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Why 6.28 Ohms?

Discussion in 'Electronic Basics' started by Richard, Aug 4, 2004.

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  1. Richard

    Richard Guest

    XL = 2 Pi f L

    I've always wondered why if f = 1 and L = 1, the reactance is 6.28 Ohms.

    Why should the reactance equal 2 times the value of Pi?
  2. v = L.di/dt

    I = Ip.sin(2.pi.f.t)

    di/dt = Ip.2.pi.f.cos(2.pi.f.t)

    V = L.I.2.pi.f <ang(90)

    Kevin Aylward
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
  3. Because there are 2*pi radians in a cycle. If you deal in natural
    frequency (radians per second) instead of cycles per second, then
  4. Because we measure frequency in complete cycles per second. If we measured
    it in radians per second, we'd be OK.

    You generate a sine wave by turning something around in a circle and keeping
    track of the height. The radian (i.e., angle where distance traveled =
    radius) is, in physics, the proper way to measure this rotation. If you
    hold out for a complete cycle, you've gone 2*Pi radians.
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