1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the phasor representation of an equation

  1. Jan 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the phasors of the following time functions:

    (a) [tex]v(t)\,=\,3\,cos\left(\omega\,t\,-\,\frac{\pi}{3}\right)[/tex]

    (b) [tex]v(t)\,=\,12\,sin\left(\omega\,t\,+\,\frac{\pi}{4}\right)[/tex]

    (c) [tex]i(x,\,t)\,=\,2\,e^{-3\,x}\,sin\left(\omega\,t\,+\,\frac{\pi}{6}\right)[/tex]

    (d) [tex]i(t)\,=\,-2\,cos\left(\omega\,t\,+\,\frac{3\pi}{4}\right)[/tex]

    (e) [tex]i(t)\,=\,4\,sin\left(\omega\,t\,+\,\frac{\pi}{3}\right)\,+\,3\,cos\left(\omega\,t\,-\,\frac{\pi}{6}\right)[/tex]



    2. Relevant equations

    A short list of conversions from a larger table in the book. These are conversions from time domain sinusoidal functions on the left to cosine-reference phasor functions on the right.

    [tex]A\,cos\left(\omega\,t\,+\,\phi_0\right)\,\,\iff\,\,A\,e^{j\,\phi_0}[/tex]

    [tex]A\,sin\left(\omega\,t\,+\,\phi_0\right)\,\,\iff\,\,A\,e^{j\left(\phi_0\,-\,\frac{\pi}{2}\right)}[/tex]



    3. The attempt at a solution

    (a) [tex]3\,e^{-\frac{\pi}{3}\,j}[/tex]

    (b) [tex]12\,e^{j\,\left(\frac{\pi}{4}\,-\,\frac{\pi}{2}\right)}\,=\,12\,e^{-\frac{\pi}{4}\,j}[/tex]

    (c) [tex]2\,e^{-3\,x}\,e^{j\,\left(\frac{\pi}{6}\,-\,\frac{\pi}{2}\right)}\,=\,2\,e^{-3\,x}\,e^{-\frac{\pi}{3}\,j}\,=\,2\,e^{-3\,x\,-\,\frac{\pi}{3}\,j}[/tex]

    (d) [tex]-2\,e^{\frac{3\pi}{4}\,j}[/tex]

    (e) [tex]4\,e^{j\,\left(\frac{\pi}{3}\,-\,\frac{\pi}{2}\right)}\,+\,3\,e^{j\,\left(-\frac{\pi}{6}\right)}\,=\,7\,e^{j\,\left(-\frac{\pi}{6}\right)}[/tex]


    I have a question especially with (d), the answer is given as...

    [tex]-2\,e^{j\,\left(\frac{3\pi}{4}\right)}\,=\,-2\,e^{j\,\left(\frac{\pi}{4}\right)}\,=\,2\,e^{-j\,\left(\frac{\pi}{4}\right)}[/tex]

    I don't understand how they did the last two conversions in the given answer! Can someone please explain, and say whether the others are correct as well?

    Thanks:smile:
     
    Last edited: Jan 15, 2008
  2. jcsd
  3. Jan 16, 2008 #2
    what you have to know is just euler formula: exp(ix)=cos(x)+isin(x).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Find the phasor representation of an equation
Loading...