Reactance of Inductive Circuit

Solve for L: L=X/(2πf). Is this a trick question?

I don't think you can do that, you have 2 different things....

"An inductor of L(in Henry) inductance offers reactance Xl (in Ohms) given by
Xl = 2 ∏f*L.
called inductive reactance.
Where f is the frequency of the voltage applied.
(reactance and resistance aren't the same)

At an AC frequency, henries produce a reactance which is measured in ohms, but it still is a different quantity than resistance ohms."

http://forum.allaboutcircuits.com/threads/converting-henries-to-ohms.12995/

I would think Z (impedance) might be a better description to use than resistance in this case. Yes?

Well impedance(Z) is defined as the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of ohmic resistance and reactance...So this is the total he's looking for...

So that means that you can combine the resistance value with the inductive reactance value to obtain the total resistance value of the circuit ?

"An object of uniform cross section has a resistance proportional to its resistivity and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for superconductors, which have a resistance of zero.

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constant (although they can depend on other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called "Ohmic" materials.

In other cases, such as a diode or battery, V and I are not directly proportional, or in other words the I-V curve is not a straight line through the origin, and Ohm's law does not hold. In this case, resistance and conductance are less useful concepts, and more difficult to define. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance",^[1][2] as it corresponds to the inverse slope of a chord between the origin and an I-V curve. In other situations, the derivative may be most useful; this is called the "differential resistance"."

If you measured the 3.77 ohms with an ohmmeter, that's the resistance, not the inductive reactance. A real coil (as opposed to the fictional type in homework problems) will have both inductive reactance and resistance. The resistance will be constant whether it's DC or AC of any frequency. The inductive reactance, Xl=2πfL, will be zero at DC and will be proportional to the AC frequency. The total reactance, Xt of the coil is the vector sum of the resistance and the inductive reactance, where the two vectors will be at 90 degrees. So by Pythagorean's theorem:

Xt=sqrt(R^2 + Xl^2) = sqrt(R^2 + (2πfL)^2)

In the original post, Tony wrote "Xl=3.77 ohm", so it was a given, not measured with an ohmmeter.

To me, it would be much clearer if it were written "X_L=3.77 Ohms" or "X_L=3.77Ω". CR4 does have the subscript and superscript capabilities in the toolbar. It IS worth the trouble to use them!

In any case, it should be read "Ex sub Ell", which means "Inductive reactance". In that case, your original post was correct, if written "L=X_L/(2∏f)", [to my aging eyes, π (lower case Pi) is virtually indistinguishable from "n" (lower case N), so I use capital Pi] so

L=3.77/(2*3.14*60)=1.00 Henry.

"The total reactance, Xt of the coil..." should be: "The total impedance, X of the coil...".

I understand that you intended the "t" to indicate "total", but that is superfluous, since as you indicate, impedance is the vector sum of resistance and reactance, at 90° from each other. Reactance is either inductive or capacitive, and does NOT include resistance.

Is this a "homework problem"? I'll take the definition that a "homework problem" is one that is assigned by a teacher or instructor to be done at home. Since Tony is pretty clearly trying to learn this without the assistance of a teacher (look at his previous posts), I choose the attitude that it is not homework, and commend him for his effort!

Excellent post!

Learning without the assistance of a teacher.

Yes, most of the time I try to learn this way, its not that I don't like or need teachers, its that it's difficult to find a teacher that is interested in learning a student rather than teaching to one.

I have discovered that there are 3 types of teachers:

1. In it for the money and the status. This type will say something once and expect the student to instantly memorize the material, when the student asks for an explanation, the teacher will say something like " get it, got it, good.

2. Has a picture of Einstein on the wall in their office and thinks that every formula for everything must be memorized and those that can't must be retarded and deserve to be publicly ridiculed and flogged.

3. Those that like what they are doing and wake up every morning eager to pass on their knowledge because they know that no man is an island and it takes many people with different talents to create a community.

There are plenty of 1&2, but few of 3.

I remember in school that there was always the big push to memorize everything and if you didn't or couldn't you were either a cheater or a moron.

When I got into the working world, I noticed that every person, doctor, engineer, lawyer,carpenter etc had a library of reference manuals in their office or workshop.

I felt happiest knowing that I was in the company of cheaters and morons.

"...it takes many people with different talents to create a community."

Incredibly true! If we all wanted to do the same thing, then nothing would get done!

Unfortunately, it was a number of years after I retired from my teaching career that I came to anything approaching a full realization of those differences. This is especially true regarding the processes that occur in different human brains while attempting to achieve similar results. I know that I was a very good teacher for at least a few of my students, but I'm just as sure that I was not a good teacher for some who, for whatever reason, could not follow my thought processes.

A real inductor is a combination of a resistor and ideal inductor in series. All about circuits has a good explanation about this.

Which "book" are you referring to? Knowing the inductance in Henries does not tell you anything about the Inductive Reactance in Ohms until you factor in the frequency. Similarly, knowing the Inductive Reactance in Ohms tells you nothing about the inductor's Impedance in Ohms until you factor in the inductor's resistance as well.

The formula for the Impedance (Z) Ohms of an inductor is Z = R + jXl or Z = Sqrt (R² + X²) at an angle of arctangent(Xl/R), so if all you know is the magnitude of Z without the angle it's impossible to determine the value of the resistance and inductance. For example, your inductor could be a helix made from a length of 2" bus bar, not much resistance but a lot of distributed inductance; or it could be a length of #36 wire, not much inductance but a lot of resistance.

The only way to determine what's in the black box is to step the frequency from DC up and record the current and voltage. Your DC measurement will give you R, and at 60Hz you'll have Z which you can now plug into the above formulas to calculate Xl (after some algebra); there are other ways depending upon the test instruments at hand.

You cannot calculate the inductance of the coil given just its resistance.

The inductance will depend on a number of factors which have little to do with measured Ohmic resistance.

For instance :-

1. Core material - An air core will have lower inductance than will a ferrous core for the same coil parameters.

2. The number of turns of wire in the coil - A coil with say 200 turns of wire of 5 Ohms resistance will have greater inductance than will a coil of 100 turns wound with finer wire also measuring 5 Ohms.

3. Coil length - The longer the coil, the lower the inductance. The longer magnetic circuit creates greater opposition to the magnetic flux, and so it is weaker.

4. Coil diameter - The greater the diameter the greater the inductance. Bigger diameter creates a larger coil cross section area which results in lower flux opposition and higher inductance.

L = xl / 2 pi F

That's essentially what Rixter said in his original post #1, although since you omitted the parentheses, yours is technically wrong.