Confusion regarding to polar form representation of AC quantity

  • Thread starter mdnazmulh
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Main Question or Discussion Point

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◦
or,
[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◦?
 

Answers and Replies

  • #2
berkeman
Mentor
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6,527
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◦
or,
[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◦?
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?
 
  • #3
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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?
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?
 
  • #4
vk6kro
Science Advisor
4,081
40
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]
 
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  • #5
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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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