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Phasor simplification

  1. Mar 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Can someone explain how wLT /_ theta

    could be written as wL /_ theta X T /_ (theta - 90)

    (w, L and T are all constants)


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 23, 2014 #2

    Simon Bridge

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    By wL /_ theta X T /_ (theta - 90)

    do you mean ##\omega L \angle\theta\times T\angle (\theta-90^\circ)## ?

    Following:
    http://en.wikiversity.org/wiki/Phasor

    You seem to be asking how we can say:$$\omega LT e^{i\theta} = \omega L e^{i\theta}Te^{i(\theta-\frac{\pi}{2})}$$ ... multiply it out and see what the phasor looks like.

    Where did you get this relation from?
     
  4. Mar 23, 2014 #3
    The book says that a sinusoidal voltage v(t)=Vcos(wt+ ##\theta##) can be defined by the phasor V=V##\angle \theta## where ##\theta## is the phase angle

    The actual relation is
    V=##wLI\angle \theta##
    and that it can be written in the form
    V=##(wL\angle\theta)## x ##I\angle(\theta-90)##

    so then that should mean ##wLIe^{(wt+\theta)}## can be written in the form
    ##wL e^{(wt+\theta)}Ie^{(wt+\theta-90)}##...?
     
  5. Mar 24, 2014 #4

    Simon Bridge

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    So ##v(t)=Re[Ye^{\omega t}]## so ##Y=Ve^{j\theta}## and you write it as ##Y=V\angle\theta##

    You should be able to translate the notation back into the cosine form to see what is happening.
    I have a feeling your book is trying to talk about the phase difference between the voltage across an inductor and the current through it.
     
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