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hidayah
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Why does the Loop Rule arise as a consequence of conservation of energy?
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!
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.
Nenad said: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.
traversing this loop will get you back to a different potential when you return to your starting point
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 (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
Tide said:The hum is real but your explanation is not.
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.
i never implied anything different
traversing this loop will get you back to a different potential when you return to your starting point
the purely electrical potential at a point does not have two different values at the same instance of time
Tide 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"
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.
In any case, I think we should put the burden back onto the original poster whose question is ambiguous and unclear.
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.
Tide said:I am stretching nothing and I understood exactly what you meant by the word "when."
Reread what I wrote in my previous post.
Your first statement says (a) the potential at a given point has two different values - at the same time - ...
... - while your second says
(b) the different values at a point can only occur at different times.
Which is it?
If (a) then the potential is multivalued and nonphysical which makes it moot.
If (b) then you were in fact implying some temporal element in the loop theorem.
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.
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
"the purely electrical potential at a point does not have two different values at the same instance of time."
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?
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?
Indeed! However, with regard to KVL, you're interested in potential differences. In that regard, there can be no difference between the potential at a given point and the potential at the same point!there is still a concept of how much work...
Tide said:rjb,Indeed! However, with regard to KVL, you're interested in potential differences.
In that regard, there can be no difference between the potential at a given point and the potential at the same point!
Think of it as hills and valleys. Their heights and depths may vary in all kinds of strange and fantastic ways but the elevation at a given point at a given instant in time is a single value. The peak of Mt. Everest cannot be both 29,000 feet above sea level and 2,500 feet below sea level at the same time - no matter how you draw a loop on your topographic map.
Tide said:There can be no potential difference between a point and itself - however much work you need to physically traverse a loop.
...
And that is true whether we're talking gravitational potential, electrostatic potential, vector potential or nuclear potential and it's true whether we're including time varying fields or topography. At a given instant, a point cannot be at two or more different potentials.
Think about this: If the potential (electrostatic and/or electromagnetic) is multivalued, how could you possibly derive fields from them if the corresponding electric and magnetic fields are gradients, curls or time derivatives of those potentials?
fields come first
the line integral on the left is actually the sum of all of the voltages of these components
rbj said: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
[tex] \oint_{s} \mathbf{E} \cdot d\mathbf{s} = - \frac {d\Phi_{\mathbf{B}}} {dt} [/tex] ?
that first integral, on the left hand side, is a voltage. do you get zero?
jdavel said:The current is caused exclusively by Faraday's Law.
jdavel said:The only other thing that can make electrons move is Coulomb's Law.
The directed sum of the electrical potential differences around a circuit must be zero.
(Otherwise, it would be possible to build a perpetual motion machine that passed a current in a circle around the circuit.)
This law has a subtlety in its interpretation, because in the presence of a changing magnetic field the electric field is not conservative and it cannot therefore define a pure scalar potential—the line integral of the electric field around the circuit is not zero. Equivalently, energy is being transferred from the magnetic field to the current (or vice versa). In order to "fix" Kirchhoff's voltage law for this case, an effective potential drop, or electromotive force (emf), is associated with the inductance of the circuit, exactly equal to the amount by which the line integral of the electric field is not zero by Faraday's law of induction.
Motional emf is ultimately due to the electrical effect of a changing magnetic field. In the presence of a changing magnetic field, the electric potential and hence the potential difference (commonly known as voltage) is undefined (see the former) — hence the need for distinct concepts of emf and potential difference. Technically, the emf is an effective potential difference included in a circuit to make Kirchhoff's voltage law valid: it is exactly the amount from Faraday's law of induction by which the line integral of the electric field around the circuit is not zero. The emf is then given by L di/dt, where i is the current and L is the inductance of the circuit.
Given this emf and the resistance of the circuit, the instantaneous current can be computed with Ohm's Law, for example, or more generally by solving the differential equations that arise out of Kirchhoff's laws.
perhaps this might help Tide and i to sing the same tune.
The Loop Rule, also known as Kirchhoff's Voltage Law, is a principle in circuit analysis that states that the sum of all voltage drops in a closed loop must equal the sum of all voltage rises in that loop.
The Loop Rule is a consequence of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted. In a closed loop circuit, the energy provided by the voltage source must equal the energy dissipated by the resistors, in accordance with this law.
Yes, the Loop Rule can be applied to any circuit, regardless of its complexity. It is a fundamental principle in circuit analysis and is used to solve for unknown voltages and currents in a circuit.
The Loop Rule is used in a variety of practical applications, such as designing and troubleshooting electrical circuits. It is also used in the development of electronic devices, such as computers, smartphones, and other electronic equipment.
In general, the Loop Rule holds true for all circuits. However, there are some cases where it may not apply, such as in circuits with rapidly changing magnetic fields or in circuits with non-conservative elements, such as capacitors or inductors. In these cases, more advanced principles, such as Faraday's law or the Maxwell-Faraday equation, must be used to analyze the circuit.