat
a real wire as if it were an ideal wire. Then KVL can't be used and you
must use the full induction relation for a physical wire.

The confusion with AC vs DC is because in a DC circuit the time dependent terms are
gone so you are only left with resistances. These are distributed too in
a real circuit but you can still apply KVL by integrating the differential VI
drop around the actual circuit- because different parts of the circuit are
decoupled at DC.

But you cannot do this in an AC circuit because the equivalent schematic will change.
Parts of the circuit will couple to other parts and in different ways depending
on the frequency.

A simple example is the power line in your house. At 500 MHz, the schematics
won't look anything like they do at 60 Hz if they are to accurately model the
circuit. And at 500 MHz, the component values of the equivalent circuit
will change depending on where I sit in my house. This is not the case at 60 Hz.

In sum,
-KVL, KCL work only for schematics, not physical circuits.
-KVL, KCL can still work for a DC but not AC physical circuit by integrating the differential VI drops around the circuit

Edit: Oh yes, and as for the OP, it has nothing to do with conservation of energy.