# Talk:Electrical reactance

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## Sign of reactance

How come

${\displaystyle Z=R+jX}$

and

${\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}$

when reactance is called inductive when X < 0? Isn't ${\displaystyle X_{c}=1/(\omega C)>0}$?

I believe the formula for reactance is missing a minus sign, it should be
${\displaystyle X_{C}={\frac {-1}{\omega C}}={\frac {-1}{2\pi fC}}}$
I didn't change it because I'm not sure of that. --Monguin61 05:44, 15 December 2005 (UTC)

It is now spelled out in the article that the reactance is given by
${\displaystyle X=X_{L}-X_{C}}$
-Larq 15:39, 1 April 2006 (UTC)

Well...X_C does not carry a MINUS sign! Both terms (X_C, X_L) are positive. MLange

look at this Link [1] --217.68.190.225 21:23, 6 February 2007 (UTC)

Yes, that page clearly shows the negative sign in front of the capacitive reactance. Sometimes the capacitive reactance is written as the imaginary expression with i (or j) in the denominator; since the reciprocal of i is -i, that makes the imaginary part negative. MLange is possibly hung up on the way it can be written without the explicit minus sign. Dicklyon 23:38, 6 February 2007 (UTC)

I have tagged it as factually disputed. There are numerous textbooks that don't define it with a negative sign: https://books.google.com/books?id=FNJ6Ay0UNRkC&pg=PA218 https://books.google.com/books?id=z8GlVgTKiCEC&pg=PA31, https://books.google.com/books?id=0yJ3blaI7b8C&pg=PA82 the list goes on... and on and on https://books.google.com/books?id=DM8aHZ4qe9cC&pg=PA59, https://books.google.com/books?id=kNbGGpuJyjMC&pg=PA19, https://books.google.com/books?id=2k8jCwgx7gIC&pg=PA231 5.12.38.28 (talk) 18:51, 29 November 2015 (UTC)

## why immaginary?

why is the reactance considered as an immaginary quantity and resistance as a real quantity?is there any physical significance? --Anand1000 11:24, 17 December 2005 (UTC)

This is a source of lots of confusion. The quick answer is that sometimes using imaginary numbers during calculations can make these calculations a lot simpler. Just remember this: All actual measurements, all actual quantities in nature, are _real_ - never imaginary. In electrical engineering the use of a particular method of calculation (an excellent one, have no doubt), has become so prevalent that sometimes the distinction between the model and the "actual physics" is blurred. Reactance is purely a property that some circuits have in this model (sometimes called the "j-omega model" - j being the same as i in mathematics (j^2=i^2=-1)).

A longer answer would go something along this:

1: Someone (probably very clever) once realized that many circuits, in many circumstances, are well approximated by a simple system of first-order linear differential equations.

2: Such equations can be very elegantly solved using Laplace or Fourier transforms. Laplace transforms are an extension of Fourier transforms. Fourier transforms allow us to express (almost) any function as a sum of many sine and cosine functions of different frequencies.

3: Using fourier transforms, the electronics community soon realized that many computations occured every time fourier transforms were used. These steps were then often skipped in calculations, and over time, the original origin (Fourier transforms) has become less obvious, in typical calculations done by todays engineers.

--Avl 09:12, 8 February 2006 (UTC)

Isn't j just a unit vector toward an imaginary dimension?Jolb 05:50, 9 March 2007 (UTC)
Reactance is not considered imaginary by everyone. Indeed, this article currently describes capacitive reactance as real, which is quite common. This may be the physical significance that is sought in other discussion here. --gaussmarkov 15:09, 6 September 2007 (UTC)

## Is this the reciprocal of susceptance?

Susceptance: the reciprocal of reactance.

whereas the susceptance page says that it isn't (it calls it the inverse, but that means the same thing (I even checked!)), at the bottom of the article. Which is right? I think the other page probably is, but that's just from a glance - I haven't studied complex numbers in much detail yet. --Smin0 16:32, 8 October 2006 (UTC)

It's only the same when the resistance is zero. The imaginary part of the reciprocal is not the same as the reciprocal of the imaginary part, when real part is nonzero. But, the error seems to have been fixed already here. Dicklyon 23:32, 6 February 2007 (UTC)

