NEC Table 9

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muhandas

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I know that some aspects of NEC Table 9 have been discussed before, at least in the NEC forum, but not the part for which I need help to understand.
Note 2, at the bottom of the Table, defines Effective Z as Rcos(θ) + Xsin(θ), that is as a linear combination of the resistive and reactive terms. However, as I remember it, impedance for a series circuit of resistance R and Inductive reactance X is calculated by a vector sum of the resistive and reactive components, that is, Z=sq.rt(Rsquared.+Xsquared). {in fact, resistive and reactive components are usually calculated by R=Zcos(θ) and X=Zsin(θ).} What am I missing?
I was first made aware that something looked odd (to me) when I noticed that for every wire size smaller than AWG No.2 the Effective Z was smaller than the resistance for conductors in the same type of conduit. That didn?t make sense to me and looking at Note 2 compounded my confusion.
Now, this Table has been around in this format for ages. So, it is obviously something that I am missing. Can anyone help this confused engineer?
Many thanks,
Heinz R.
 
Let me introduce a little thing called "the Q factor"

?Q? = Alternating Current Adjustment: Alternating current circuits No. 2/0 and larger must be adjusted for the effects of self-induction (skin effect). The "Q" adjustment factor is determined by dividing alternating current resistance as listed in NEC Chapter 9, Table 9, by the direct current resistance as listed in Chapter 9, Table 8.

Commentary here

As it applies in voltage drop-

Let bring in a factor called the "Q" factor....

it fits in like this -
VD=Q x K x I x D
CM​

See reference to earlier code cycles for table 8 chapter 9. Not because of code that it is so, but because these charts allow us to calculate Rt and Xt. This is used in regard to the conduit surrounding the conductor(s) and total impedance to the current flow.

Q as a Multiplier

For ac dircuits, the dc Resistance Constant (K) must be adjusted for the effects of eddy current and skin effect. The Q-Factor multiplier is calculated by dividing the ac resistance (chapter9 table 9) by the dc resistance (chapter9 table 8.) as listed in the NECode. Eddy currents and skin effect are insignificant for conductors No. 1/0 and smaller and their effects can be ignored.

Scary part? This is from a Mike Holt book 1993 - getting older...but I still remember somethings...(CRS shops me at times)

So as can be seen, "secret" forces conspire to offer evidence as to why the GRC needs to be increased due to inductive reactance effect when using metal pipe. Preferred for results PVC, then Aluminum, then Steel, in regard to fighting Q factor build up.

Here is a q factor table -

Size COPPER ALUMINUM
AVG ... PVC.......AL.......STEEL... PVC.......AL..... STEEL
MCM - Conduit Conduit Conduit Conduit Conduit Conduit
2/0 -- 1.0341 1.0341 1.0341... 1.0062 1.0062 1.0062
3/0 -- 1.0052 1.0704 1.0313... 1.0317 1.0317 1.0317
4/0 -- 1.0197 1.1019 1.0362... 1.0000 1.0000 1.0000

250 -- 1.0097 1.1068 1.0485... 1.0035 1.0626 1.0153
300 -- 1.0256 1.1422 1.0489... 1.0042 1.0749 1.0184
350 -- 1.0354 1.1717 1.0627... 1.0083 1.0909 1.0413

400 -- 1.0280 1.1838 1.0903... 1.0201 1.1153 1.0397
500 -- 1.0465 1.2403 1.1240... 1.0142 1.1321 1.0613
600 -- 1.0748 1.3084 1.1682... 1.0198 1.1615 1.0765


A little long in the tongue, but best I can do on short notice.
__________________
 
A ton of thanks for your quick and thorough response to my question. I'm going to need a bit of time to wrap my brain around all the info you provided. I hope you don't mind if after digesting the answer I have other questions. As I said, what bothered me was that Z in the table was less than R; I had never seen that. I had thought that skin effect might be involved somehow, but I could,'t figure out how, and certainly couldn't come up with numbers or equations.
By the way, I'm no spring chicken either, and that would be putting it mildly.
Tx. again.
Heinz R.
 
Rocky:
I've had a chance to study your reply at length and what you explain in context of the skin effect indeed makes a lot of sense to me. But the problem I'm having is with the smaller than AWG #2 wire sizes which, by your own comment even, are not affected very much by skin effect.
If, fas an example, you look at AWG #8 Copper in PVC, you will see that ac resistance is 2.56 Ohms/Km, while Effective Z is 2.26 Ohms/Km. How can Z be less than R?
All wires smaller that AWG #2 seem to behave similarly, with Z smaller than R. The smaller the wire the greater the difference. And that's where my confusion No. 1 is.

Confusion No. 2 deals with the equation used to define Effective Z in Note No. 2 at the bottom of Table 9. Impedance Z, as memory serves me, is always calculated by the vector sum of its resistive component R and reactance X, that is as the sq. root of the sum of the squares of R and X. The equation in Note 2 is nothing like that.
 
Standby, there are some real brainiacs in here , if we can get them to come out and play. I can get a good base hit, but willing to call for help to get a homerun knocked out of the park.

It's a little on the late side, but let me throw this out for consideration into the grand scheme of X and R effects -

240.4(D) because of the nature of small wire.

Will get back to it tomorrow.
 
Thanks for reply. 240.4 (D) doesn't really get into the computation of Z or why Z is smaller than R. By the way, I used the Equation that defines effective Z (Note 2 at the bottom of table 9) at other power factors, specifically a p.f of 0.45 and Z became much smaller than R. For quite unrealistic power factors such as 0.3 (almost purely inductive load) Z becomes even smaller than that, in effect R becomes almost negligible. At 60 Hz. I have aproblem understanding that.
Thanks for your help. I look forward to your and the "brainiacs" ideas on this.
Heinz R.
 
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