# Why is residential wiring known as single phase?

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#### jim dungar

##### Moderator
Staff member
I couldn't have put it better.
Then why did you say you needed two phases, when the circuit works because of the two voltages?

#### mivey

##### Senior Member
Are you serious?
It is obfuscation to ask that a mathematical equation be able to be solved in other permutations?

Yes, I would expect any student taking a course to be able to solve a single equation for a for a single unknown.
But of course. But as I know you know, if either the first subscript or the second subscript of the voltages are not the same, the subtraction result is going to be a voltage larger than either of the two voltages. We both know that we have 240v and 120v voltages, not 360v voltages so to set up a calculation to produce that result is misleading at best.

For those following along:
Vxy - Vzy = Vxz (second subscripts match and go away and we are left with the remaining 1st-2nd subscript result)
Vxy - Vxz = Vzy (first subscripts match and go away and we are left with the remaining 2nd-1st subscript result)

The valid subtractions with the voltages we have are:
Vab - Van = Vnb (1st subscripts match)
or
Vab - Vnb = Van (2nd subscripts match)
or
Vba - Vbn = Vna (1st subscripts match)
or
Vba - Vna = Vbn (2nd subscripts match)

The obfuscation comes from comparing these differences, which is not what we are doing:
Vxz - Vxy (first subscripts match)
Vxz - Vzy (no subscript match)

In other words, we do not have these resultant voltages:
Vab - Vbn = 1.5*Vab = 3*Vnb
nor
Vba - Van = 1.5*Vba = 3*Vna

#### Besoeker

##### Senior Member
Then why did you say you needed two phases, when the circuit works because of the two voltages?
Ah. Two voltages.
Progress again.:thumbsup:
What is the relationship between those two voltages?

#### mivey

##### Senior Member
That is not a posting of the waveforms from the circuit where you had {Vbn@180? connected in parallel with Vnb@0?} which was in series with a parallel connection of {Van@0?and Van@0?}.
That is the waveform you would have for the voltages I have between the n & b terminals in my circuit.

I am surprise you would not have noticed the difference.
I am surprised you think it is not representing the voltages in my circuit. Can you please explain how the voltages I have labeled in my circuit are not represented by a graph of two sinusoidals displaced by 180?? I mean, that was the whole point of making my generator example in the first place. If you did not follow it, then I can understand why you failed to get my point.

#### rattus

##### Senior Member
I know what I'll do. I will draw my phasors in the same direction.

120Vrms@PI L2---------->N---------->L1 120Vrms@0

Are V1n and V2n in phase? Of the same phase?

Well no. Because the phase angles on L1 and L2 did not change. Whattya know? The voltages are separated in time by half a period--PI radians. One is the inverse of the other.

#### gar

##### Senior Member
120321-211 EDT

An experiment to try.

Get two equal resistors. Connect one to phase A and the other to phase B from the center tapped secondary with the other end of the resistors going to neutral. The current in each resistor will be in-phase with its voltage.

Tie the two hot wires from the resistors together. Run this wire pair thru a current transformer and measure the current. What is the current? Are those two currents the same phase? Are the voltages the same phase?

.

#### jim dungar

##### Moderator
Staff member
But of course. But as I know you know, if either the first subscript or the second subscript of the voltages are not the same, the subtraction result is going to be a voltage larger than either of the two voltages. We both know that we have 240v and 120v voltages, not 360v voltages so to set up a calculation to produce that result is misleading at best.

It must have been a tough assignment, I have no idea how you arrived at 360V.

If the voltages can be combined to produce a higher voltage, than by the virtue of mathematics then one of them should be able to be subtracted from the higher value without providing a misleading answer.

Here let me do the simple phasor manipulation for you.
Van+Vnb=2Vab
2Vab = 240V@0?|-------------------->
Van = 120V@0?|--------->
2Vab-Van =120V@?? this requires the phasors to be connected tail to tail or head to head
So |--------------------> -|---------> = |--------->---------> = --------- I'll let you put in the direction.

Now
Van-Vbn=2Vab
2Vab = 240V@0?|-------------------->
2Van = 120V@0?|--------->
2Vab-Van =120V@?? this requires the phasors to be connected tail to tail or head to head
So |--------------------> -|---------> = |--------->---------> = --------- I'll let you put in the direction.

Why?

#### jim dungar

##### Moderator
Staff member
What is the relationship between those two voltages?
They are in phase. Just like I have repeated in the past.

It is the way your circuit is wired, not the phasing of the voltages.
I asked before, can the circuit be made to work by relocating and swapping one of your SCRs?

#### jim dungar

##### Moderator
Staff member
That is the waveform you would have for the voltages I have between the n & b terminals in my circuit.
No it is not.

I am waiting for someone to post an actual oscilloscope display of your paralleled Vbn and Vnb in series with your paralleled Van and Van outputs.

#### jim dungar

##### Moderator
Staff member
I know what I'll do. I will draw my phasors in the same direction.

120Vrms@PI L2---------->N---------->L1 120Vrms@0

Are V1n and V2n in phase? Of the same phase?

Well no. Because the phase angles on L1 and L2 did not change. Whattya know? The voltages are separated in time by half a period--PI radians. One is the inverse of the other.

Have you rewired the transformer?
Are you simply redrawing phasor directions while ignoring the subscripts? Because they no longer match.
You have phasors pointed in the same direction but you are saying they have different angles. This is not a proper representation of phasors, so I do not want to guess at what you are attempting to prove.