Susceptance is the imaginary part of the admittance. Just as reactance is the imaginary part of the impedance. It is not accurate to define susceptance as the reciprocal of reactance. However, admittance is the complex reciprocal of impedance. Same way, conductance is not the reciprocal of the resistance (except in DC circuits). The text need to be fixed promptly. The way it is presented it may appear that the frequency dependence is there only for the imaginary part but it is not true.chami 14:28, 12 August 2011 (UTC) — Preceding unsigned comment added by Ck.mitra (talkcontribs)

## Sign of capacitive reactance?

It seems to me that a reactance is capacitive when less than zero, and inductive when greater than zero. But some others want capacitive reactance to be positive, which I suppose can mean that the adjective "capacitive" flips the sign or takes the absolute value of the imaginary part of the net complex impedance. Is there a reliable source for this approach? Or for either approach?

Please respond if you have a source in support of one approach or the other, and enter a vote. Which convention should we use in this article, or should we talk about both? I'll start with one of each:

## Where the sign comes from

The confusion regarding the sign of the reactance term in impedance stems largely from the fact that it has no direct physical significance on its own. Impedance has a magnitude (giving the V-I amplitude relationship) and a phase (giving the V-I phase relationship); writing impedance in polar form makes this clear, using the cartesian form can make some calculations easier, but does not aid understanding.

The impedance of an ideal capacitor is given by

${\displaystyle Z_{C}={1 \over j\omega C}=j{-1 \over \omega C}={1 \over \omega C}e^{j(-{\pi \over 2})}\quad }$

The reactance being the imaginary part of impedance is given by

${\displaystyle \mathrm {X} _{C}=-{1 \over \omega C}\quad }$

The impedance of an ideal inductor is given by

${\displaystyle Z_{L}=j\omega L=\omega Le^{j{\pi \over 2}}\quad }$

Thus the reactance is given by

${\displaystyle \mathrm {X} _{L}=\omega L\quad }$

Reactance is only significant in AC circuits where both the voltage and current continuously change sign; this is why a phase shift can modify the sign.

I have just done a significant rewrite of the article on electrical impedance, which I believe explains this fairly clearly.

--DJIndica 12:54, 3 June 2007 (UTC)

The sign falls out of the metric signature. Differentiating a complex exponential with respect to time results in scaling it by the time coefficient in the phase. In the timelike ( (1,3), (+,-,-,-), etc) signature the temporal frequency is by default positive. In spacelike ( (3,1), (-,+,+,+), etc) signature the spatial frequency (wavenumber) is positive by default. The timelike signature predominates in electrical engineering, hence the convention for reactance. Theotherjoebloggs (talk) 01:33, 21 January 2017 (UTC)

## A controversial suggestion?

I believe is is somewhat misleading to have such a long article on reactance, given that its only significance is as the imaginary part of impedance; changing the reactance changes the magnitude and phase of the impedance.

The same argument could be made for resistance (the real part of impedance), however given that this is always taught first and is equal to the impedance for the common case of voltage and current in phase, the resistance article seems more valid.

Why are we concerning ourselves with the order in which things are taught? How is that relevant? If it is relevant then we should also consider the educational status of the readers etc etc for the same reason. I really think this is getting way out of hand. This should be (in my opinion) a simple page covering just the topic simply and then with a little more depth and link to pages on impedance etc as appropriate. PedantEngineer (talk) 07:17, 15 February 2017 (UTC)[pedant engineer]

I really feel it may be beneficial to remove the reactance article entirely and have it redirect to the reactance section in the article on impedance, however this may be impractical if people constantly recreate the article.

I will make changes here myself quite soon, but I would be interested to hear any counter arguments (reasons why it is helpful to explain reactance as an independent concept).

--DJIndica 12:54, 3 June 2007 (UTC)

I disagree with the observation that the only significance of reactance is as the imaginary part of impedance. But I agree with keeping this article brief relative to the impedance article. My impression is that the term reactance is used much less frequently in general writing about electronics than the term impedance. And when it is used, reactance usually appears with reference to impedance.
Electricians working in industrial environments and electrical engineers on power projects will very often use the term VAR so I wouldn't agree that it is an unusual term at all and for the sake of correct understanding of AC circuits as well as consistency in wiki pages it should never be an unusual term and the sign should never be omitted. Neither thing is a mere byproduct of the mathematics. Both have a very real significance and any further circuit analysis needs reactance to be understood and the sign to be in place.
If the sign is omitted here but in place (as it should be everywhere) on any page that discusses the more general 'impedance' confusion will be the result. Much of this discussion has been centred around the consistency of related wiki pages. I'm all for that and vehemently opposed to anything that undermines it. In my view, any discussion about omitting the negative sign is simply an argument for validating sloppy notation simply because it is the norm to have sloppy notation. The notation is no less sloppy if this norm is carried into a wiki page.
My pedantic 2c worth :-)

