# Complex voltage and current RMS Values & complex power

#### Abdelrahman123

Joined Nov 2, 2016
6
I want someone explain when rms is complex. From the definition of it, it should be the effective dc value that gives the same effect and since dc values aren't complex how come in the text book (Alexandar fundamentals of electric circuits 9th edition) consider in problems some rms to complex and use this theory in proving complex power.
From the equation
Vrms = square root of ( (1/T) * integration(v(t)^2))
Integration boundaries: 0 to T
even if v(t) is under the x-axis due to charging a source v(t) ^ 2 will be above the curve and the integration should always be positive.
Therefore, no imaginary parts are to exist.
(even in case some miraculous happened that the integration is negative should Vrms be just imaginary not cmplex)

I hope someone help!

#### Papabravo

Joined Feb 24, 2006
14,684
First point is that when v(t) is a complex function the concept of above or below the x-axis has no meaning. There is no x-axis in the complex plane. There is only the real axis and the imaginary axis. A typical complex function with a constant amplitude might look like:

$$v(t)\;=\;2e^{j\omega t}\;=\;2(cos(\omega t) + j\; sin(\omega t))$$

This describes a circle of radius 2 in the complex plane. So tell me again what is your problem with this function?

• Abdelrahman123

#### MrChips

Joined Oct 2, 2009
22,095
You are fixated on thinking that complex numbers must have √-1.
If v(t) is real then Vrms will be real.
If v(t) is complex then Vrms will be complex.

#### WBahn

Joined Mar 31, 2012
26,301

#### MrAl

Joined Jun 17, 2014
7,849
I want someone explain when rms is complex. From the definition of it, it should be the effective dc value that gives the same effect and since dc values aren't complex how come in the text book (Alexandar fundamentals of electric circuits 9th edition) consider in problems some rms to complex and use this theory in proving complex power.
From the equation
Vrms = square root of ( (1/T) * integration(v(t)^2))
Integration boundaries: 0 to T
even if v(t) is under the x-axis due to charging a source v(t) ^ 2 will be above the curve and the integration should always be positive.
Therefore, no imaginary parts are to exist.
(even in case some miraculous happened that the integration is negative should Vrms be just imaginary not cmplex)

I hope someone help!
Hi,

I think Vrms can resolve to a single number but not for the reason you have shown. In between values might be called complex RMS for convenience, but i think we need to see the article you are talking about here.
Recall that any sinusoid with a phase shift still resolves to a single RMS value, however an in between value might still have an imaginary part.
If we can see the text you refer to we can tell more about how the author is using that terminology. We dont have to see the whole book, just that one part where he uses it in the manner in which you speak.

#### Papabravo

Joined Feb 24, 2006
14,684
Hi,

I think Vrms can resolve to a single number but not for the reason you have shown. In between values might be called complex RMS for convenience, but i think we need to see the article you are talking about here.
Recall that any sinusoid with a phase shift still resolves to a single RMS value, however an in between value might still have an imaginary part.
If we can see the text you refer to we can tell more about how the author is using that terminology. We dont have to see the whole book, just that one part where he uses it in the manner in which you speak.
This sounds like "new physics" to me. What is an "in between" value? You do know that the real number line is continuous and there are no "in between" values -- don't you?

#### MrAl

Joined Jun 17, 2014
7,849
This sounds like "new physics" to me. What is an "in between" value? You do know that the real number line is continuous and there are no "in between" values -- don't you?
Hi,

It's interesting that you brought this up even though that's not what i was talking about. Try to point to the square root of 2 on the number line.

But what i was really taking about was an intermediate value from an intermediate calculation. This is a very simple concept. Say we want to calculate the sum of 1+3+5. We might do it like this:
First, 1+3=4
Then once we have that, 4+5=9
So here the intermediate value is 4, and the final value is 9.

In complex math the intermediate value could be the complex result for example, and the final value might be the phase angle or the amplitude or both, depending on what we intended to calculate. It's as simple as the addition example above so it depends highly on the application what we think of as the intermediate value and final value, and there could be several intermediate (in between) values from in between calculations.

But as a side note try to point to the square root of 2 and then tell me how you did it.

#### Papabravo

Joined Feb 24, 2006
14,684
Hi,

It's interesting that you brought this up even though that's not what i was talking about. Try to point to the square root of 2 on the number line.

But what i was really taking about was an intermediate value from an intermediate calculation. This is a very simple concept. Say we want to calculate the sum of 1+3+5. We might do it like this:
First, 1+3=4
Then once we have that, 4+5=9
So here the intermediate value is 4, and the final value is 9.

In complex math the intermediate value could be the complex result for example, and the final value might be the phase angle or the amplitude or both, depending on what we intended to calculate. It's as simple as the addition example above so it depends highly on the application what we think of as the intermediate value and final value, and there could be several intermediate (in between) values from in between calculations.

