Calculating Power Factor for an RC Circuit with Given R, C, and Frequency

[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

 

[alphysicist]

Hi 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$$\oslash$$

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

 

[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.

 

[alphysicist]

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.

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

cos(theta) = R / Z

 

[just.karl]

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

 

[alphysicist]

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

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

 

[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?

 

[alphysicist]

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?

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.

 

[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.

 

[alphysicist]

Sure, glad to help!

 

[jessiepink]

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

 

[turin]

Can you tell me what the "w" represents in (1/wC) Thanks so much

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

 

[jessiepink]

thank you!