Re: Omega

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.