Why is residential wiring known as single phase?

[Rick Christopherson]

Phase is not a time function if you use the IEEE definition that has been referenced so many times above. From that definition phase is the fractional (non-dimensional) measurement of a position of some point in the period of a periodic function relative to a reference point in that period. This definition allows measurement over many periods modulo 1.

Hmmm. Maybe we should stop calling the waveforms time-varying functions? Hey, I have an idea! Since we draw them left-to-right, then let's just start calling them right-varying functions. Brilliant, Right? See, that way we can say that phasors are a function of right, right?

Although you may have waves that vary with time, the idea of phasors is to remove that time variation and relate the various signals relative to one another.

Another brilliant deduction of logic. You must have gone to the Rattus school of static phasors too.

Phasors for Y connected sources are usually drawn from a single point (call it neutral) because this provides a useful graphical view of the entire source circuit. From this layout it is easy to visually see a resultant phasor from the difference of two points.

And what earth shattering purpose is this phasor diagram? Is it so we can quickly see that the sum of the phases is zero? Yup, I find myself forgetting that all the time and need to keep drawing it so I can remember.

 

[Rick Christopherson]

If one doesn't know the difference between phasors and vectors, one should not 't criticize others.
who do!

You're right. I accidentally typed vectors. I'll correct that.

Please enlighten us, oh Mystical One. Did your phasors become static simply because you drew them with ink? :lol:

So please enlighten us about your static phasors.

 

[rattus]

You're right. I accidentally typed vectors. I'll correct that.

So please enlighten us about your static phasors.

At the risk of receiving a sarcastic reply I will do just that.

Rotating phasors are of the form:

Vpk[cos(wt + phi) + jsin(wt + phi)]------functions of time

Static phasors are of the form:

Vrms[cos(phi) + jsin(phi)]------------not functions of time

 

[pfalcon]

If one doesn't know the difference between rotating and fixed phasors, one should not be criticizing those who do.

So you should stop eh?

Phase is not a time function if you use the IEEE definition that has been referenced so many times above. From that definition phase is the fractional (non-dimensional) measurement of a position of some point in the period of a periodic function relative to a reference point in that period. This definition allows measurement over many periods modulo 1.

Like it or not, in mathematics ALL sinusoidals are frequently referred as time intervals from 0 to 2PI. And as emphasized above, and which I keep repeating though you don't listen: Phase is an overloaded word. You keep switching which definition you're using to suit your needs. But to the def you just used: As frequently used in mathematics the time interval of a sinusoidal wave form is the period from 0 to 2PI. It's used in this method so that mathematicians can refer to distinct parts of the curve without confusion. It may or may not correspond to any physical reality. In our present case it corresponds very well to 1/60 sec.

Although you may have waves that vary with time, the idea of phasors is to remove that time variation and relate the various signals relative to one another.

Nonsense. The idea of phasors is to solve problems graphically on paper instead of calculating with a slide rule. Which requires that you understand how the system varies with time in order to apply the phasors correctly.

On the subject of RMS --- it is convenient and appropriate to use the RMS value as the magnitude of the phasor rather than the peak value of the waveform. Stout explains this on p 11 of his book on "Analysis of A-C Circuits".

Sure, 120Vrms is convenient rather than using the actual peak values. That doesn't relieve you of the responsibility of understanding how the wave varies over time. Nor does it relieve you of the responsibility of understanding the direction of the peak magnitudes at any given instant.

Phasors for Y connected sources are usually drawn from a single point (call it neutral) because this provides a useful graphical view of the entire source circuit. From this layout it is easy to visually see a resultant phasor from the difference of two points.

Three-phase graphs are drawn from a single point for mathematical convenience and paper space. Once you unstack the phasors by moving them to the origin they are technically not phasors any more since you removed their relationship to each other. That's a fact the mathematicians presume you know and they continue referring to them as phasors by presuming you continue to understand that the underlying relationships are still important.

pfalcon: The RMS value is the effective heating value of an AC voltage or current.
For example, 120Vrms across a resistor produces the same amount of heat as does 120Vdc.
120Vrms is a magnitude, always positive; tack on a phase angle and you have a static phasor.

