rattus said:
1. If you don't understnad my use of rises and drops, you cannot understand my argument.
I do understand your argument. You want to call these two voltage sources out of phase because that is how you
(we--including myself) view them when we look at a load center, or such. This is fine, because from that particular perspective, they appear to be out of phase.
This is the flexibility of being able to view circuits from a particular perspective.
However, once you draw a phasor diagram or a circuit schematic, you lose this flexibility of calling them out of phase, or even of opposite polarity--unless you
also add a negative sign to the voltage?s magnitude. From a phasor diagram or circuit schematic perspective, the two voltage sources are not out of phase, and they have the same polarity.
From what I have been able to gather over the past several days, you are trying to take this
perspective of the two sources being out of phase, and trying to make it an
absolute in the diagram, and this is something that you cannot do (again, without adding the minus sign).
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I thought of an analogy this morning on my drive to a project site. Let?s go back to the TV remote (aka clicker).
It has 2 AA batteries connected in series with the negative terminals down and the positive terminals up, as shown to the left. The two 1.5 voltages add together to give us 3 volts total.
When we change our reference point to be at the point between those two batteries, and we use a volt meter to measure the voltages from our reference point, our volt meter will record the upper battery as having +1.5 volts, and the lower battery as having ?1.5 volts. This is shown by the Red text. So we would (could) call them out of phase (or reversed polarity).
Our point of reference has changed, but the batteries have not. This would be like crossing out the labels on the batteries an putting our own markings on it (as shown in Red Text).
You, on the other hand, are trying to redefine the battery itself and say that it is turned upside down, with its positive terminal down and the negative terminal up, and the voltage still being the positive voltage printed on the label (as shown to the right). When you add these two batteries up (i.e. connect them together) you get a total of zero volts across them.
rattus said:
2 Let's see some proof that a summation cannot include subtraction.
I don?t mean for this to sound derogatory, but there is no other way I can say this. I don?t have text books going back far enough to cover such an elemental topic. This is mathematics taught in Elementary School. Summation is addition. Summing a positive number and a negative number is still summation. Subtracting two positive numbers is not summation of a negative, but by definition, is subtraction.
OK, I just thought of a perfect example of why these are different: Add 2 and 3 and you get 5. Now subtract 2 and 3, and what do you get?--well, since I didn?t tell you which number to subtract from the other number, you could end up with either +1 or ?1. However, if I tell you to add 2 and a (-3), then it makes no difference which number you put first, the answer will always be ?1. That is the difference between summation and subtraction,
and that is the reason why Kirchoff?s Law specifically states directed summation.
By the way, this is also why vector analysis is cummutative, as I mentioned in my previous posting. This is also why when I rearranged your original diagram, I got a different answer. It is analogous to subtracting 2 and 3 without specifying which one to start with.
That's why we don't do this is electrical circuit analysis.
rattus said:
3. How is it that my summation equals zero like it should?
Because you added the minus sign, but called it subtraction. If you had added the minus sign to the phasor/vector, then we wouldn?t be having this argument, and you would also see that the direction is the same as what I have been trying to tell you.
p.s. I know that I have now answered this question more than once. Don?t keep asking the same question expecting the answer to change.
rattus said:
4. What would happen if we performed the summation in a CW direction?
Then
all of the phasors would be pointing in the opposite direction, and the answer would still be the same. This is why I told you that Kirchoff doesn?t care if it is CCW or CW, so long as you don?t do both.
rattus said:
5. I am addressing this issue. If you refuse to respond, then you forfeit the game because that post disproves your notion about subtraction.
I know your tactics already. You want to distract the discussion away from a difficult problem in the hopes that it will be forgotten and everyone moves on. I fully intend to extend this discussion into the 3-phase wye system, and I actually look forward to that. However, we cannot go down that road until we fix this one first, or we will still have the same problems then.