But as a side note try to point to the square root of 2 and then tell me how you did it.
The location of the √2 and all other irrational numbers is inherent in the construction of the real number line. Are you telling me you don't know how it is done?

#### MrAl

Joined Jun 17, 2014
7,849
The location of the √2 and all other irrational numbers is inherent in the construction of the real number line. Are you telling me you don't know how it is done?
HI again,

If we are going to ask silly questions, then are you telling me that you dont know if i know how it is done or not? What i am asking is not to construct a number line, i am asking you to point to a certain numerical value.
What is interesting is that you cant actually point to it because any time you think you've pointed to it, you've only pointed to an approximation of it or if you try to side step that using the theory of a number line then you would sort of 'cheat' and do it theoretically by pointing to what you would call sqrt(2), without specifying the value. But isnt it interesting that we cant point to it without using an approximation, and that means we didnt really point to it. Compare to pointing to just the integer "2", which we could probably say we did. We could even point to 3.1 or 9.56 .
This is getting a little off track though because i was not originally talking about this at all. If you are interested maybe we could talk in PM's.

#### Papabravo

Joined Feb 24, 2006
14,684
HI again,

If we are going to ask silly questions, then are you telling me that you dont know if i know how it is done or not? What i am asking is not to construct a number line, i am asking you to point to a certain numerical value.
What is interesting is that you cant actually point to it because any time you think you've pointed to it, you've only pointed to an approximation of it or if you try to side step that using the theory of a number line then you would sort of 'cheat' and do it theoretically by pointing to what you would call sqrt(2), without specifying the value. But isnt it interesting that we cant point to it without using an approximation, and that means we didnt really point to it. Compare to pointing to just the integer "2", which we could probably say we did. We could even point to 3.1 or 9.56 .
This is getting a little off track though because i was not originally talking about this at all. If you are interested maybe we could talk in PM's.
All right here it is:
https://en.wikipedia.org/wiki/Real_line#/media/File:Real_number_line.svg
The real number line is a continuum and includes all the rational and irrational numbers. You can locate the √2 with arbitrary precision. You can accept it or not as the mood moves you -- I really could care less. In addition since it is a continuum, there are no in between values.

#### MrAl

Joined Jun 17, 2014
7,849
All right here it is:
https://en.wikipedia.org/wiki/Real_line#/media/File:Real_number_line.svg
The real number line is a continuum and includes all the rational and irrational numbers. You can locate the √2 with arbitrary precision. You can accept it or not as the mood moves you -- I really could care less. In addition since it is a continuum, there are no in between values.
Hi,

Ha ha, so you've side stepped the issue. By calling it the square root of 2 you've bypassed the entire exercise. You were supposed to point to it, perhaps with a 'dot'. But dont worry about it for now.

This is related a little to trying to find the circumference of say a country or state on a map. We know it should be finite, but yet we only get an approximation that is usually less than what it really is.

#### WBahn

Joined Mar 31, 2012
26,301
I want someone explain when rms is complex. From the definition of it, it should be the effective dc value that gives the same effect and since dc values aren't complex how come in the text book (Alexandar fundamentals of electric circuits 9th edition) consider in problems some rms to complex and use this theory in proving complex power.
From the equation
Vrms = square root of ( (1/T) * integration(v(t)^2))
Integration boundaries: 0 to T
even if v(t) is under the x-axis due to charging a source v(t) ^ 2 will be above the curve and the integration should always be positive.
Therefore, no imaginary parts are to exist.
(even in case some miraculous happened that the integration is negative should Vrms be just imaginary not cmplex)

I hope someone help!
I think you are mixing up some things.

If I have a sinusoidal voltage then the complex representation is merely a way of tracking the phase angle relative to some reference. The amplitude of the voltage can be given using the actual amplitude or the RMS value (or, less commonly, the peak-to-peak value).

The RMS value is not complex.

#### WBahn

Joined Mar 31, 2012
26,301
HI again,

If we are going to ask silly questions, then are you telling me that you dont know if i know how it is done or not? What i am asking is not to construct a number line, i am asking you to point to a certain numerical value.
What is interesting is that you cant actually point to it because any time you think you've pointed to it, you've only pointed to an approximation of it or if you try to side step that using the theory of a number line then you would sort of 'cheat' and do it theoretically by pointing to what you would call sqrt(2), without specifying the value. But isnt it interesting that we cant point to it without using an approximation, and that means we didnt really point to it. Compare to pointing to just the integer "2", which we could probably say we did. We could even point to 3.1 or 9.56 .
This is getting a little off track though because i was not originally talking about this at all. If you are interested maybe we could talk in PM's.
You can point to √2 just as accurately as you can point to 2.

