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## Homework Statement

This is the circuit:

http://img129.imageshack.us/img129/3566/pfcog8.jpg [Broken]

Assume voltage is in rms and f is 50Hz.

I have to do three things.

First, calculate and compare true power vs apparent power in the load.

Second, find the value of a capacitor placed in parallel that would bring the LOAD to unity power factor.

Finally, calculate the real power in the circuit (both transmission and load impedances) with and without this capacitor, and compare them.

## Homework Equations

## The Attempt at a Solution

I didn't have a problem with the first part.

The load impedance is (8 + j3) ohms.

Power worked out to be 6212.33 + j2367.12. So true power was 6312.33 W and apparent was 6741.57

I'm having trouble with the second part. I've been told that I need to use:

Z

_{corrected load}= Z

_{c}|| (Z

_{r}+ Z

_{L})

which becomes Z

_{corrected load}= [Z

_{c}* (Z

_{r}+ Z

_{L})] / [Z

_{c}+ (Z

_{r}+ Z

_{L})]

But I'm not sure how to manipulate this to give me the value of Z

_{c}.

And I can't even start the third part until I've worked this out.

Please help.

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