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Converting phasor to time domain

  1. Dec 14, 2016 #1
    1. The problem statement, all variables and given/known data
    af912705e8.jpg

    2. Relevant equations


    3. The attempt at a solution

    I am extremely confused. Everywhere I go to look on how to convert phasors into time domain I get a different answer. I am trying to convert -j to the time domain. My notes says to find the Im(phasor). I have explained in the image above what my lecture notes say, what the question is and what my answer is.

    Here is the provided answer in the notes:
    cc0c5f1fb6.png

    Can anyone provide me with a universal method ?
     
  2. jcsd
  3. Dec 14, 2016 #2

    NascentOxygen

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    Staff: Mentor

    First, sketch the given phasor on the complex plane, with x-axis Real and y-axis Imaginary.
     
  4. Dec 15, 2016 #3
    764c31500c.jpg
     
  5. Dec 15, 2016 #4

    NascentOxygen

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    Staff: Mentor

    Right.

    There is a standard way to describe angles, on a graph. What angle would you associate with the line you have drawn? (For this angle, we need both magnitude and sign.)
     
    Last edited: Dec 16, 2016
  6. Dec 15, 2016 #5
    Measuring from the positive side of the X axis, I would say an angle of -90degrees.
     
  7. Dec 15, 2016 #6
    Angle should be -90 degrees I think. or - pi/2 rads
     
  8. Dec 15, 2016 #7

    rude man

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    Note that (1) the frequency (1000 Hz here) is not included in the phasor.
    (2) you have assumed 1V peak. More generally, a phasor is Vpkexp(jθ) ⇔ Vpksin(ωt + θ).
    But you have the phase right; -j = exp(-jπ/2). This is an identity. And -jπ/2 = -90 deg so the phase is -90 deg and the time expression is what you wrote above.
     
  9. Dec 16, 2016 #8

    NascentOxygen

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    Staff: Mentor

    Right. That's the angle/phase taken care of.

    What is the magnitude (i.e., length) of the line you drew on that graph?
     
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