# RLC series circuit: Determine C so that P.F.=X

1. Jun 19, 2012

### EVriderDK

Hey.

If a a circuit is too inductive, and has a power factor of 0.6, how would i find a capacitor in series or parallel that would give a power factor of 0.8?

I think that i could do it with 3 equations and 3 unkowns like this:

1: Q=XL*I^2
Z=X*I^2
2: tan(P/Q)=$\varphi$
tan(P/Z)=Y
3: cos(Y)=0.8

Then solve for X and Y and Z?

2. Jun 20, 2012

### Ratch

EV,

What are your knowns? R? L? Frequency? What?

Ratch

3. Jun 20, 2012

### EVriderDK

I found out. See pic :)

#### Attached Files:

• ###### PFC.jpg
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4. Jun 20, 2012

### Ratch

EV,

What is L? What is R? How about a phasor diagram.

Ratch

5. Jun 20, 2012

### EVriderDK

Ratch

L is the size of the inductor (self inductance), and R is the size of the resistor (resistance)

L would be L=(Q/(I^2))/(2*∏*f) Where Q/(I^2) = X_L the inductive reactance
R would be P/(I^2)

Last edited: Jun 20, 2012
6. Jun 20, 2012

### Ratch

EV,

So if you know the inductive reactance Xl, and the resistance R, and they compute to a power factor of 0.6, can you firgure out what the reduction in inductive reactance should be to get a 0.8 power factor?

Ratch

7. Jun 21, 2012

### EVriderDK

Well, when XL change, Q change, and when R change, P change, so that should be possible.

I cannot see how though.

8. Jun 21, 2012

### Ratch

EV,

Installing a compensating cap does not change R. I think you need to study the theory behind the power factor some more.

Ratch

9. Jun 21, 2012

### EVriderDK

Ratch.

I know, as you can see in the picture. P stays the same.

If P does not change, then R does not change.

10. Jun 21, 2012

### Ratch

EV,

What picture?

What is P, the apparent power?

Ratch

11. Jun 21, 2012

### EVriderDK

PFC.jpg in #3

No. S is apparent, Q is reactive and P is the effective

12. Jun 21, 2012

### SammyS

Staff Emeritus
Here's the figure !

13. Jun 21, 2012

### Ratch

EV,

A power triangle diagram would have been nice. I just noticed, the page you referenced gives the solution you want. C = 2.422 uf in the lower right corner. What else do you want to know?

Ratch

14. Jun 21, 2012

### EVriderDK

Nothing. As i wrote, i found out :)

15. Jun 21, 2012

### Ratch

SammyS,

Call it a figure if you wish. That is a list of values for a bunch of undefined quantities. It wasn't until he explained which quantities defined the power triangle that I understood how everything was related, and the answer was already present.

Ratch

16. Jun 21, 2012

### EVriderDK

Sorry, thourght P, Q and S was standard.