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Inductors and Alternating Current and ELI the ICE man.

deltav sine

The rate of change throughout a sine wave cycle.

In the last posts about an Inductor, Through the Looking Glass – Duality -The Inductor” and “The Inductor – Part II” my goal was drive home the idea of duality:  It is very similar but sometimes a mirror image of capacitor so I was jokingly calling it the “Twisted Sister”.  Maybe a better analogy is “the codgety old man”, you can even call it Gary if you want.  The reason why is push on it (apply voltage) and it will flow current when it wants to and once it does finally get moving, it doesn’t want to stop.   Inductance can be thought of as the inertia of electrical.   Big inductors are like freight trains, and little inductors are like compact economy cars.   Both take a little extra to get them going, but the freight train takes a lot more.

A Series LR circuit,

A Series LR circuit,

The voltage across an inductor can be expressed as VL = L*ΔI.  When the current attempts to change all the time such as an AC sine wave, the inductor does not have time to cope with the change before the next one happens.  (Kind of like Gary trying to cope with changes in society. 🙁 ).   Imagine two people pushing on an automobile.  One person pushes on the front and one pushes on the back and they alternate on pushing.   If each one pushes for a long time the car may move forward and then backwards.  But, if it is only short pushes, the car may not move at all.

This is expressed in the formula for inductive reactance, XL:


XL of a 100mH inductor at various frequencies.

XL of a 100mH inductor at various frequencies.

The table to the left shows how the reactance changes with frequency. Remember a capacitor has less reactance at higher frequencies, but completely blocks flow at DC or 0 Hz.  The inductor flows better at DC and blocks more at higher frequencies.  (I guess we are back to the “twisted sister” analogy again .)

Please note that as we talk about the inductor here, we are still talking about an ideal inductor.   A real inductor has real wire, and sometimes a lot of wire, so it has some resistance built right in the inductor.   In the circuit diagram show above, the series resistance may a true external resistor, but it may also represent the resistance within the wires.  It is much easier to analyze and learn the problem by thinking of separate pure elements.   These are called “lumped” components, but a real device often has the elements distributed throughout each device.   (This is true for capacitors as well.)

On the first picture in this post, you will notice the voltage or pressure into our circuit will have the least amount of change during the peak periods.   Also the voltage will have been the same polarity through a complete 1/2 cycle between zero crossing points.   Since the inductor dislikes change, the current through the inductor would ideally lag the voltage by 90 degrees.   Again we will be dealing with our old friend the right triangle, and Pythagoras.  Before jumping into that I would like to give you a little memory device I picked up in the army to remember the lead/lag relationship.   (This is the only one I learned while in the army I would write on my blog :). )   ELI the ICE man.    Voltage (E) leads current (I) in an inductor (L), and current leads voltage in a capacitor (C).


1000 Hz sine wave input into the circuit in picture 2.

if the voltage source in our circuit was set at 1000 Hz, then our formula gives us an inductive reactance, XL, of 628.3 Ω.  The impedance in the total circuit is:
√(10002 + 628.32) or 1181Ω total impedance.  Usually this is called lagging impedance to differentiate it from a capacitor.

I will be taking about 3 posts to explain in detail how to calculate impedance in many circuits so this will be very quick and version of what will be coming in detail.   Since the inductor is lagging by 90 degrees we can find the exact lag of the total circuit is the sine(degrees lag) = XL / Z. In this case it comes out to be 32° lagging.

ciruit1 degs

One cycle of the 1000 Hz wave in the circuit shown above.

The total current in the circuit is 1v pk / 1181 or 0.847 mA.   The voltage across the resistor will be 1000 * 0,847 ma or 0.847 volts lagging the input voltage by 32°.  Kirchoff’s voltage law still applies so the voltage across the inductor is Vin – Vr at each moment giving the graph shown above.  This is shown a little better in the graph to the right.

The next electrical theory post will probably be some about real inductors and some stories about my experience with some in both DC and AC circuits.

Thank you for supporting my blog I hope I have made it worth your time.

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3 comments to Inductors and Alternating Current and ELI the ICE man.

  • This is the only way to understand Voltage and Current in an inductor. Inductors and capacitors are tuned circuits…the LOOP antenna is also a TUNED CURCUIT.
    Application of the ELI and ICE principles will render you the perfect antenna. This is a requirement for the Element IV Amateur Class License.

    Now get started, build a LOOP antenna and apply what you have learned here.
    Learn this, understand this and you will command the principles of AC/RF.

    Thanks, to the author.

    • Gary

      Sorry I did not approve this for so long…. I have been up to my neck in stuff and have been neglecting this site. I am very gald this was helpful to you. Thanks for the complement. And BTW… I may play with some of those loop antennas pretty soon… but it will be some crazy stuff I won’t publish… it is far out there stuff… even for me.

      Gary Fox

  • […] Inductors and Alternating Current and ELI the ICE man. […]

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