Power factor and VA vs Watts

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jghrist said:
Now you have me confused. I was about to admit that indeed Z can be thought of to vary with time because X = L?di/dt. I'm afraid that I don't follow your argument about equivalent R value and "resistance-equivalent ohmage."
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It's not an argument. It's simply applying Ohms Law to continuously varying voltage and current of a reactive load. Just as E/I=R, the R-equivalent of Z is v(t)/i(t). See pdf linked below. Be sure to view page 2.

http://forums.mikeholt.com/attachment.php?attachmentid=4487&d=1270676574

I can't agree.
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I understand if we are not on the same page.

The heat dissipated in a resistor depends on the total current flowing through the resistor.
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I concur completely. However, an ideal reactive component has impedance, of which none is resistive. Yet the total current flows through (in and out) of these components. Theoretically speaking, does an ideal reactive component convert electrical energy to heat? Now the same question for a real reactive component? ...and if it converts energy to heat, why?
 
What??

What??

Smart $ said:
It's not an argument. It's simply applying Ohms Law to continuously varying voltage and current of a reactive load. Just as E/I=R, the R-equivalent of Z is v(t)/i(t). See pdf linked below. Be sure to view page 2.
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Smart, where do you get this stuff? And, what does it mean anyway? Impedance is defined for the steady state only, and it does not vary! We beat this horse to death some time ago.

Better give us a solid reference on this one. Sounds like a home-grown theory to me.
 
rattus said:
But there is. The equation in question was derived from,

v(t) = Vm*sin(wt)
i(t) = Im*sin(wt + theta)

The term "cos(theta)" turns out to be the power factor.
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The theta (more usually termed as phi) is a phase displacement. For a given frequency that is a time displacement between current and voltage.
For instantaneous quantities there is no time element thus no time displacement.
 
Now wait a minute!

Now wait a minute!

jghrist said:
So, impedance becomes infinite when I is zero? And I thought R was constant and X was a constant times di/dt.

I stand corrected.
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R is constant and Z is constant for a constant frequency.

Xl = 2*pi*f*L

Xc = 1/(2*pi*f*C)

The whole concept behind Ohm's law is that R is constant. We can extend Ohm's law to reactances and impedances which must also be constant.

Impedance and reactance cannot be used with instantaneous equations.
 
Besoeker said:
The theta (more usually termed as phi) is a phase displacement. For a given frequency that is a time displacement between current and voltage.
For instantaneous quantities there is no time element thus no time displacement.
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Your statement does not make sense. The argument for the trig functions must be in radians, not seconds. e.g., the units of "wt" are radians.

Theta is the lead or lag as the case may be between the voltage across and the current through a load. e.g., the general form for i(t) is,

i(t) = Im*sin(wt + theta)

Theta is described as a phase angle in,

[Kerchner and Corcoran, (Alternating-Current Circuits, 3rd edition, John Wiley & Sons, 1951)]

If you think otherwise, give us a solid reference.
 
jghrist said:
So, impedance becomes infinite when I is zero? And I thought R was constant and X was a constant times di/dt.

I stand corrected.
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The curve labeled "impedance" in the graph is mislabeled... sorry, forgot to mention. That curve depicts nothing more than v(t)/i(t)... (and for rattus' sake) it is what I call the R-equivalent of Z (PS: if there is a conventional terminology for this, please let me know so I can please the electric gods :roll:). It shows how current is "hindered" in relation to the applied voltage. So while the numerical impedance (Z) value is a constant, the physical instantaneous "hindrance" is not.

Anyway, the second part of my post was far more important to the discussion... but it seems you guys are hellbent on pointing out any triviality that doesn't fit into some neatly-arranged-and-packaged-for-you concept, while ignoring anything of major contribution to the discussion.
 
rattus said:
Your statement does not make sense. The argument for the trig functions must be in radians, not seconds. e.g., the units of "wt" are radians.

Theta is the lead or lag as the case may be between the voltage across and the current through a load. e.g., the general form for i(t) is,

i(t) = Im*sin(wt + theta)

Theta is described as a phase angle in,

[Kerchner and Corcoran, (Alternating-Current Circuits, 3rd edition, John Wiley & Sons, 1951)]

If you think otherwise, give us a solid reference.
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Bes' statement makes perfect sense to me. There are no known models of power systems where the concept of instantaneous power having a phase angle has any use what so ever.

As for your reference, I have no clue as to the context nor what the authors were trying to show. I suspect if we had the reference available, we may have a different conclusion. But no way for any of us to tell.

As for finding a reference that says," Instantaneous power does not have a phase angle" - that is a little silly. Who is going to discuss a concept that has no value?

cf

cf
 
rattus said:
The whole concept behind Ohm's law is that R is constant. We can extend Ohm's law to reactances and impedances which must also be constant.

Impedance and reactance cannot be used with instantaneous equations.
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Ohm's Law is a mathematical formula which describes the numerical relationship between three measures of discrete electrical phenomenon elements. Nothing more, nothing less.

...and Ohm's Law is not broken when R is a varying value :cool:
 
Smart $ said:
The curve labeled "impedance" in the graph is mislabeled... sorry, forgot to mention. That curve depicts nothing more than v(t)/i(t)... (and for rattus' sake) it is what I call the R-equivalent of Z (PS: if there is a conventional terminology for this, please let me know so I can please the electric gods :roll:). It shows how current is "hindered" in relation to the applied voltage. So while the numerical impedance (Z) value is a constant, the physical instantaneous "hindrance" is not. ...
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No, there is no term I am aware of that describes, "R-equivalent of Z". Nor am I aware of any term/model that describes 'physical instantaneous "hinderance" '

Smart $ said:
...Anyway, the second part of my post was far more important to the discussion... but it seems you guys are hellbent on pointing out any triviality that doesn't fit into some neatly-arranged-and-packaged-for-you concept, while ignoring anything of major contribution to the discussion.
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If the above is an example of a, "major contribution to the discussion", yes that is suitable for ignoring.

cf
 
Smart $ said:
Ohm's Law is a mathematical formula which describes the numerical relationship between three measures of discrete electrical phenomenon elements. Nothing more, nothing less.

...and Ohm's Law is not broken when R is a varying value :cool:
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No, It isn't broken. It may not apply. It depends on the model.

cf
 
Cold Fusion said:
Bes' statement makes perfect sense to me. There are no known models of power systems where the concept of instantaneous power having a phase angle has any use what so ever.
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You mean no models known to you.

As for your reference, I have no clue as to the context nor what the authors were trying to show. I suspect if we had the reference available, we may have a different conclusion. But no way for any of us to tell.
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You rely on reference texts too much, IMO. I'd be willing to bet that you have cracked open, much less read, less than 1% of all texts on the subject.

As for finding a reference that says," Instantaneous power does not have a phase angle" - that is a little silly. Who is going to discuss a concept that has no value?
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Anyone who contests the notion. Just the same as you discussing a matter that you claim has no value here.
 
Cold Fusion said:
If the above is an example of a, "major contribution to the discussion", yes that is suitable for ignoring.
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You make my point :cool:

Rather than going back to the second part of the post mentioned and commenting on it, you'd rather nitpick about a trivial rambling. ;)
 
rattus said:
...

Theta is described as a phase angle in,

[Kerchner and Corcoran, (Alternating-Current Circuits, 3rd edition, John Wiley & Sons, 1951)]

If you think otherwise, give us a solid reference.
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I have seen theta and phi used both ways. However, the more common usage seems to be phi (φ) is phase angle while theta (θ) is the difference of two phase angles (φ1 – φ2).
 
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