Why is residential wiring known as single phase?

[T.M.Haja Sahib]

. But there is not a given single direction for a positive direction.

Who denies it?

 

[mivey]

But not both at the same time.

That's because you are thinking linearly. Don't be constrained to think like Khan. One option for the one positive direction is either towards or away from the neutral point. Similiar to currents from Earth or to Earth. Like from or towards a point charge (back to physics fundamentals). Like voltage above or below a bus (like in sequence analysis).

 

[mivey]

Who denies it?

Those who say the positive direction for both winding halves must be in one linear direction across both windings say the only correct direction is from end to end.

 

[T.M.Haja Sahib]

That's because you are thinking linearly. Don't be constrained to think like Khan. The one positive direction is either towards or away from the neutral point. Similiar to currents from Earth or to Earth. Like from or towards a point charge (back to physics fundamentals). Like voltage above or below a bus (like in sequence analysis).

You mean currents in the two hot conductors sometimes move in the same direction at the same time?
What do you mean exactly?
(By the way,who is Mr.Khan?)

 

[rbalex]

But why reduce it at all?

Seems to me that when determining the phase of a waveform, we must consider the position of the waveform as I understand the definition. Consider,

sin(wt + 180) = -sin(wt)

The plot of this function, from either expression, is a shifted sine wave, and the phase is,

ph2 = (wt + 180)

we can't have it both ways.

You keep insisting on extracting the wrong set of element of the equation. If you go back to the definition I cited and read it for comprehension, you will see the phase of the function as you (emphasized for mivey's sake) have written it is, or can validly be reduced to, wt. Of course, no one has to accept the citation, but it would be nice if they countered with a authoritative alternate definition (not wikipedia) that I can pick at or their own, "Well, that's how I understand it."

 

[T.M.Haja Sahib]

Those who say the positive direction for both winding halves must be in one linear direction across both windings say the only correct direction is from end to end.

The winding in a 120/240v center tap transformer is wound either clockwise or anticlockwise throughout.You mean the two halves can be wound in opposite directionsne clockwise,the other anticlockwise?If so,where is the practical application?

 

[mivey]

You mean currents in the two hot conductors sometimes move in the same direction at the same time?
What do you mean exactly?

I mean that a direction can also be from or to a bus. That does not constrain it to be in a straight line. I hesitate to use this illustration but it seems you are not familar with bus usage or point charges so: if you were standing on the North Pole, which direction is South? The answer is any direction along the Earth away from where you stand, of course. The same with point charges and other "busses" like Earth in that a positive direction is not constrained to be linearly all in one direction.

(By the way,who is Mr.Khan?)

From "The Wrath of Khan". The hero (Kirk) defeats the bad guy (Khan) by moving his spaceship off of the "X-Y" plane of conflict to a different "Z" coordinate to get a shot at Khan. Although an intellectual giant, Khan was noted to be thinking two-dimensionally and would not anticipate a vertical move. Thus, I said do not be constrained to think of a positive direction to only mean in one linear direction.

The winding in a 120/240v center tap transformer is wound either clockwise or anticlockwise throughout.You mean the two halves can be wound in opposite directionsne clockwise,the other anticlockwise?If so,where is the practical application?

That is not what I am saying. Perhaps the other part of my response will clear that up for you.

 

[mivey]

You keep insisting on extracting the wrong set of element of the equation. If you go back to the definition I cited and read it for comprehension, you will see the phase of the function as you (emphasized for mivey's sake) have written it is, or can validly be reduced to, wt. Of course, no one has to accept the citation, but it would be nice if they countered with a authoritative alternate definition (not wikipedia) that I can pick at or their own, "Well, that's how I understand it."

I was not going to respond as you continue to ignore your rather obvious math error. I suspect I am wasting my breath as you are so enamored with what you are doing with your Trig reduction that you are overlooking the fundamental parts of the math. But I'll give it another shot: Your source does not support your reduction. Your source plainly shows that the phase constant is part of the phase along with the time portion. Any good calculus text or physics text will show the same thing.

You have shifted the function and changed its phase, but do not realize it. The phase indicates a position on the waveform. You shifted the phase position and then call it the same as the phase position on a different waveform. All you have done is said you can shift a waveform to make it have the same phase as a different waveform. That is nothing we do not already know.

 

[mivey]

...but it would be nice if they countered with a authoritative alternate definition (not wikipedia) that I can pick at or their own...