#### mivey

##### Senior Member
It must have been a tough assignment, I have no idea how you arrived at 360V.
Then maybe you were not being misleading at all. The math may just be unfamiliar to you and you made an honest mistake.

Your first exercise was to take 240@0? and subtract 120@180?. How you do not know this yields 360@0? is beyond me.

Your next exercise was to take 240@0? and subtract 120@0?. This, of course, yields 120@0?

If the voltages can be combined to produce a higher voltage, than by the virtue of mathematics then one of them should be able to be subtracted from the higher value without providing a misleading answer.
There is nothing wrong with my methodology and my post is correct.

Here let me do the simple phasor manipulation for you.
Van+Vnb=2Vab
2Vab = 240V@0?|-------------------->
Van = 120V@0?|--------->
2Vab-Van =120V@?? this requires the phasors to be connected tail to tail or head to head
So |--------------------> -|---------> = |--------->---------> = --------- I'll let you put in the direction.

Now
Van-Vbn=2Vab
2Vab = 240V@0?|-------------------->
2Van = 120V@0?|--------->
2Vab-Van =120V@?? this requires the phasors to be connected tail to tail or head to head
So |--------------------> -|---------> = |--------->---------> = --------- I'll let you put in the direction.
That, sir, is some of the worst labeling and notation I have ever seen. How can you possibly expect to do any phasor manipulations for me? I know you own a copy of Blackburn's "Protective Relaying" book. He has a good section on voltage labels and proper use of subscripts. You would do well to review that section.

I suspect they would but I am not even going to attempt to try to interpret the mess you just posted.

I'll take the high road on that question.

No it is not.
Yes, it is.

I am waiting for someone to post an actual oscilloscope display of your paralleled Vbn and Vnb in series with your paralleled Van and Van outputs.
If you do not understand that the Vbn and the Vnb in my example are two sinusoidal waveforms with a 180? displacement, then I really don't know how posting an actual oscilloscope display of Vbn and Vnb that will display two sinusoidal waveforms with a 180? displacement is going to help you.

#### jim dungar

##### Moderator
Staff member
Your first exercise was to take 240@0? and subtract 120@180?. How you do not know this yields 360@0? is beyond me.
Actually, the mistake is in assigning an angle of 180? to this voltage in the first place.
The math does work when you acknowledge the double negative in your methodology.

#### mivey

##### Senior Member
If you do not understand that the Vbn and the Vnb in my example are two sinusoidal waveforms with a 180? displacement, then I really don't know how posting an actual oscilloscope display of Vbn and Vnb that will display two sinusoidal waveforms with a 180? displacement is going to help you.
Below are the waveforms for the voltages in my generator example (slightly offset so the plots don't lay right on top of each other).

Here is the coupling of the voltages from my generators on the left side of my example (V@0? and V@180?) with the voltages from the center-tapped transformer on the right side of my example (V@0? and V@0?):

Here are the waveforms for the voltages from the generators:

Here are the waveforms for the voltages from the center-tap transformer:

Here they are on one plot:

#### mivey

##### Senior Member
Actually, the mistake is in assigning an angle of 180? to this voltage in the first place.
The math does work when you acknowledge the double negative in your methodology.
You set up the exercise so you take ownership of any mistakes you allege are there.

You will note that my voltages from the left side of my generator that have a 180? displacement use the "industry standard blah blah blah" terminals for naming the voltages. One voltage Vx1x0 has a phase angle of 0? and the other voltage Vx1x0 has a phase angle of 180?. This displacement was obtained by using identical generators but simply rotating the shaft of one 180? relative to the other.

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#### jim dungar

##### Moderator
Staff member
That, sir, is some of the worst labeling and notation I have ever seen. How can you possibly expect to do any phasor manipulations for me? I know you own a copy of Blackburn's "Protective Relaying" book. He has a good section on voltage labels and proper use of subscripts. You would do well to review that section.
I do not plan to take any phasor instruction from someone that cannot figure out that a result of 360V must be due to poor direction assignment, and instead blames the math.

#### mivey

##### Senior Member
Ah. Two voltages.
Progress again.:thumbsup:
What is the relationship between those two voltages?
Maybe time to revisit #2241 again. I thought it was a nice example.

#### rattus

##### Senior Member
Have you rewired the transformer?
Are you simply redrawing phasor directions while ignoring the subscripts? Because they no longer match.
You have phasors pointed in the same direction but you are saying they have different angles. This is not a proper representation of phasors, so I do not want to guess at what you are attempting to prove.

No transformer involved. They are simply voltages from a black box.

The voltages are the voltages seen at nodes 1 & 2. They are not necessarily the value of the phasors; that is left as an exercise to the student.

#### jim dungar

##### Moderator
Staff member
Maybe time to revisit #2241 again. I thought it was a nice example.
Circuit does not work with one voltage.
Circuit does work with two voltages.

So?

#### mivey

##### Senior Member
I do not plan to take any phasor instruction from someone that cannot figure out that a result of 360V must be due to poor direction assignment, and instead blames the math.
I'm quite sure your pride won't let you take instruction from me, that is why I suggested you learn from Blackburn. But I'm sure he would also agree that 240@0? - 120@180? = 360@0?

#### rattus

##### Senior Member
I'm quite sure your pride won't let you take instruction from me, that is why I suggested you learn from Blackburn. But I'm sure he would also agree that 240@0? - 120@180? = 360@0?

Yep! That's the way phasors work!

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