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.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)
AC resistance is the resistance of a conductor at high frequencies. It is due to Lenz's law.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
I don't know why you included the - sign. See the attachment.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
My question is - how is reactance derived?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
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.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
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?