I suspect you don't need to hunt for an "authoritative alternate" definition as your own reference disputes what you claim. You have made up your own definition and somehow declare it is the same as your reference. Then you request an authoritation definition to dispute your own made-up one? I guess I'm just a glutton for punishment but how about I just give you something to pick at?

For a sinusoidal waveform, consider the location on the waveform at some instant and given by X & Y coordinates or a magnitude and phase:

X+jY = √(X²+Y²)?e^jΦ = |Z|?e^jΦ where Φ is the phase at the referenced instant and indicates the angle from the positive x-axis.

For the negative we have:
-X-jY = √(X²+Y²)?e^(jΦ?Π) = |Z|?e^(jΦ?Π) where (Φ?Π) is the phase for the negative vector.

Obviously, the vectors are pointing in opposite direction and have two different phases. Now I could play a "reduction" game and extract part of the phase like this:
|Z|?e^(jΦ?Π) = |Z|?e^jΦ?e^?jΠ

Now I have one waveform with |Z|?e^jΦ and the other with |Z|?e^jΦ?e^?jΠ. I could see that both have an "e^jΦ" component and erroneously declare that X+j?Y and -X-jY have the same phase. That is an obvious math error because the vectors do not have the same angle from the reference axis (which is the definition of phase).

That is what you are doing when you declare that both waveforms have the same "characteristic phase", using your made-up term. You attempt to justify it by making up this fake "math" term that is not supported by your reference (nor any other I would suspect). How about you show me an authoritative reference for "characteristic function of the phase value". This is total nonsense and just plain bad math.

 

[rbalex]

I was not going to respond as you continue to ignore your rather obvious math error. I suspect I am wasting my breath as you are so enamored with what you are doing with your Trig reduction that you are overlooking the fundamental parts of the math. But I'll give it another shot: Your source does not support your reduction. Your source plainly shows that the phase constant is part of the phase along with the time portion. Any good calculus text or physics text will show the same thing.

You have shifted the function and changed its phase, but do not realize it. The phase indicates a position on the waveform. You shifted the phase position and then call it the same as the phase position on a different waveform. All you have done is said you can shift a waveform to make it have the same phase as a different waveform. That is nothing we do not already know.

Apparently you won't (I already know you're fully capable) read the cited definition for comprehension.

The cited example in the definition indicates ?? the phase of a function cos (ωt+φ₀) as a function of time is φ(t) = ωt+φ₀." It's hard to diagram sentences here, but in simple English, "the phase ... is ... ωt+φ₀" would be the primary clause. That is, per the definition, ωt, the time element of the general function, is also part of the phase of the general function. rattus just wants to define φ₀ as zero - which is fine as a specific case.

I don't need differential equations to know the initial value is φ₀ - that was already defined in the general equation. And I don't need state-variables, Hamiltonians, Lagrangians, Eigen-values or Eigen-vectors, Fourier Analysis or transforms, matrix inversions (all of which I've studied) or any other math beyond trig and algebra to analyze this properly within the constraints of the cited definition.

You don't have to agree with what it clearly says, but I won't do your homework for you - you cite an authoritative counter definition beyond your own recollections.

 

[mivey]

Apparently you won't (I already know you're fully capable) read the cited definition for comprehension.

I did read it. Let me explain it to you, again. The phase has a time dependent component and a constant φ_0.. φ₀ is the placeholder for the constant. Assuming φ₀ = 0? for the first waveform, 180? is the constant for the negative of that waveform. If you don't like 0? then we can also look at a different phase constant. Let the constant for the first waveform be 30?. The second waveform would have a constant of 210?. In other words. the constants φ₀₁ = 30? and φ₀₂ = 210?. It is NOT that they both have the same φ₀ like you are thinking. That is not how the phase of a waveform works. No authoritative reference should be required for you to see that as a simple pencil and piece of paper should tell you that.

I don't need differential equations to know the initial value is φ₀ - that was already defined in the general equation. And I don't need state-variables, Hamiltonians, Lagrangians, Eigen-values or Eigen-vectors, Fourier Analysis or transforms, matrix inversions (all of which I've studied) or any other math beyond trig and algebra to analyze this properly within the constraints of the cited definition.

Well you sure as shootin' need something because you are making a mess of this analysis. I'm not sure what I could do to help as you refuse to see the math for yourself. Perhaps you are over-thinking it. Negative signs are a bane for those not paying attention to the math. You have been caught by this and simply can't see past it.

