Inductive Reactance

[Ratchit]

codan,

I think the problem is that no matter were you look on the internet people write differing things about the same subject matter so it's difficult from my perspective--still being a kid --- to try & make heads or tails out of it all---very confusing.
Just when you think you have a handle on something, somebody writes or you read something to the contrary.

This is where the mathematics comes into play & can sort the Hearsay from the reality, the only problem is then some people talk in basic--very very basic math language like myself & others talk in Algebra or whatever it is & then it becomes confusing all over again & it's like trying to Lip Read Chickens from my side of things!.

Could the answers or debates be kept in basic math language so people with less brain cells like myself can have a chance at answering or understanding things?

Please don't stop the debate but just in English guys?

I have no idea what you are trying to say or to what you are referring. I thought we were communicating in English, and describing physical relationships by mathematics. You have to be more specific in describing your point of complaint.

Ratch

Hopelessly Pedantic

 

[MrAl]

Hi everybody,

I am stumbling on a question i have to answer, i have tried to figure out what the answer is "not" rather than what the correct answer is so you can see i have made a descent attempt at answering this myself, which i have.
My argument for each one is listed below each supposed answer, obviously i am not getting something right??.

The Question is: a, b, c, or d

Inductive Reactance is measured in Ohms because it:


a: Absorbs Power
(No, because Inductive Reactance absorbs Energy & returns Energy)?

b: is the ratio of the emf of self induction of an AC circuit to the current
( No, emf is the potential difference across a source of electricity when no current is flowing)

c: is the equivalent resistance of an AC circuit
(No Resistance dissipates power, Inductive Reactance absorbs Energy & returns Energy)


d: is the Admittance of an AC circuit
(No, Admittance is a measure of the current admitted, while Reactance is the measure of how much a circuit reacts against change in current over time?)

As you can see i am having an issue?

Thank You

Hi there,


Sometimes it is simpler just to adopt something new instead of trying to understand from the standpoint of other things you already know.

In any case, another way of looking at it is that reactance is "out of phase resistance".
A resistance that is out of phase with a true resistance (like an inductor in series with a resistor) will have to be handled differently than two 'regular' resistors...

Two resistors in series:
I=V/(R1+R2)

Resistor in series with inductor:
I=V/sqrt(R^2+(w*L)^2) or I=V/sqrt(R^2+X^2)

where we note that the square of the reactance had to be added to the square of the resistance, then we had to take the square root to get the right value whereas with the two resistors we just had to add them together.

 

[ljcox]

ljCox,

X = is correct. cot is removed in order to leave the magnitude is ωL."
The cot can have a magnitude of ∞. The cos at most is 1. How can you justify "removing" cot? That's what you did above in your "V = I*ωL cos ωt --> Vmax = ωL*Imax, so ωL is the inductive reactance" statement. This is because I*ωL is the magnitude of I*ωL cos ωt. Note, this is not my statement, it came from the first attachment in one of my arevious posts.

Yes, but what is the magnitude of ωL*cot ωt? It is infinity, which does not make sense for finding the reactance. The magnitude of I*ωL cos ωt is I*ωL , because the maximum of cos ωt is 1 .

As I said, you don't need to integrate. It can be done as they did in the book with differentiation. That's where the cot term came from.

If you want to find the reactance by the impedance method, then Z(s) = V(s)/I(s), take the LaPlace transform L{V/I} = L{I(t)*Lω*cos(ωt)/I(t)*sin(ωt)} = L{Lω*cot(ωt)} = jLω for a sinusoidal function. The LaPlace transform does the integration. See Electrical impedance - Wikipedia, the free encyclopedia for a derivation using Euler's formula. Euler's formula does the differentiating this time.

But on the page I scanned, they come to the same equation as the network analysis books do, ie. it leads to the same result and is easier.

E = iR + L di/dt.

Haliday is only doing transient analysis here, not steady state AC analysis. So your reference is not valid.


So I would say that is why the network anlysis books don't bother with the - sign.

As long as one knows that the induced voltage is counter to the applied voltage, and writes the equations accordingly, things should work out OK.

Ratch
Hopelessly Pedantic

The above is becoming confusing.
1. You don't appear to have read what I said about ωL cot ωt

The book states that you take the magnitude. ie. ωL
Remember that the magnitude of A sin x is A.

However, as I said originally, I'm not completely happy with this as a proof.

2. It makes no difference whether you are doing a steady state or transient analysis.

It is easier to use L di/dt rather than -L di/dt. See attachment.

The Wikipedia reference you posted did not include the - sign except for the rate of change of flux.

3. I normally use Laplace to solve DEs as it is much easier. So I'll explore what you suggested later.

 

[codan]

Hi Everyone,

MrAl,
Yes i see what you mean with looking at things from a different point of view, thanks for that.

Ratchit,

No there's no complaint & sorry if it sounded like that, i was refering to the math notation like
≈∫∞κωσρξλ∑ψηζεδγτΨΣ≥≤Γ§ΛΔφ it's more a lack of knowledge from my side & not knowing what these symbols are or what they stand for or the values of such?
About the only one i have an idea of is ω which i think is angular velocity?
I am trying to educate myself from the internet as i have very little to no schooling to date--that's life i guess.

