Camara Power Sample Exam Prob.#10

[mhelms_2]

For those who don't have the book:

A 60 Hz, three phase, 208 V system carries a total load of 200+j150 VA. What is most nearly the total capacitance required to correct the power factor?

A) 0.001 uF

B) 5 uF

C) 9 uF

D) 500 uF

I used the equation Xc = V2 / Q,

but the book had Xc = (sqrt 3) ( V2 /Q).

Why the sqrt 3? I don't find that formula in thde refernce manual.

 

[mhelms_2]

By the way,

after finding Xc, he converts to capacitance and gets 5.31 x 10-6 uF.

 

[Lielec11]

I have both the Camara refernce manual and the power practice problems. Which #10 are you referring to? his problems are separated by chapter?

 

[Lielec11]

I find a different answer when I do it. You need to use the equation XC = XR, where XC is the capacative reactance and XR is the reactance of the load.

To find the reactance due to the load use the following;

Z = (1.732*V)2/S = (1.732 * 208)2 / (200 + j150) = 415.33-j311.5

Therefore, XR = -j311.5

XC = XR .... -j/wC = -j311.5 ... 1/wC = 311.50 ... C = 1/ (2pi*60*311.5)

Therefore, C = 8.5uF which is closest to 9uF

Sqrt(3) is used for 3-phase power. I believe you are supposed to include it within the parenthesis before you square the voltage. (1.732*208V)2 not 1.732*(208V)2

Someone else please verify I did this correctly.

 

[mhelms_2]

Thanks for the response. In regards to the sqrt of 3, Camara has it outside of the V2/Q, and not with V. That's what is confusing me.

I got 9 uF as well.

 

[Lielec11]

Which Camara question are you referencing? My version of the book has questions by chapter (i.e. Chapter 27, #1, #2, etc.). Which chapter is your question from, it may help me find our answer in the reference manual.

 

[mhelms_2]

It's the Power Sample Exam booklet

 

[Lielec11]

I wonder if the solution manual is just wrong? It is very common for solution manuals to have misprinted or simply wrong information.

 

[knight1fox3]

I wonder if the solution manual is just wrong? It is very common for solution manuals to have misprinted or simply wrong information.

Certainly a possibility. Just ask Kaplan...

 

[Johnlittle864 PE]

I also can't understand the root3 in his equation. I also solved and get ~9uF. (I can't stand this guys rounding in this book!) He uses the root 3 again the same way in problem #12 just two below. This is the book with 160 problems in it. I see they would cancel out and don't bother my solution method for #12, but I wish I new the correct answer for #10!

 

[Lielec11]

Wait is this camara or Kaplan book?

 

[Johnlittle864 PE]

I was refering to Camara, Power Sample Exams" Copyright 2011. There a 160 problems in this book.

 

[Insaf]

Irrespective of phases (1-phase or 3-phase), Sqrt(3) should not be part of the equation; answer will be 9 microF. Without investigating, many of us always use sqrt(3) for three phase system, but not the case always like this. In this case, phase to phase or line voltage already accounted, so don't need to use sqrt(3).

We can examine the problem, based on 1-phase basis; Kvar required=150/3=50 and line to neutral voltage 208/1.732=120 V. Now Xc=120^2/-50=-288 ohm. Finaly C= (-1)/(2*pi*60*288)=9.1 micro Farad.

In conclusion, original calculation considered line to line voltage and 3-phase kvar required for correction whereis 1-phase calculation accounted line to neutral volatgee and kavr required for single phase; both give the same capacitor value. There is no room for sqrt(3).

Thanks,