Why does the Loop Rule arise as a consequence of conservation of energy?
what's the deal with the terminology here?? are we talking about Kirchoff's Voltage Law (KVL)?Tide said: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!
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 said: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.
no, i am not. (and i am not sure what i said to be construed to mean that.)Nenad said:Are you implying that 'loop' or 'mesh' analysis does not work for AC circuits?
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.If you are implying this, you might want to rethink your statement.
Please explain how the electrical potential at a point can have two different values?traversing this loop will get you back to a different potential when you return to your starting point
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.Nenad said: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 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."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
i'm sorry you don't like it.Tide said:The hum is real but your explanation is not.
the purely electrical potential at a point does not have two different values at the same instance of time.Please explain how the electrical potential at a point can have two different values?
Tide said:The loop rules apply to an instant of time.
Well, yes, you did. You saidi never implied anything different
followed bytraversing this loop will get you back to a different potential when you return to your starting point
If the electrical potential at a point has two different values and if those two different values cannot be at the same instant then you must have returned to the starting point at a different time than when you started.the purely electrical potential at a point does not have two different values at the same instance of time
here i made the mistake of using the word "when". i do not offhand know how else to concisely word it, but "when" did not mean at a later time than starting. you can still, conceptually traverse the loop with a test charge in an instant of time (getting back to your starting point at the same instant of time) and you will have a line integral of the total amount of work done on that test charge. if there is no time-varying magnetic field, then the line integral done at that instant of time is zero because an electrostatic field is conservative. but if there is a non-zeroTide said:rbj,
Regarding my comment: "The loop rules apply to an instant of time." you said
"i never implied anything different."
Well, yes, you did. You said
"traversing this loop will get you back to a different potential when you return to your starting point"
i said "purely electrical" when i could have been more clear by saying "purely electrostatic". the point i was making was that at an instant of time there is one unambiguous electrostatic potential for that point because classical electrostatic fields are conservative fields (i think the OP was sorta referring to that when he says "Conservation of energy". in that case KVL is completely accurate. but a more general electromagnetic field is not necessarily conservative and in that case KVL is not perfectly valid.followed by
"the purely electrical potential at a point does not have two different values at the same instance of time."
If the electrical potential at a point has two different values and if those two different values cannot be at the same instant then you must have returned to the starting point at a different time than when you started.
if the OP meant "KVL" when he said "Loop rules", i think it was reasonably clear. it was the other thread (Convervation of charge) that i didn't get right away.In any case, I think we should put the burden back onto the original poster whose question is ambiguous and unclear.
I am stretching nothing and I understood exactly what you meant by the word "when." Reread what I wrote in my previous post.i think you're stretching it a little to imply that by using "when" i meant that it had to be two different instances of time for starting and ending the closed loop.
i'm glad to read that. then there is no misunderstanding. nowhere did i mention anything about KVL at different times. (by "changing magnetic field" i mean the instantaneous rate of change at some instant of time, what the calculus prof. calls "the derivative".)Tide said:I am stretching nothing and I understood exactly what you meant by the word "when."
i've been very careful (except for saying "when" in a context of an instant of time and "purely electrical", meaning no magnetic component, when i should have said "purely electrostatic"). you said that i implied that this deviation from KVL had something to do with different times or that my explanation had something to do with different times and i never said that. it is you, Tide, that needs to carefully read what the other is saying and not inject something unsaid into it.Reread what I wrote in my previous post.
only if there is a changing magnetic field and then comparing the potential if there was no movement of the test charge to the resulting potential if the test charge was moved around a closed curve that encircled some of that changing magnetic field. same point in space, same instance of time, but different potentials if you include the magnetic effects. (of course they can't be different if you are only considering electrostatic effects.)Your first statement says (a) the potential at a given point has two different values - at the same time - ...
i never said anything about "different times" (until you brought it up and only to say that i ain't saying anything about "different times"). you are the first (and only) person to bring this up. i am saying something about different circumstances (for comparison purposes). like "compare scenario A at some point in space and some instance of time to scenario B at the same point in space and the same instance of time." that is what is different. i never said anything about different times.... - while your second says
(b) the different values at a point can only occur at different times.
ah! now you said something meaningful that we can talk about. i respectfully disagree with what you say here (it's not "nonphysical" at all, perhaps a nonconservative field, but certainly not nonphysical). and i have stated my alternative above. this might be something tangible to argue about. maybe not.Which is it?
If (a) then the potential is multivalued and nonphysical which makes it moot.
no, only you are.If (b) then you were in fact implying some temporal element in the loop theorem.
fine by me. (it wasn't just semantics. you made a factual statement, i said i never implied otherwise, then you made another factual statement saying that i did imply otherwise which was not true.)We've already spent more time on the semantics than is warranted and, again, I suggest we return the burden to the original poster who posed an ill-stated and ambiguous question.
Your subsequent statements:the electrical potential is single-valued!
andit won't be a single electrical potential
and now you add:the purely electrical potential at a point does not have two different values at the same instance of time.
referring to a multivalued potential. Then, of course, you addit's not "nonphysical" at all
in reply to mynow you said something meaningful
I'm sure glad you recognize that I am making progress! Thanks!then the potential is multivalued and nonphysical which makes it moot.
wow! i said that? well, i guess i did, but you didn't quote the entire context. there's a qualification:Tide said:My original, central and persistent statement:
"the electrical potential is single-valued!"
Your subsequent statements:
"it won't be a single electrical potential"
and, if you had quoted the clarification later, that we all have read, i had already said that "electrostatic" would be a better word, but "purely electrical" has the same connotation. it means to exclude magnetic effects. so i think i've been immunized against any liability there.and
"the purely electrical potential at a point does not have two different values at the same instance of time."
it's not non-physical at all. we can certainly conceive of a situation where there are both electrostatic fields and non-zero changing magnetic fields.and now you add:
"it's not 'nonphysical' at all"
referring to a multivalued potential.
So, while we're at it, please address my original question to you: How is a (pointwise) multivalued potential physical?
this deviation from KVL (which happens only in the presence of a changing magnetic field, did i say that before? - it seems that this important qualification is going unnoticed) is about the sum of a bunch of voltages (call them "potential differences" if you like, but this concept of potential is a bit problematic in this case of changing magnetic fields because there ain't any single valued potentials, so then what the hell do they mean?) around a closed loop that you would think would add to zero, but they don't.Tide said:Specifically, you're interested in the potential difference from one point to the next and, more to the point, how can the there be a difference between the potential at a given point and the potential at the same point?