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Confusion regarding to polar form representation of AC quantity

  1. Oct 17, 2009 #1
    I'm sure my question is very simple to most of u guys. But I have the following confusion.
    Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is
    v= -4 - 16 j .
    I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex plane.
    It's magnitude comes out to be 16.49
    For phase angle,
    [tex]\phi[/tex] = arctan (-16/-4) = 75.96◦
    To shift 75.96 degrees from 1st quadrant to 3rd quadrant I can approach in 2 ways. like
    [tex]\phi[/tex] = 75.96+ 180 = 255.96◦
    [tex]\phi[/tex] = 75.96- 180 = -104.04◦

    Thereby in polar form, v can be written like either v= 16.49[tex]\angle255.96[/tex] or, v= 16.49[tex]\angle-104.04[/tex].
    From mathematical point of view both the polar forms of v are ok.
    My question is that from electrical engineering viewpoint which polar form is to be written i.e. which phase angle is preferred in practice 255.96◦ or -104.04◦?
  2. jcsd
  3. Oct 17, 2009 #2


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    Staff: Mentor

    From the EE point of view (at least mine), you always picture phase starting at the real axis, and rotating counter-clockwise. So which answer would that give you?
  4. Oct 17, 2009 #3
    Well according to your statement, I have to prefer 255.96◦ as phase angle of the voltage source. Now the question rises is that phase angle preferred in EE practice?
    I had to ask it because so far in those books of EE that I've been studying, I have not seen any AC voltage/current in polar form whose phase angle is that much large like 255.96◦. By the way I'm now at the beginning of 2nd year of EE course. I haven't come across a lot of circuit analysis books in 1st year. Those books I was studying always have kept phase angle of any AC quantity in the interval of -180[tex]\leq[/tex][tex]\phi[/tex][tex]\leq[/tex]180. So, if I follow those books then I would have to select -104.04◦.

    This thing is confusing me. Mathematically both phase angles' terminating line indicates the same phasor. But I want to know in the practice of electrical engg. field which phase angle is preferred by the engineers?
  5. Oct 17, 2009 #4


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    Science Advisor

    When you are comparing the phase relationship of two waveforms you would normally compare them as 0 to +180 degrees and 0 to -180 degrees.

    For example, if a voltage waveform is to the right of the corresponding current in a circuit (as seen on an oscilloscope display), it is said that the current is "lagging " the voltage and this is given a negative angle depending how far out of alignment the two sinewaves are.

    See the diagram on the following page:
    http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ACCircuit/PhaseAngle.html [Broken]
    Last edited by a moderator: May 4, 2017
  6. Oct 17, 2009 #5
    Thank u so much vk6kro. Your link which explained phase angle in such a simple manner helped me a lot. Thank u again.
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