# Confusion regarding to polar form representation of AC quantity

## 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,
$$\phi$$ = arctan (-16/-4) = 75.96◦
To shift 75.96 degrees from 1st quadrant to 3rd quadrant I can approach in 2 ways. like
$$\phi$$ = 75.96+ 180 = 255.96◦
or,
$$\phi$$ = 75.96- 180 = -104.04◦

Thereby in polar form, v can be written like either v= 16.49$$\angle255.96$$ or, v= 16.49$$\angle-104.04$$.
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◦?

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berkeman
Mentor
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,
$$\phi$$ = arctan (-16/-4) = 75.96◦
To shift 75.96 degrees from 1st quadrant to 3rd quadrant I can approach in 2 ways. like
$$\phi$$ = 75.96+ 180 = 255.96◦
or,
$$\phi$$ = 75.96- 180 = -104.04◦

Thereby in polar form, v can be written like either v= 16.49$$\angle255.96$$ or, v= 16.49$$\angle-104.04$$.
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?

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$$\leq$$$$\phi$$$$\leq$$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?

vk6kro
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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Thank u so much vk6kro. Your link which explained phase angle in such a simple manner helped me a lot. Thank u again.