• ErnieM

#### BR-549

Joined Sep 22, 2013
4,938
In a dc circuit.....the current is in time and proportional to the voltage. Resistance limits current.....reactance separates it. Reactance separates the peak current from the peak voltage. Ohm's proportionality fails. The complex math.......restores the proportionality for this time difference.

#### MrAl

Joined Jun 17, 2014
7,849
You can point to √2 just as accurately as you can point to 2.
Hello again,

Well, both you and Papa claim to be able to do this but neither one of you has actually done it yet.
I can *say* that someone can point to the square root of Mars, but does that mean it can actually be done?

The difference here is theory vs actually doing it. Another example would be counting to infinity. We know that we will reach infinity with the progression 1,2,3,... but no one, ever, has done this and actually reached infinity, yet in theory we know it to be true. To prove it by purely doing it is impossible though.

Back on to the main topic:
I can only guess that the author was quoting a value from a calculation maybe just before the end result. This is because in general the square of a complex number is a complex number and the integral of a complex number is a complex number and the square root of a complex number is a complex number, so maybe he is calling this intermediate calculation a complex RMS value. That's why i thought it would be good to see the original paper so we can figure out if there is some weight to this view or it was just a mistake of some kind.

#### WBahn

Joined Mar 31, 2012
26,301
Hello again,

Well, both you and Papa claim to be able to do this but neither one of you has actually done it yet.
I can *say* that someone can point to the square root of Mars, but does that mean it can actually be done?

The difference here is theory vs actually doing it. Another example would be counting to infinity. We know that we will reach infinity with the progression 1,2,3,... but no one, ever, has done this and actually reached infinity, yet in theory we know it to be true. To prove it by purely doing it is impossible though.

Back on to the main topic:
I can only guess that the author was quoting a value from a calculation maybe just before the end result. This is because in general the square of a complex number is a complex number and the integral of a complex number is a complex number and the square root of a complex number is a complex number, so maybe he is calling this intermediate calculation a complex RMS value. That's why i thought it would be good to see the original paper so we can figure out if there is some weight to this view or it was just a mistake of some kind.
Tell you what. You point to the number 2 on a continuous number line and I will point to √2 with the same level of accuracy and precision. Whatever claim you make that I'm not really pointing at √2 I will make right back that you aren't really pointing at 2.

#### MrAl

Joined Jun 17, 2014
7,849
Tell you what. You point to the number 2 on a continuous number line and I will point to √2 with the same level of accuracy and precision. Whatever claim you make that I'm not really pointing at √2 I will make right back that you aren't really pointing at 2.
Hi,

Ok, so now you are asking me to do something first before you can point to sqrt(2).
So you seem to require someone else to do something before you can perform a task of any kind Why cant you point to 2, Is it that you cant point to 2 either? So after several back and forth messages, i still dont see anyone pointing to sqrt(2), and now i dont even see anyone pointing to 2.

What is so hard about pointing to sqrt(2) ?
I think i will go to the store and purchase 2 oranges.
I think i will go to the same store and purchase sqrt(2) apples.
What will i come home with?

#### WBahn

Joined Mar 31, 2012
26,301
Hi,

Ok, so now you are asking me to do something first before you can point to sqrt(2).
So you seem to require someone else to do something before you can perform a task of any kind Why cant you point to 2, Is it that you cant point to 2 either? So after several back and forth messages, i still dont see anyone pointing to sqrt(2), and now i dont even see anyone pointing to 2.
I'm getting a bit tired of your childish games. You know damn well what we are talking about -- you just don't want to admit it.

Here: How ever accurately you try to locate 2, I will locate sqrt(2) just as accurately. Or the other way around. Despite this being a quantized approximation of a continuous number line. Depending on the order in which this image was constructed, either sqrt(2) is located exactly and 2 is an approximate location, 2 is located exactly and sqrt(2) is an approximation location, or both are approximations. You can't tell from the final image which of these holds.

What is so hard about pointing to sqrt(2) ?
I think i will go to the store and purchase 2 oranges.
I think i will go to the same store and purchase sqrt(2) apples.
What will i come home with?
Now you are just trying to confuse the issue by mixing a counting concept with a measuring concept. More of your silly obfuscation games.[/QUOTE]

#### MrAl

Joined Jun 17, 2014
7,849
Hello again,

From your extremely negative response i think this is not the forum to discuss such issues with everyone.
I have to realize sometimes that not everyone is into this kind of physical discussion of reality, and yes often it can look absurd.
There is much debate about some things that seem very silly, such as whether or not a hole in the ground actually exists, but this is probably not the right forum to discuss this either.

So with that let us get back to the original topic.

#### ErnieM

Joined Apr 24, 2011
8,058
The sqr(2) is located exactly a distance of sqr(2) away from the origin.

Now hand me exactly half a piece of chalk.