Circuits II Polyphase System Help

[md5fungi]

Homework Statement

"Determine x for which the power factor at the source is in unity."

The data given is in the diagram; The impedance of the capacitors is the only thing we don't know. The load and sources are balanced.

Homework Equations

Just the basics: Kirchoff's Current Law, possibly some Loop/Mesh equations?, basic Polyphase system properties.

The Attempt at a Solution

Basically I was taught that if I needed to find the impedance of the capacitor in this particular setup, I could represent the circuit as a 240angle0 source in series with the load and equivalent capacitor (-jx/3) in parallel with each other. The impedances resistor and additional load in this example can be combined to make it easier. But the only way I can solve for x as far as I understand is form an equation involving the current through the combined load and current through the capacitor, so that they add up to the current through the source. However, since we aren't given the current through the source, I am very confused.

Any ideas? (This isn't homework really, just a practice problem from an old test that is supposedly going to help me with an exam I have this Friday)

 

[unplebeian]

First find the current going into the loads. Luckily you have a balanced 3 phase system otherwise it would be difficuilt to solve it. Consider each phase individually.

So if the current is 5-j10 (I am just using some number here calc it by V/Z) and it should be a lagging current due to an inductive load, you need to put a capacitor in parallel to get a unity pf.

So previously the source provided a current had a reactive component of -j10. With the addition of the cap, you want the cap to absorb a current of the same magnitude but opposite phase to cancel it out and get unity pf. So the cap current must be +j10. Hence the impedance of the cap must be (240+j0)/(+j10). Once you have the impedance use that to find the capacitance 1/(2*pi*f*C)= |Impedance|

To check your answer calculate the impedance of the cap and the load (75 angle 25 || 10). There should be no reactive component (or very little due to rounding off errors)

C= 14.94uF from my calcs.

 

[md5fungi]

Thanks; I actually finally realized how the fact the power factor was in unity could help me this morning and managed to solve it. Thanks for your help and time, though!

 

[unplebeian]

Thanks; I actually finally realized how the fact the power factor was in unity could help me this morning and managed to solve it. Thanks for your help and time, though!

Did you get the same answer as I did?