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Phazor question

  1. Jul 17, 2009 #1
    for this signal
    [tex]
    I_s(t)=sin(t)
    [/tex]
    i have this equation
    [itex]
    I_L(1-CL+jCR+jcz)=I_s
    [/tex]
    then the next line is
    [tex]
    I_L(1-CL+jCR+jcz)=j
    [/tex]

    why they substitute j with I_s
     
  2. jcsd
  3. Jul 18, 2009 #2
    [tex]
    sin(t)=cos(\frac{\pi}{2}-t)=cos(t-\frac{\pi}{2})
    [/tex]
    the formula of the signal is
    [tex]
    Is=Acos(\omega t+\phi)
    [/tex]
    then we transform it to the phasor representation formula
    [tex]
    Is=Ae^{j\phi}
    [/tex]
    so we get
    [tex]
    Is=1e^{-j\frac{\pi}{2}}
    [/tex]
    and when we look at this expression as oilers formula we get
    the Is=-j

    so why its written Is=j
    ?
     
  4. Jul 19, 2009 #3

    CEL

    User Avatar

    [tex]e^{j\theta} = cos(\theta) + j sin(\theta)[/tex]
    for [tex]\theta = \frac{\pi}{2}[/tex]
    [tex]e^{j\frac{\pi}{2}} = cos(\frac{\pi}{2}) + j sin(\frac{\pi}{2}) = 0 + j.1 = j[/tex]
     
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