Why 6.28 Ohms?

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?

 

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

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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

 

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.