Is there a site somewhere that explains these symbols so i can get a better understanding of these?

Thank You

 

[ljcox]

No there's no complaint & sorry if it sounded like that, i was refering to the math notation like
≈∫∞κωσρξλ∑ψηζεδγτΨΣ≥≤Γ§ΛΔφ it's more a lack of knowledge from my side & not knowing what these symbols are or what they stand for or the values of such?
About the only one i have an idea of is ω which i think is angular velocity?

In the maths associated with network analysis, ω is the "angular frequency" so ωt = 2 Pi f t. (I can't find Pi in the symbols)
Thank You you're welcome

Attached is a proof of XL that I'm happy with.

 

[Ratchit]

ljcox,

1. You don't appear to have read what I said about ωL cot ωt
Sure I have. In post #14 of this thread you wrote, "Hence X = v/i = ωL cos ωt / sin ωt". I disagreed with X = v/i = ωL*cot( ωt). I said that X(s) = ωL*LaPlace{cot( ωt)} or X = jωL .

2. It makes no difference whether you are doing a steady state or transient analysis.

No need to introduce R into the equation as Haliday and Resnik do if you are only interested in inductive reactance. They do it because they are writing about transient analysis.

It is easier to use L di/dt rather than -L di/dt. See attachment.

As long as the voltage polarities agree with Kirchoff's law, then everything will work out correctly.

The Wikipedia reference you posted did not include the - sign except for the rate of change of flux.

Same answer as above.

3. I normally use Laplace to solve DEs as it is much easier. So I'll explore what you suggested later.

OK.

Ratch
Hopelessly Pedantic

 

[mel8030]

Is there a site somewhere that explains these symbols so i can get a better understanding of these?

Thank You

hello codan
What is your math level? algebra,trig or calc?
I don't think these post are helping you much, except for MrAls post .
In my case, it took much exposure to the concepts in different math, science and electronic classes before it finally sunk in.

Does this link help?


There is also a free online electronics course put out by the Navy.
this is the link for module 2 :
**broken link removed**

There are some good lectures on Youtube, from basic to advanced. The video with the guy in bright green shirt are good
https://www.youtube.com/watch?v=a2cHVII7lFU&feature=related

 

[ljcox]

Codan,
The first 2 attachments by mel8030 above look good. I did not look at the third.

However, a word of warning about the second attachment. It uses the electron current flow convention, ie. it states that current flows from - to + whereas the first uses the conventional flow convention ie. + to -

I first learnt the electron convention but when I became an engineering student (several years after leaving school) the uni used the conventional flow convention.

Certainly, electrons flow from - to +, but electrons are not the only charge carriers.

For example:- Protons, positive ions, positrons, etc. all flow from + to -.

I eventually realised that the conventional flow (ie. + to -) is better for engineering calculations as it fits in better with the maths.

 

[Ratchit]

ljcox,

Right on! It is counter-intuitive, but in calculations, using the charge carrier polarity to determine direction of charge flow can really confuse a newbie. That is because charge carriers can be of different polarities even within the same series circuit, as in a PN junction or a electrochemical reaction, where +ions and electrons can exist and move in the same liquid at the same time.

To keep everything straight, for calculation purposes, a convention was developed which stipulates that charge carriers are positive, and flow out of the positive terminal of a voltage source. If the current calculation result is a negative value, then the known direction of the positive charge carriers is opposite to what the assumed direction was. If it is really necessary to know the direction of the actual charge carriers, it can be reasoned as follows. If the charge carriers are positive, then the answer is as given. If the charge carriers are negative as electrons are, then remember that a flow of positive charges is equivalent to a flow of negative charges in the opposite direction. So for calculations, we don't worry about the polarity of the charge carriers or their real direction of movement. That is figured out after the calculation is finished, if it is really necessary to do so.

It is easily observed that electrical equipment manufacturers use the conventional method to mark their parts and equipment. Notice the arrow on a diode assumes a positive charge carrier. A ammeter is marked such that positive charges, if they existed in a wire, would deflect the meter.

Ratch
Hopelessly Pedantic

 

[ljcox]

Well said, Ratch.

Codan, the other point I forgot to mention is that in the second attachment, the "Left Hand Rule" applies to electron flow. For conventional flow, we use the "Right Hand Rule"

It is known as Fleming's Right Hand Rule.

 

[codan]

Hi Everyone,

I would just like to say thanks for the continued support on questions like this, although i don't understand some of the math what i do understand is i had better get my finger out & learn some more.
The attachments etc really help a lot.



mel8030

Thanks for the links to the sites they are helpful, i found a lot of Lectures on YouTube as mentioned but the download speed i have becomes very slow when i use my limit which is normaly the first day of the new month & i feel like throwing the computer out the window ha.
I'm sure you know the feeling, just when you think you have found something of real value it takes ten hours to try to dowload it & then the link gets broken because it is taking to long.

Like everyone knows Technology is a wonderful thing, but only if you can afford it.

Thanks everyone.

 

[slimabidi]

Thanks very much for the replies