You don't have to agree with what it clearly says

I do agree with your source. You are just trying to make your source say something it does not say.

but I won't do your homework for you - you cite an authoritative counter definition beyond your own recollections.

I cited your own reference which counters what you are saying in the manner I described above and in previous posts.

 

[rbalex]

I did read it. Let me explain it to you, again. The phase has a time dependent component and a constant φ_0.. φ₀ is the placeholder for the constant. Assuming φ₀ = 0? for the first waveform, 180? is the constant for the negative of that waveform. If you don't like 0? then we can also look at a different phase constant. Let the constant for the first waveform be 30?. The second waveform would have a constant of 210?. In other words. the constants φ₀₁ = 30? and φ₀₂ = 210?. It is NOT that they both have the same φ₀ like you are thinking. That is not how the phase of a waveform works. No authoritative reference should be required for you to see that as a simple pencil and piece of paper should tell you that.

Well you sure as shootin' need something because you are making a mess of this analysis. I'm not sure what I could do to help as you refuse to see the math for yourself. Perhaps you are over-thinking it. Negative signs are a bane for those not paying attention to the math. You have been caught by this and simply can't see past it.

I do agree with your source. You are just trying to make your source say something it does not say.

I cited your own reference which counters what you are saying in the manner I described above and in previous posts.

I note you have conspicuously avoided the English lesson.

 

[mivey]

I note you have conspicuously avoided the English lesson.

I feel like I'm in the Twilight Zone or something.

I read your "English lesson" to say the phase had a time dependent portion and a constant. I said the same thing. What "avoidance" are you talking about?

How about a specific example:
Consider the waveforms given by A?cos(ω?t + φ₀)

For the first waveform, let A=10, ω=377, and φ₀=30? (or 0.5236_rad). For the second waveform (the inverse) we have A=10, ω=377, and φ₀=210? (or 3.6652_rad). At t = 0.001 seconds we have:

First waveform: A?cos(ω?t + φ₀) = 10?cos(377?0.001_rad + 0.5236_rad) = 10?cos(0.9006_rad)

Second waveform: A?cos(ω?t + φ₀) = 10?cos(377?0.001_rad + 3.6652_rad) = 10?cos(4.0422_rad)

The first waveform has a phase of 0.9006_rad or 51.6?. The second waveform has a phase of 4.0422_rad or 231.6?.

These angles show the phase of the waveforms. We can't just subtract 180? from one of them and say we have the same waveform and the same phase. Subtracting 180? will make you compare two different waveforms (one being the inverse of one of the previous waveforms, i.e., shifted by 1/2 cycle).

Plain enough English for you?

 

[pfalcon]

Need a score card to keep track of the posts between visits :?

That's right. It can produce forces that are opposite in direction at 180? displacements.
Did not say it wasn't important, just that it was not contradictory to my position.
If you think they contradict, then you do not understand what I have said. Evidently, I have not been able to get you to read what I am actually saying.

Those who say the positive direction for both winding halves must be in one linear direction across both windings say the only correct direction is from end to end.

Which absolutely no one has said. Rather we've said:

But not both at the same time.

And that this fact is critical to understanding the circuit. You claim you know it's important to understand the instantaneous circuit and then immediately blow it off. Usually followed by an attack claiming we're trying to claim that the direction doesn't change over time. Sahib never claimed the circuit doesn't change direction yet you ascribe him to being like Kahn.

You keep claiming opposing voltages, they're not. At any given instance all the electrons, all the voltage, all the power, all the current are all flowing in one direction. On the other half of the cycle they're moving in the opposite direction. But never, never, never are they moving in two separate directions. It's a gradient from one end of the secondary to the other and you're just poking your probes in the middle. To be out of phase those little coulombs of charge would have to move in different directions at some time during the cycle.

 

[mivey]

Which absolutely no one has said. Rather we've said:

But not both at the same time.

And that this fact is critical to understanding the circuit. You claim you know it's important to understand the instantaneous circuit and then immediately blow it off. Usually followed by an attack claiming we're trying to claim that the direction doesn't change over time. Sahib never claimed the circuit doesn't change direction yet you ascribe him to being like Kahn.

Who in the world has said they move in two different directions at the same time? What is critical to understand is how we define direction. I contend that there are two valid ways to define the direction because the voltage can produce forces in two valid directions.

You keep claiming opposing voltages, they're not. At any given instance all the electrons, all the voltage, all the power, all the current are all flowing in one direction. On the other half of the cycle they're moving in the opposite direction. But never, never, never are they moving in two separate directions.

