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Inductive Reactance

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codan

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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
 
What a confusing question?

It certainly isn't a or c.

Admittance is the inverse of impedance..

I bet b, the self induced EMF in the inductor will counteract the applied EMF and therefore the current - impedance.
 
What a silly*/strange/odd question.

My first reaction was answer (c)
This is certainly wrong, but, reactance is sometimed likend to "AC resistance" in over simplified explanations.

Thinking a bit more, the answer (b) seems to be most correct.
EMF vs PD, I think your are comparing this too much with a loaded battery/generator, which an inductor with an AC current flowing through it is not.

So as (a) and (d) are just plain wrong, the correct answer is (d).
(On edit - Isn't it amazing, when you see something several hours after you have written it, the mistakes just jump out at you! THE CORRECT ANSWER IS (b), I had already said that (d) was wrong!)

JimB

* On refelection, maybe not so silly.
It got you thinking, and thinking to gain understanding is an important part of learning.
 
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The Question is: a, b, c, or d

Inductive Reactance is measured in Ohms because it:

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)
You are correct that, in the strict sense of the word, emf only applies to sources. But I believe your instructor is loosely using the term to indicate the voltage across any element, i.e. emf is equated with voltage. If you assume that, then "b" is the correct answer.
 
Hi everybody,

Thanks very much for the replies--much appreciated.

If you can bare with me on this i still have some questions as i don't like to write down an answer until i get a grip on what i am trying to understand regarding it.

I still have some issues--of course, as i don't fully understand.

There's no doubt i will confuse myself trying to piece this together so belt me over the head at any time!

For DC the maximum current flowing through a coil -Inductor- is limited only by the resistive element of the coils windings in Ohms, and which in turn is determined by the ratio of voltage over current, V/R, (Ohms Law).

For an AC circuit, the opposition to current flow through the coils windings not only depends upon the inductance of the coil but also the frequency of the AC waveform.
The opposition to current flowing through a coil in an AC circuit is determined by the AC resistance of the circuit.
But resistance is always associated with DC circuits so to distinguish DC resistance from AC resistance which is also known as Impedance, the term Reactance is used.
Like resistance, reactance is also measured in Ohm's but is given the symbol X to distinguish it from a purely resistive value and as the component is an inductor, the reactance of an inductor is called Inductive Reactance.

The self-induced emf is directly proportional to the rate of change of the current through the coil which creates a back emf resisting current flow.

So with all that being the case could not the Answer to the original question be either (b) or (c)?

Just to try to lean one way or another the equation for Inductive Reactance is:

XL =2pi f L


L of course is Inductance & is the resistance of a circuit element to changes in current.

So seeing that the equation for Inductive Reactance has a resistance value associated with it is it fair enough to assume that Answer (c) may be considered?
If that makes sense?
Thank You
 
Resistance invariably refers to the resistive element. If you add reactive elements then it is referred to as impedance not resistance. On that basis I would say (c) is not an alternate answer.
 
As I said earlier in the thread reactance is sometimes said to be "AC resistance" to give a simplified explanation. This is however dangerously wrong if you want to have a greater understanding.

When AC flows through a resistor, the current and the voltage are in phase.

When AC flows through a capacitor, the current leads the voltage by 90 degrees.

When AC flows through an inductor, the current lags the voltage by 90 degrees.

The phase difference between voltage and current is what makes the fundamental difference between resistance and reactance.
Resistance dissipates power as heat, reactance does not dissipate power.

However, there is a concept of AC resistance, as the frequency is increased the losses in an inductor or a capacitor will increase.
These losses are attributed to resistance, not a resistance you can measure with DC, but it is still there as an AC resistance dissipating power.

So, back to the original question, no (c) is not a correct answer in this case.

JimB
 
Thanks again for the replies,

The replies have helped me a lot in trying to understand Inductive Reactance.

JimB your explanation is very helpful.

Am i correct in saying that Inductive Reactance is an "opposition" to current flow & not resistance?

Thank You
 
Yes ...................
 
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Codan,

There's no doubt i will confuse myself trying to piece this together so belt me over the head at any time!

OK. You asked for it.

For DC the maximum current flowing through a coil -Inductor- is limited only by the resistive element of the coils windings in Ohms, and which in turn is determined by the ratio of voltage over current, V/R, (Ohms Law).

So far, so good. Except that V=IR should be called the resistance formula and Z=IR the impedance formula, not Ohm's law. Ohm's law rightly refers to the linearity of the V vs I curve which is not of interest here. See **broken link removed** and **broken link removed** .

For an AC circuit, the opposition to current flow through the coils windings not only depends upon the inductance of the coil but also the frequency of the AC waveform.

