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NNTP-Posting-Date: Sun, 30 Jun 2024 13:05:40 +0000
From: john larkin <jlarkin_highland_tech>
Newsgroups: sci.electronics.design
Subject: Re: Omega
Date: Sun, 30 Jun 2024 06:05:41 -0700
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On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com>
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...

2 * pi.

If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.

A capacitor current depends on the rate of change of the voltage. 

  I = CV/T

A 1 volt peak 1 Hz  sine wave has its max rate of change at the zero
crossing, and that rate is 2pi volts/second. So 1 farad driven with a
1 Hz 1 volt peak sine wave has a peak current of 2pi amps.

You can Spice all that to get a feel for things.