See? There it is. What direction are you talking about? One option says the positive direction is defined as one linear direction across both windings (one way or the other), the other says the positive direction is directed from or to the neutral. I have shown circuits and generator sources that show both are valid.

It's a gradient from one end of the secondary to the other

That is one option. It is a choice, not a given.

To be out of phase those little coulombs of charge would have to move in different directions at some time during the cycle.

Really? What about the one little coulomb charge in the middle of the winding? Are the other charges all moving towards it or away from it? Review basic physics before answering.

 

[rbalex]

I feel like I'm in the Twilight Zone or something.

I read your "English lesson" to say the phase had a time dependent portion and a constant. I said the same thing. What "avoidance" are you talking about?

How about a specific example:
Consider the waveforms given by A?cos(ω?t + φ₀)

For the first waveform, let A=10, ω=377, and φ₀=30? (or 0.5236_rad). For the second waveform (the inverse) we have A=10, ω=377, and φ₀=210? (or 3.6652_rad). At t = 0.001 seconds we have:

First waveform: A?cos(ω?t + φ₀) = 10?cos(377?0.001_rad + 0.5236_rad) = 10?cos(0.9006_rad)

Second waveform: A?cos(ω?t + φ₀) = 10?cos(377?0.001_rad + 3.6652_rad) = 10?cos(4.0422_rad)

The first waveform has a phase of 0.9006_rad or 51.6?. The second waveform has a phase of 4.0422_rad or 231.6?.

These angles show the phase of the waveforms. We can't just subtract 180? from one of them and say we have the same waveform and the same phase. Subtracting 180? will make you compare two different waveforms (one being the inverse of one of the previous waveforms, i.e., shifted by 1/2 cycle).

Plain enough English for you?

Assuming we have been discussing the various voltages of the same single-phase system, the phase of the voltage functions, ωt+φ_0, is the same for all of them. In fact, they MUST be the same; i.e., they definitely have the same time element, ωt, and they MUST have had the same initial value φ_0, either directly or through trigonometric reduction - unless you demand that polarity is an essential characteristic of phase. You can chase as many other irrelevant rabbits as you wish.

 

[mivey]

Assuming we have been discussing the various voltages of the same single-phase system, the phase of the voltage functions, ωt+φ_0, is the same for all of them. In fact, they MUST be the same; i.e., they definitely have the same time element, ωt, and they MUST have had the same initial value φ_0,

LOL. I guess the joke's on me. All the derivations, math definitions, claims of a different way to look at things, and "trigonometric reductions" of the phase and your whole argument really boils down to the same thing some of the others have been saying: you believe there is only one valid positive direction for voltages.

...through trigonometric reduction..

Your own concoction of manipulating phase constants that is not supported by any real math or physics reference I have seen.

unless you demand that polarity is an essential characteristic of phase.

My demands do not matter. It is the math of oscillating systems that makes it so. As I have said several times, any good calculus or physics text will show that.

You can chase as many other irrelevant rabbits as you wish.

Thanks. I'll leave it to you once again to keep living your dream.

 

[jim dungar]

Who in the world has said they move in two different directions at the same time?

Why I believe you do in the next few sentences.

...two valid directions.

...the positive direction is directed from or to the neutral...

Could you please site reference material that describes both to and from as indicating a single direction? I have not been able to find a single dictionary or thesaurus that does.

One person facing the sky and falling backwards and a second person facing the earth and falling forward, taken out of context (not using all of the adverbs and adjectives) it appears the bodies are moving in different directions (i.e. one is backward and one is forward), but the reality is both are falling down neither is falling up.

 

[rbalex]

LOL. I guess the joke's on me. All the derivations, math definitions, claims of a different way to look at things, and "trigonometric reductions" of the phase and your whole argument really boils down to the same thing some of the others have been saying: you believe there is only one valid positive direction for voltages.
...

Per your standard MO, you again haven't read too carefully. I have routinely said direction doesn't matter; nor does amplitude. In fact, any set of measured points in the same single phase system will yield the same phase - no matter how you measure it (I've said that several times too).

 

[Besoeker]

It should be possible in your scope to display in X-Y mode the phase difference between V1 to N and V2 to N and also that between V1 to N and N to V2.

I suggest that you review posts #439 and #440.
I've explained the same point a number of times over. From as far back as post #224.

Now, how about you answer the simple question I asked you in post #756?