--07:17, 15 February 2017 (UTC)PedantEngineer (talk)[pedant engineer]

--gaussmarkov 15:40, 6 September 2007 (UTC)
In the light of the discussion in the following section I decided to add in the Physical significance section, rather than remove or pare down the article. This, however, has not changed my opinion that reactance is only useful with some knowledge of the resistance; sometimes the reactance dominates the impedance, but you need to have some idea of the resistance to know if this is the case. The one true exception is the special case in which there is a resonance where the phase of the impedance is zero (point 3 in the Physical significance section). I think this can more usefully be explained in terms of impedance than by saying the reactance is zero.
In conclusion I would state that reactance is a mathematical convenience, which can be very useful in some calculations, but is not helpful in trying to understand the voltage-current relationship in AC circuits.
--DJIndica 01:26, 14 September 2007 (UTC)
And I would still counter that it's very useful in trying to understand voltage-current relationships in AC circuits, especially because in very many situations (like an isolated inductor or capacitor, or a series-resonant circuit at any frequency other than resonance) it can be assumed to totally dominate the real part of the impedance. Dicklyon 03:02, 14 September 2007 (UTC)

## Discussion of physical significance of reactance

This discussion was initiated at User talk:Dicklyon; I copied it from there. --DJIndica 23:38, 23 June 2007 (UTC)

Hi Dicklyon,

Your 20 June 2007 edit of the reactance article raises an interesting issue. I did the previous edit in which I tried to stress that reactance on its own is not a useful quantity for determining the voltage-current relationship.

Strictly speaking I was incorrect to say that no physical information can be obtained from the reactance alone:

• The value of reactance places a lower limit of the magnitude of the impedance
• A reactance of zero implies the current and voltage are in phase (the only situation in which a specific value for the either the magnitude or phase of the impedance can be determined with knowledge of only the reactance) and conversely if the reactance is non-zero then there is a phase difference between the voltage and current

The reason I put so much emphasis on this physical insignificance is because I have found that too many people are under the impression that reactance is a quantity that can be used independently. As far as I can see, the only reason for ever expressing impedance in cartesian form is to simplify the addition of impedances, I don't believe it is useful for gaining physical insight.

Of course you are absolutely correct in stating that reactance gives limited physical information, but I fear this could lead someone not familiar with the concept to think that reactance on its own is a useful physical quantity. In My comment on the talk page I suggested that there should be no article on reactance, simply a redirect to the reactance section of the impedance article. In the end I decided this was impractical as people would probably keep re-creating the article, so I just tried to make things clear in the article.

I would appreciate your thoughts on this issue. --DJIndica 19:11, 21 June 2007 (UTC)

