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Euler's identity for phasor

  1. Feb 28, 2006 #1
    for phasor, v = 20V e^(-j60) and i = 0.5A e^(-j30)
    how can i write them in v(t) and I(t) ??
    pls help


    thanx
     
  2. jcsd
  3. Feb 28, 2006 #2

    chroot

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    Use Euler's identity and take only the real part.

    [itex]e^{j \theta} = \cos \theta + j \sin \theta[/itex]

    - Warren
     
  4. Feb 28, 2006 #3
    i got v(t) = 20V cos (wt - 60 ) and i(t) = 0.5A cos(wt - 30)
    from here,how to find p(t)??
    a hint is given but i don't understand : coa A cos B = 1/2[cos(A+B) + cos(A-B)]
     
  5. Feb 28, 2006 #4

    chroot

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    Power is voltage * current, yes?

    Multiply your v(t) and i(t) to get p(t).

    The cosine identity was given to you to help you with the simplification.

    - Warren
     
  6. Feb 28, 2006 #5
    so what is A and B?? is it -60 and -30??
     
  7. Feb 28, 2006 #6

    chroot

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    A is the argument of the one cosine function; B is the argument of the other.

    When you multiply two cosine functions, with arguments A and B, you can use the identity you provided to simplify.

    In this case, A = wt - 60, and B = wt - 30.

    - Warren
     
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