See emphasis. In elementary school you should have learned that magnitudes are absolute value terms without direction that may be derived from underlying terms that have direction. They are neither positive nor negative. The magnitudes are
A ------------ N
N ------------ B
without any arrow heads because they're magnitudes: no direction: no arrow head.

The assigned phase angle must be derived from the underlying terms under identical conditions.
From 0<T<PI then A>N>B therefore A angle is 0 and B angle is 0.
From PI<T<2PI then A<N<B therefore A angle is PI and B angle is PI.

You don't get to set an arbitrary direction based on your choice of reference point. The angle is determined by the instantaneous polarity.

BTW, I learned to subtract in elementary school.

But apparently forgot you're not supposed to subtract voltages in series when you left college.

 

[rattus]

So you should stop eh?


Like it or not, in mathematics ALL sinusoidals are frequently referred as time intervals from 0 to 2PI. And as emphasized above, and which I keep repeating though you don't listen: Phase is an overloaded word. You keep switching which definition you're using to suit your needs. But to the def you just used: As frequently used in mathematics the time interval of a sinusoidal wave form is the period from 0 to 2PI. It's used in this method so that mathematicians can refer to distinct parts of the curve without confusion. It may or may not correspond to any physical reality. In our present case it corresponds very well to 1/60 sec.


Nonsense. The idea of phasors is to solve problems graphically on paper instead of calculating with a slide rule. Which requires that you understand how the system varies with time in order to apply the phasors correctly.


Sure, 120Vrms is convenient rather than using the actual peak values. That doesn't relieve you of the responsibility of understanding how the wave varies over time. Nor does it relieve you of the responsibility of understanding the direction of the peak magnitudes at any given instant.


Three-phase graphs are drawn from a single point for mathematical convenience and paper space. Once you unstack the phasors by moving them to the origin they are technically not phasors any more since you removed their relationship to each other. That's a fact the mathematicians presume you know and they continue referring to them as phasors by presuming you continue to understand that the underlying relationships are still important.



See emphasis. In elementary school you should have learned that magnitudes are absolute value terms without direction that may be derived from underlying terms that have direction. They are neither positive nor negative. The magnitudes are
A ------------ N
N ------------ B
without any arrow heads because they're magnitudes: no direction: no arrow head.

The assigned phase angle must be derived from the underlying terms under identical conditions.
From 0<T<PI then A>N>B therefore A angle is 0 and B angle is 0.
From PI<T<2PI then A<N<B therefore A angle is PI and B angle is PI.

You don't get to set an arbitrary direction based on your choice of reference point. The angle is determined by the instantaneous polarity.

But apparently forgot you're not supposed to subtract voltages in series when you left college.

What can I say? Ignorance in action!

 

[Rick Christopherson]

Static phasors are of the form:

Vrms[cos(phi) + jsin(phi)]------------not functions of time

No Houdini. That's nonsense. You've simply pretended to suppress the rotating component, but we already do that with phasors in the first place. Without the time varying component, this simply becomes a number. As a complex number, we can represent it as a vector, but not a phasor. This is simply more of your voodoo math. Please cite a reference.

If anything, when we suppress the rotating component of a phasor (because it does not provide any unique information) that could be called a static phasor, but we don't make that distinction because it is always suppressed. What distinguishes a vector from a phasor is this suppressed rotation. That's why all vector math also applies to phasors. Because we suppress the extra information and give it a unique name.

 

[iwire]

I am going to close this thread for 24 hours, I urge all participants to take a breath, get back on the subject, drop the jabs, the insults, the underhanded remarks etc.

I plan on reopening it in about 24 hours unless the other mods feel otherwise.

At that time you will all be free to continue but with civility.