I'm a stickler for correctness, as you noticed. Within that limit, working to not confuse the reader is a good idea. So I appreciate your efforts there. But sometimes, when it dominates resistance, reactance alone may be enough to get what you need out an analysis, so don't exclude that posibility. Dicklyon 19:19, 21 June 2007 (UTC)
The fact that "when it dominates resistance, reactance alone may be enough" illustrates my point beautifully; knowledge of the resistance is required in order to verify that reactance dominates, hence knowledge of both reactance and resistance (i.e. impedance) is necessary to know whether reactance alone is enough. Ultimately this means that reactance alone is never enough (except for the one special case in which reactance equals zero).--DJIndica 22:25, 21 June 2007 (UTC)
Sure, but there are still uses for reactance. For example, when analyzing a resonant tank circuit, where the R determines the Q, you won't know the Q if all you have is reactance. But you can still get everything you need to know about the behaviour of the skirts of the filter, away from resonance. You can then specify limits on the R to get the Q you want. You don't have to start knowing R to do quantitative things with X. Dicklyon 23:05, 21 June 2007 (UTC)
I'm not so familiar with resonant tank circuits, i've been reading through RLC circuit and cannot see how the behavior at the skirts (far off resonance?) is determined by the reactance. Is it due to the resonance condition which occurs when ZC + ZL = 0 (determined by reactance); this seems to be an example of that single situation in which an actual numerical value can be obtained for a voltage-current relationship: X = 0 → θ = 0 (i.e. voltage and current are in phase). I would appreciate it if you could you clarify this for me.
Maybe we need to focus on a series RLC circuit driven by a voltage source. At resonance, the reactances add to zero, as you note, and the parasitic R of the inductor determines how much voltage you get across it. But away from resonance, the reactance dominates that resistance, so you can get a pretty accurate estimate of all the voltage and current amplitudes and phases using only the main R and the reactance of the LC, assuming that the C has neglibigle series or parallel R (usually a good approximation). Dicklyon 17:05, 23 June 2007 (UTC)
Actually, you can leave out the R and just look at a series RC driven by a voltage source. Except at resonance, you can get a good approximation to the current that flows due to the applied AC voltage. At resonance, the current goes to infinity until you add the loss (series R) of the inductor. Or use a parallel RC (tank circuit) driven by a current source, for similar results. Dicklyon 17:14, 23 June 2007 (UTC)
Of course you need to know the resistance in order to know how far off resonance you have to be before the reactance starts to dominate, but I guess you don't need to know it very precisely.--DJIndica 17:28, 23 June 2007 (UTC)
My agenda is that I feel that the "limited physical information" statement will mislead people; maybe we should keep it but add details about what information can be obtained. I feel that the two bullet points above describe the only information about the impedance that can be obtained from reactance alone (I should add also that the sign of the reactance determines whether voltage leads or lags the phase), but we could add specific instances in which they are useful such as calculating the resonance condition in a tank circuit. What are your thoughts and could you suggest further specific examples.--DJIndica 16:42, 23 June 2007 (UTC)
Feel free to work on a better way; this was my quick way to convert "no information" into something that is more correct. I recommend you find some books and look at how they treat it; I don't think I have great recommendations handy. Dicklyon 17:05, 23 June 2007 (UTC)
I will add further details soon. I'll also copy this discussion to the reactance talk page so that people can follow the thinking behind the recent edits to the article. Thank you, this has been illuminating for me.--DJIndica 17:28, 23 June 2007 (UTC)
Isn't capacitive reactance a simple and leading physical example of reactance? --gaussmarkov 15:44, 6 September 2007 (UTC)

## Resistive reactance?

In the lead, the following is stated:

   * If \scriptstyle{\Chi > 0}, the reactance is said to be inductive
* If \scriptstyle{\Chi = 0}, then the impedance is purely resistive
* If \scriptstyle{\Chi < 0}, the reactance is said to be capacitive


I don't know if the use of "impedance" in the second line is a mistake or not, so I won't edit it. But it sure looks fishy. Any commentary would be welcome. 18:29, 26 August 2007 (UTC)

Nevermind. Silly me, I wasn't paying much attention. 213.113.60.145 18:33, 26 August 2007 (UTC)

## Charge flow vs. current flow

This article was recently edited to change "no current flows in the dielectric" to "no charge flows in the dielectric". While I take the point that was being made it is absolutely standard to talk about a "flow of current", in the same way we would talk about the "flow of a river" even though a river is just a flow of water. I have made "current" a wikilink in case there are any readers confused about the definition. --DJIndica (talk) 15:00, 25 March 2008 (UTC)

## Article title

Hello, "Electronics refers to the flow of charge (moving electrons) through [b]nonmetal[/b] conductors". Indeed, electronics as a branch of electrical engineering deals chiefly with semiconductor components as semi-active components. Inductors are occasionally used in electronic devices, but they're chiefly used for power/AC purposes. Thus, the (electronics) in the title is misleading. The text of the article mentions "electronics" zero (0) times.

