May 17th, 2018, 06:14 AM  #1 
Member Joined: Aug 2017 From: India Posts: 50 Thanks: 2  3 phase AC signal resultant vector
I want to derive that the resultant of the 3 phase AC signal is a pointer around the circle or in other words the locus is a circle. Am i correct in the above statement and how to arrive at it? Please advise. The 3 phase AC are 3 sine waves with 120 degrees apart.

May 17th, 2018, 10:47 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 
Assuming all three phases have the same amplitude the resultant will always be the zero vector. You can see this geometrically by placing the three vectors tip to tail and noting that they form an equilateral triangle. 
May 17th, 2018, 01:34 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157  and I guess more importantly that the tail of the final vector is at the tip of the first.

May 17th, 2018, 04:01 PM  #4 
Member Joined: Aug 2017 From: India Posts: 50 Thanks: 2 
At a particular point in time all three waves cannot have the same amplitude.

May 17th, 2018, 05:39 PM  #5 
Member Joined: Aug 2017 From: India Posts: 50 Thanks: 2 
One will A*sin(theta) other A*sin(120 + theta) and one more A*sin(240 + theta).

May 17th, 2018, 06:37 PM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157  Quote:
Ok just add them $\begin{align*} &A\sin(\theta) + A\sin(\theta + 120^\circ) + A\sin(\theta+ 240^\circ) =\\ \\ &A\left(\sin(\theta) + \left(\sin(\theta)\cos(120^\circ)+ \cos(\theta)\sin(120^\circ)\right) + \left(\sin(\theta)\cos(240^\circ) + \cos(\theta)\sin(240^\circ)\right) \right)= \\ \\ &A\left(\sin(\theta)\sin(\theta)\dfrac 1 2 + \cos(\theta)\dfrac{\sqrt{3}}{2}  \sin(\theta)\dfrac 1 2  \cos(\theta)\dfrac{\sqrt{3}}{2}\right) = \\ &A\left(\sin(\theta)  2\cdot \dfrac 1 2 \sin(\theta)\right) = \\ \\ &0 \end{align*}$  

Tags 
phase, resultant, signal, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Resultant Force  mrbronz  Physics  3  September 25th, 2015 07:21 AM 
How to find the resultant force on the object  girlbadatmath  Physics  9  July 17th, 2014 02:24 AM 
find resultant and angle  mt055  Algebra  1  November 3rd, 2009 04:39 PM 
Signal  jokker  Algebra  1  June 29th, 2008 04:40 AM 
phase plot  question  Algebra  2  December 31st, 1969 04:00 PM 