You really mean charge flow, not "current flow". Current is charge flow, so saying current flow is like saying "charge flow flow", which is redundant and ridiculous. A better phrase is "current exists" or "current existence".

The opposition to current flowing through a coil in an AC circuit is determined by the AC resistance of the circuit.
But resistance is always associated with DC circuits so to distinguish DC resistance from AC resistance which is also known as Impedance, the term Reactance is used.
Like resistance, reactance is also measured in Ohm's but is given the symbol X to distinguish it from a purely resistive value and as the component is an inductor, the reactance of an inductor is called Inductive Reactance.

You are a little confused here. There is no difference between AC and DC resistance. Resistance is the same no matter what the frequency. Resistance and reactance both work to restrict current caused by a applied voltage. They do it by different ways, however. Resistance restricts by dissipating the energy of the circuit as heat, so that less energy is available to move the charge carriers through the resistive element. Reactance works by causing a back-voltage which lowers the current in the reactive element, but it does not dissipate any energy. Impedance is combination of resistance and reactance.

The self-induced emf is directly proportional to the rate of change of the current through the coil which creates a back emf resisting current flow.
Yes, it is the counter-voltage that reduces the current, not the dissipation of the circuit energy.

Ratch

Hopelessly Pedantic
 
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Codan,

But resistance is always associated with DC circuits so to distinguish DC resistance from AC resistance which is also known as Impedance, the term Reactance is used. Not true
Like resistance, reactance is also measured in Ohm's but is given the symbol X to distinguish it from a purely resistive value and as the component is an inductor, the reactance of an inductor is called Inductive Reactance.

There is no difference between AC and DC resistance. Resistance is the same no matter what the frequency. Not true
AC resistance is the resistance of a conductor at high frequencies. It is due to Lenz's law.

At high frequencies, the current only flows in the "skin" of the conductor ( it is sometimes called the "skin effect"). Thus the AC resistance is greater than the DC resistance since DC currents flow inside the conductor, not just in the skin.

A friend of mine once built a VHF transmitter using copper tube as the inductance for the tuned circuit. He tinned it with solder to "make it look nice" and found the Q of the tuned circuit was much lower than it had been before tinning. This is because the solder has a much lower conductivity than copper, and due to the "skin effect", the AC currents were flowing in the solder rather than the copper.

The reactance of an inductor is the voltage across it divided by the current through it. But it is more complicated than DC since the current and voltage are not in phase.

If the inductance has no resistance (ie. an ideal one) then Z = X. But if the inductor has resistance, then Z = R + jX (for sinusoidal sources only, it is more complex for non sinusoids). Where j = the square root of -1.
 
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The answer is b. The EMF that is being referred to is the "back EMF" of the inductance.

The "Ohm's Law" of inductance is
V = L di/dt. (This assumes a perfect inductance)

i = the instantaneous current through the inductance, V is the instantanous voltage across it. t = time.
This is general and applies to any situation regardless of whether the source is sinusoidal, step, ramp or any other function.

Compare with the "Ohm's Law" of capacitance
i = C dv/dt.

i = current through the cap, v is the voltage across it. t = time.
 
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ljcox,

The first part of the quote you made in your answer to me was not mine. It was Codan's.

Yes, high frequency can restrict the conduction path of a conductor, but if the same geometric shape is used for DC, such as a tube, then the resistance at DC should be the same as for the high frequency.

V = - L di/dt is the induced voltage. It has to be transposed and integrated to get inductive reactance = 2*pi*f*L . Same for capacitive reactance.

Ratch

Hopeless Pedantic
 
ljcox,

The first part of the quote you made in your answer to me was not mine. It was Codan's. I'm puzzled by this as it was quoted from your post.

Yes, high frequency can restrict the conduction path of a conductor, but if the same geometric shape is used for DC, such as a tube, then the resistance at DC should be the same as for the high frequency.
I disagree. The "skin effect" would apply in this case also.

V = - L di/dt is the induced voltage. It has to be transposed and integrated to get inductive reactance = 2*pi*f*L . Same for capacitive reactance. See below

Ratch

Hopeless Pedantic
I don't know why you included the - sign. See the attachment.

You can derive X by either integration or differentiation as in the attachment.

Thus, using their Table 3-1 if i = I sin ωt, then v = ωL cos ωt.

Hence X = v/i = ωL cos ωt / sin ωt

I was puzzled by the cos & sin terms but on the next page of the book they state "The magnitude of the impedance is ωL"

I can see what they mean, but don't fully understand it.

Can anyone help please?
 

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ljcox,

"The first part of the quote you made in your answer to me was not mine. It was Codan's. I'm puzzled by this as it was quoted from your post."

That was because I quoted Codan in my answer. See the message before that.

