# Power Factor for a RC circuit

1. Oct 23, 2008

### just.karl

Find the power factor for an RC circuit connected to a 70Hz generator with an rms voltage of 125V. The values of R and C in this circuit are 105ohms and 82.4microfarads, respectively.

The equation I think you use is P=IVcos$$\oslash$$ and also z= square root of R^2+(1/wc)^2 and cos0 = R/Z

I tried to put it together but nothing seemed to come out right, I couldn't figure out how to relate everything so that i could solve for the power factor. A push in the right direction would be nice. Thanks

2. Oct 23, 2008

### alphysicist

Hi just.karl,

This formula gives you the average power P. The power factor is just the $\cos\theta$ part.

3. Oct 23, 2008

### just.karl

I understand that, so then it would be P/IV=cos0 but what I don't understand is how you relate the capacitor and frequency into it. Since I can solve for "I" and "P" by P=V^2/R and then find "I" by P=IR.

4. Oct 23, 2008

### alphysicist

I would use the other formula for cos(theta) that is in your original post:

cos(theta) = R / Z

5. Oct 23, 2008

### just.karl

If I use cos(theta) = R / Z then I don't use the voltage at all to solve for it?

6. Oct 23, 2008

### alphysicist

No, since they give you enough to find R and Z.

7. Oct 23, 2008

### just.karl

Alright.., when I plug in the numbers it comes out to be .9987 and the answer in the back of the book says .967. So that is probably just rounding error on my part I'm guessing?

8. Oct 23, 2008

### alphysicist

I get an answer of 0.967163, so the discrepancy could be from rounding. Keep more digits and see if you get the right answer; if it still does not work, please post the actual input to your calculator.

9. Oct 23, 2008

### just.karl

Ah, I found what I did. I forgot to square (1/wC), it comes out with the right answer now. Thanks for your help! I really appreciate it.

10. Oct 23, 2008

### alphysicist

11. Jul 15, 2009

### jessiepink

Hi,
I am working on the same type problem. Can you tell me what the "w" represents in (1/wC) Thanks so much

12. Jul 15, 2009

### turin

Angular velocity (frequency), measured in radians per second, where a radian is numerically a unitless quantity equal to 1.

13. Jul 15, 2009

thank you!