Finding the Center and Radius of Circles for Scientists

[MissP.25_5]

Hi,
how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way. I need to draw 2 circles.

 

[phinds]

What have you tried so far? Those equations don't mean a thing to me, but you DO have to show some effort on your own before (or in addition to) asking for help.

 

[MissP.25_5]

What have you tried so far? Those equations don't mean a thing to me, but you DO have to show some effort on your own before (or in addition to) asking for help.

The equations are actually equations of power transmission and power reception circle diagram.
I am sorry for not having an attempt but I am stuck here.

 

[HallsofIvy]

I presume that the "[itex]P_S+ jQ_S[/itex]" and "[itex]P_R+ jQ_R[/itex]" on the left of those two equations are the complex variable "z" that is to be graphed.

An equation of the form "[itex]z= Ae^{j\theta}[/itex]", with A a real number and [itex]\theta[/itex] from 0 to [itex]2\pi[/itex], is a circle with center at 0 and radius A. An equation of the form "itex]z= B+ A{j\theta}" is a circle with center at the complex number B and radius A.

Of course, as [itex]\theta[/itex] goes from 0 to [itex]2\pi[/itex], [itex]\theta- \pi/2[/itex] goes from [itex]-\pi/2[/itex] to [itex]3\pi/2[/itex] but the graph still covers the circle, just "starting" at a different point. The first circle has center at the point [itex]j(0.81)E_R^2/X[/itex] in the complex plane, which is [itex](0, 0.81E_R^2/X)[/itex], and radius [itex]0.9E_R^2/X[/itex]. The second has center at [itex](0, -0.81E_R^2/X)[/itex] and the same radius.

 

[MissP.25_5]

I presume that the "[itex]P_S+ jQ_S[/itex]" and "[itex]P_R+ jQ_R[/itex]" on the left of those two equations are the complex variable "z" that is to be graphed.

An equation of the form "[itex]z= Ae^{j\theta}[/itex]", with A a real number and [itex]\theta[/itex] from 0 to [itex]2\pi[/itex], is a circle with center at 0 and radius A. An equation of the form "itex]z= B+ A{j\theta}" is a circle with center at the complex number B and radius A.

Of course, as [itex]\theta[/itex] goes from 0 to [itex]2\pi[/itex], [itex]\theta- \pi/2[/itex] goes from [itex]-\pi/2[/itex] to [itex]3\pi/2[/itex] but the graph still covers the circle, just "starting" at a different point. The first circle has center at the point [itex]j(0.81)E_R^2/X[/itex] in the complex plane, which is [itex](0, 0.81E_R^2/X)[/itex], and radius [itex]0.9E_R^2/X[/itex]. The second has center at [itex](0, -0.81E_R^2/X)[/itex] and the same radius.

How do you get [itex](0, -0.81E_R^2/X)[/itex] for the second circle? Shouldn't it be ##(0,-E_R^2/X)##? I forgot to mention that ##P_S##+##jQ_S## are indeed a complex number in the form Z= X+iY because P is the real power while Q is the reactive power.

 

[berkeman]

Hi,
how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way. I need to draw 2 circles.

You know that you *must* show your work in your posts of schoolwork questions here. Check your PMs.

 

[berkeman]

Thread is closed. MissP.25_5 is on a temporary vacation from the PF.