Re: Omega

On 30/06/2024 10:13 pm, Cursitor Doom wrote:

On Sun, 30 Jun 2024 11:57:21 +0100, piglet <erichpwagner@hotmail.com>
wrote:
 

On 30/06/2024 8:44 am, Cursitor Doom wrote:

Gentlemen,
>
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF.  BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...

>
>
Watch this (your question is addressed at 2:07)
>
<https://youtu.be/Vv2W5vJFqFo?si=eX3ZONUzzpNNxGtg>

 Thanks, Erich. I did wonder if radians had something to do with it.
However, knowing that 2 pi radians = 360 degrees or a full wavelength
doesn't help me understand why this figure multiplied by the frequency
multiplied by the inductance gives us the reactance of a coil. Small
omega therefore equals one second's worth of signal and I don't get
how multipying that by the inductance amounts to the reactance!

You'd probably have to master Maxwell's equations before you got it. My second year university math course was all about differential equations and how to integrate them. It never made a great deal of sense to me, but by the time I'd got through it, the differential equation involved in electronics were familiar enough that I didn't have any trouble understanding that radians per second made sense, and it didn't prompt any bursts of curiosity.
That was the point in my career where I noticed for myself that magnetism made sense as the relativistic consequence of the forces between moving electric charges, and got told that Wheeler was writing a textbook around that idea.
https://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory
He'd published it a decade earlier.
If you don't get the right education, some idea can be inaccessible.
--
Bill Sloman, Sydney
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