Transmission line problem

[saw]

Hi there, I can not get the right answer for the problem below. any help will be appriciated.

A single phase transmission line supplies a reactive load at a lagging power factor. The load draws 1.2 pu current at 0.6 voltage while drawing 0.5 pu (true) power. If the base voltage is 20 kv and the base current is 160A, calculate the power factor adn the ohmic value of the resistance of the load.

The book has only the answers which they are 0.694 and 43.375 ohm.

I got voltage: (20kv)x (0.6) = 12kv / I = (160)x (1.2) = 192 A / and Z = (12kv)/ (192 A) = 62.5 ohm

and I do not have enough info for pf.

Thanks

 

[mhelms_2]

Here is what I did to find the power factor:

True power was 0.5 pu

Apparent power is S=VI, or S=(1.2 puA)(0.6 puV)=0.72

0.5/0.72=0.694444444

Not a 100% on the way I did it, but it got the right answer.

 

[mhelms_2]

To better explain,

PF=cosX, or in terms of right triangle, cosx=adjacent/hypotenuse, which is 0.5/0.72

so, PF=0.5/0.72=0.69444

 

[saw]

Thanks for the respond. I was thinking that s = (v)x(I)x(cosx). my mistake. Thanks again.

 

[mhelms_2]

Another way to look at it:

P=V x I x PF

0.5 = 0.6 x 1.2 x PF

PF = (0.5)/(0.6 x 1.2) = 0.69444

I got the same as you on Z, but in a little different manner.