Upon reflection, the title should be electrical reactance to be consistent with electrical impedance and electrical resistance. No such user (talk) 13:56, 16 April 2009 (UTC)

I guess I have been using the term electronics carelessly. I learned electrical engineering in physics departments, in courses with "electronics" in the title. I agree with with your final conclusion.--DJIndica (talk) 15:47, 16 April 2009 (UTC)

Not correct: inductors are widely used in RF circuits, amplifiers etc. However, engineers tend to avoid the use of inductors as the are difficult to miniaturise. See, for example, any IC schematic diagram (no inductors!). Most smaller power supplies are often inductor free.chami 14:42, 12 August 2011 (UTC) — Preceding unsigned comment added by Ck.mitra (talkcontribs)

Most smaller power suppies are anything but inductor free. DieSwartzPunkt (talk) 17:07, 27 October 2012 (UTC)

## 'Buildup' removed

I removed "caused by the build-up of electric or magnetic fields in the element," because it was not true. The inertia (for the current or voltage to change) is not due to buildup of any field. It that were true, an ideal capacitor, completely discharged, would have no capacitance, and an ideal inductor, with zero current, would have no inductance, and those are not true. An ideal capacitor has the same capacitance, regardless of the voltage across its plates (and therefore regardless of the buildup of electric field). And an ideal inductor has the same inductance, regardless of the current through it (and therefore regardless of the buildup of magnetic field).

The reason for the opposition to the change in current or voltage is more subtle, and stems from the time derivative (or time integral, in an alternate formulation) that relates current to voltage, for those elements. And those derivatives (or integrals) stem from physics laws. That should be explained away from the introduction.

I also added "or voltage," on the first sentence, because a capacitor does not oppose to a change in current, but it does, to a change in voltage. Inductors oppose to a change in current. Capacitors oppose to a change in voltage. "Oppose to a change in x" means "don't allow a discontinuity in x, given finite voltages and currents."

Telaclavo (talk) 13:00, 24 March 2011 (UTC)

I sort of liked the previous formulation, regardless of impreciseness. I think that you should not remove it altogether, but rephrase it somehow to be more accurate in physical terms, and still accessible by a layperson. I'm not sure how to formulate that, though.

## Reactance and positive convention

"Although ${\displaystyle \scriptstyle {X_{L}}}$ and ${\displaystyle \scriptstyle {X_{C}}}$ are both positive by convention".

Is that a fair statement? Reactance is usually an absolute value which does not imply that it's usually "positive by convention".

ICE77 (talk) 00:08, 4 November 2015 (UTC)

I find the following even more troubling:
Both capacitive reactance ${\displaystyle \scriptstyle {X_{C}}}$ and inductive reactance ${\displaystyle \scriptstyle {X_{L}}}$ contribute to the total reactance ${\displaystyle \scriptstyle {X}}$ as follows.
${\displaystyle {X=X_{L}+X_{C}=\omega L-{\frac {1}{\omega C}}}}$
since XC is by definition (said convention) positive and equal to +1/ωC, the formula should read :${\displaystyle {X=X_{L}-X_{C}}}$. No such user (talk) 10:53, 4 November 2015 (UTC)

I agree with what you say and the statement implies that the circuit has both inductance and capacitance which is typical in tuned circuits. There will be some inductance in an RC circuit and some capacitance in an LC circuit but the statement is somewhat misleading. Maybe this should be discussed in a separate thread.

ICE77 (talk) 22:40, 8 November 2015 (UTC)

That was probably copied from a different textbook that defined Xc positive. So I've changed the sign to match the negative def, which was used elsewhere in the article. I've also deleted the "both positive by convention" part since the sign issue is now covered before. 5.12.38.28 (talk) 22:20, 29 November 2015 (UTC)

## Unit?

What is the SI unit of reactance? The unit of reactance (unit of imaginary impedance) should be the Doh. As reactive power has its own unit (VAR's Volt-Amperes Reactive) to distinguish it from real power (Watts), so should the proportionality unit have its own, too. As resistance (real impedance) has the unit Ohm, the reactance can have the unit Doh, to be understood as an abbreviation of Ohms Reactive, or Ohm-R's. The Doh could be a quasi-formal unit, much as Mho holds as the unit of conductivity (officially Siemens). It even gives rise to a mnemonic: "Inverse of Ohm is Mho, imaginary part is D'oh!" This could be known as the Annoyed Grunt relation. (The above single paragraph is intended as a work of parody though may still be subject to copyright.) Theotherjoebloggs (talk) 01:24, 21 January 2017 (UTC)

## another junk article about a phantom topic

They appear as fast as I an kill them. Sbalfour (talk) 03:51, 22 November 2017 (UTC)

Sbalfour: What the fuck are you talking about? This is a valid article about an important concept in physics, [2] which is, granted, somewhat related to other concepts, but deserves an article on its own. And it's been around since 2002. [3] No such user (talk) 10:29, 22 November 2017 (UTC)