Induction motor and Sync motor question

[iwire]

It's seems to be an easy question but I can't figure it out ...please see attached screenshot

 

[Ship Wreck PE]

I am getting answer "C" 0.96

Syn motor is 8 KVA 0.78 leading. so 8 *.78 = 6.24 KW. Acos .78 = 38.7 deg (6.24,angle 38.7 deg)

Induction motor. 30 * 208 * sq rt 3 * 0.65 lag = 7 KW. Acos .65 = -49.4 deg (7, angle -49.4 deg)

Add together with Calculator (Casio is real easy) (6.24 angle 38.7) + (7 angle -49.4) = 9.53, -8.5 deg

Cos -8.5 deg = .989 PF "C" is the closest???

What answer is in the book?

 

[iahim]

For induction motor:

S=10,800VA

P=7,020W

Q=8,207VAR

For synch motor:

S=8,000VA

P=6240W

Q=-5006VAR

Total:

P=13,260W

Q=3201VAR

S=13640VA

pf=0.97

I'm not sure yet why I'm getting a different result.

 

[iahim]

I am getting answer "C" 0.96

Syn motor is 8 KVA 0.78 leading. so 8 *.78 = 6.24 KW. Acos .78 = 38.7 deg (6.24,angle 38.7 deg)

Induction motor. 30 * 208 * sq rt 3 * 0.65 lag = 7 KW. Acos .65 = -49.4 deg (7, angle -49.4 deg)

Add together with Calculator (Casio is real easy) (6.24 angle 38.7) + (7 angle -49.4) = 9.53, -8.5 deg

Cos -8.5 deg = .989 PF "C" is the closest???

What answer is in the book?

I think you calculated the complex power incorrectly. For Sync motor should be 8<38.7. For Induction motor: 10.8<-49.4. If you add them up, the angle is -13.5, so pf is 0.97.

 

[iwire]

hmm The answer in the book is D.... 0.92

that is the reason i m pretty confused...

 

[iahim]

iwire,

What answer are you getting?

 

[Ship Wreck PE]

When I add the polar vectors, I get 0.98 lagging

When I add the Rectangular components, I get 0.97 lagging

The question asks for most nearly, so I think there are some small mathematical differences in which way you solve the problem but I think the books answer is incorrect.

 

[iahim]

I agree that the solution in the book is incorrect, but the results should be closer when you solve with the two methods.

 

[iwire]

I found 0.97 too..

I just check with the author. He made correction on the answer. it's 0.97

 

[iahim]

iwire,

What book is that?

 

[iwire]

iwire,

What book is that?

Alex Graffeo book

 

[iahim]

Thanks! I did consider buying that book, but I already have the GA Tech binder and EPRM. I was looking for some more practice exams (I did CI, SpinUP and NCEES).

 

[iwire]

Thanks! I did consider buying that book, but I already have the GA Tech binder and EPRM. I was looking for some more practice exams (I did CI, SpinUP and NCEES).

I have CI, NCEES, Graffeo practice exams. As for GA Tech, do you have a index page? I need to make one

 

[iahim]

No, I don't have an index, but I used color coded post-it flags to tab it. That works better for me.