Homework Help: Finding line-to-line voltages

1. Oct 26, 2016

eehelp150

1. The problem statement, all variables and given/known data
Assuming balanced 3 phase circuit and abc positive phase sequence:
The RMS value of line-to-line voltage between Phase A and C is V = 208∠10°

Find the line to line voltage between Phases A and B (magnitude + angle)
Find the line to line voltage between Phases B and C (magnitude + angle)
Determine the phase to neutral voltage Van, Vbn, Vcn ((magnitude + angle)

2. Relevant equations
These were in my professor's notes:

3. The attempt at a solution
I have no idea how to do this. Are the relevant equations I posted correct? Any hints would be appreciated.

2. Oct 26, 2016

cnh1995

Yes, but in these equations, VAN is assumed to be the reference phasor. In the question, you have Vac∠10° which means VAN is no longer the reference phasor. In a balanced three phase system, what is the phase difference between VAN and VAC? (Refer the equations you posted).

3. Oct 26, 2016

eehelp150

30 degrees?

4. Oct 26, 2016

cnh1995

Yes. So what will be VAN when Vac=208∠10?

5. Oct 26, 2016

eehelp150

208 * sqrt(3) ∠40?

6. Oct 26, 2016

cnh1995

No. What is magnitude relationship between line and phase voltages?

7. Oct 26, 2016

eehelp150

1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?

8. Oct 26, 2016

cnh1995

Correct.

9. Oct 26, 2016

eehelp150

I mistyped something in the prompt.
Vca = 208<10 (could this be a typo?)

Would Van still be 120<40? This is the "phase to neutral" voltage, correct?
How would I find Vab, Vbc?

10. Oct 26, 2016

cnh1995

No. Magnitude will not change but phase angle will.
So what would be Vac? Find Vac and use the relation between Vac and Van from your equations.
What is the angle between Vac and Vab? What is the angle between Vac and Vbc? Refer the equations again. But first find Vac from Vca.

11. Oct 26, 2016

eehelp150

Van = 120<-20?
Vac = 208<130?
Vab = 208<10?
Vbc = 208<-80?

12. Oct 27, 2016

cnh1995

No. Angle of Vca is 10°. What is the angle of Vac? Vac and Vca are anti-parallel phasors.

13. Oct 27, 2016

eehelp150

Is it a 90 degree difference? so -80 or 100?

14. Oct 27, 2016

cnh1995

It's a 180 degree difference.

15. Oct 27, 2016

eehelp150

So:
Vca = 208<10°

Vac = 208<190°
Vab = 208<-110°
Vbc = 208<-230°

16. Oct 27, 2016

cnh1995

If the angle of Vac=θ, then θ=180-angle of Vca.
Edit: I am imagining all this in my head without drawing it on paper and this is a mistake. Yes, angle of Vac is 190 degrees.

17. Oct 27, 2016

eehelp150

so
Vab = 208<-110
Vbc = 208<-230

Van = 120<190+30
Vbn = 120<(190+30)-120
Vcn = 120<(190+30)-240

These correct?

18. Oct 27, 2016

Yes.