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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

    http://www.anasoft.co.uk
    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
    XL=f*L
     
  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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