"Yes, high frequency can restrict the conduction path of a conductor, but if the same geometric shape is used for DC, such as a tube, then the resistance at DC should be the same as for the high frequency.
I disagree. The "skin effect" would apply in this case also.

The skin effect effectively makes the geometry of the conductor into a tube. The thickness of the tube wall will vary with the frequency.

"I don't know why you included the - sign. See the attachment."

The minus sign represents a back voltage opposite to what is driving the current through the inductor. Just about every physics book represents it that way. I don't know why your attachment does not.

"You can derive X by either integration or differentiation as in the attachment."

Yes.

"Thus, using their Table 3-1 if i = I sin ωt, then v = ωL cos ωt.

Hence X = v/i = ωL cos ωt / sin ωt"

So X = ωL*cot ωt ? I don't think so.

V = I*ωL cos ωt --> Vmax = ωL*Imax, so ωL is the inductive reactance.

I was puzzled by the cos & sin terms but on the next page of the book they state "The magnitude of the impedance is ωL"

I can see what they mean, but don't fully understand it.

Can anyone help please?


Sure, |Z| = √(X^2+R^2) . So if no R is present, |Z| = X . Ratch
 
The skin effect effectively makes the geometry of the conductor into a tube. The thickness of the tube wall will vary with the frequency. Yes, I see what you mean.

"I don't know why you included the - sign. See the attachment."

The minus sign represents a back voltage opposite to what is driving the current through the inductor. Just about every physics book represents it that way. I don't know why your attachment does not. I have not seen it with a - sign. My attachments are from network analysis books. See the new attachment - copied from another book

"You can derive X by either integration or differentiation as in the attachment."

Yes.

"Thus, using their Table 3-1 if i = I sin ωt, then v = ωL cos ωt.

Hence X = v/i = ωL cos ωt / sin ωt"

So X = ωL*cot ωt ? I don't think so. You have missed the point below about magnitude.

V = I*ωL cos ωt --> Vmax = ωL*Imax, so ωL is the inductive reactance.

I was puzzled by the cos & sin terms but on the next page of the book they state "The magnitude of the impedance is ωL"

I can see what they mean, but don't fully understand it.

Can anyone help please?


Sure, |Z| = √(X^2+R^2) . So if no R is present, |Z| = X . Obviously - see below Ratch
My question is - how is reactance derived?
X = ωL*cot ωt is correct. cot is removed in order to leave the magnitude is ωL.

I'm curious to know if there is another derivation.
 

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ljcox,

"The minus sign represents a back voltage opposite to what is driving the current through the inductor. Just about every physics book represents it that way. I don't know why your attachment does not. I have not seen it with a - sign. My attachments are from network analysis books. See the new attachment - copied from another book"

Did you check a physics book?

"So X = ωL*cot ωt ? I don't think so. You have missed the point below about magnitude.

V = I*ωL cos ωt --> Vmax = ωL*Imax, so ωL is the inductive reactance."

Not so, see the line above this one where I equate the voltage and current maximum or magnitude to each other. A lot of physics books do it this way.

"My question is - how is reactance derived?"
I just did it.

"X = ωL*cot ωt 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?

"I'm curious to know if there is another derivation. "

Sure, it can be set up as a differential equation and integrated. See a good physics book to see how.

Ratch
Hopelessly Pedantic
 
ljcox,

"The minus sign represents a back voltage opposite to what is driving the current through the inductor. Just about every physics book represents it that way. I don't know why your attachment does not. I have not seen it with a - sign. My attachments are from network analysis books. See the new attachment - copied from another book"

Did you check a physics book? Yes, see attachment and comments below.

"So X = ωL*cot ωt ? I don't think so. You have missed the point below about magnitude.

V = I*ωL cos ωt --> Vmax = ωL*Imax, so ωL is the inductive reactance." Where did this come from?

Not so, see the line above this one where I equate the voltage and current maximum or magnitude to each other. A lot of physics books do it this way.

"My question is - how is reactance derived?"
I just did it.

"X = ωL*cot ωt 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.

"I'm curious to know if there is another derivation. "

Sure, it can be set up as a differential equation and integrated. See a good physics book to see how.
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.

Ratch
Hopelessly Pedantic
The Physics book states that V = -L di/dt as you said, but that is to show that the EMF opposes the change in current according to Lenz's Law.

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.

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

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Hi Everyone,

Thanks for the comments once again.

It's good to see a healthy debate about subjects as we can all learn from them.
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?

ljcox:
I see your an Aussie as well--good stuff!

I have attached a Derivation of the Inductive Reactance equation although it's not in Algebra if that's the notation your formula's were in, it may be of help?
Sorry about the four small attachments, i don't think there in order either looking from my end?

I just posted this to late & now i see that the Algebra is gone on another post.

Thank You
 

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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
 
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