Calculating R and C on an AC circuit.

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Homework Statement

There is a circuit formed by a capacitor and a resistor with an AC source of 212V. It is known that the currentr that goes through the circuit is 0.5A, with a phase angle of pi/8 rad in relationship with the tension and that the power consumed by the circuit is 50W.
What are the values of the condenser and the resistance?
What's the value of the impedance?

Homework Equations

E=Em*sin(wt)
I=Im*sin(wt-phi)
tan(phi)=(wL-1/wC)/(R)
MeanPower=Im*Em*cos(phi)
Ismv=(Im^2)/2
Esmv=(Em^2)/2
Im=Em/Z
Z=sqrt(R^2+(wL-1/wC)^2)

The Attempt at a Solution

First I get Im=1
Then from the power equation I get Esmv=54.1V
Then I get Em
Then I use Im=Em/Z and tan(phi)=(wL-1/wC)/(R) to get an equations' system with the variables I have to calculate. I say wL=0 because there are no inductors.
So I calculate R = 108.16 Ohm
And then C = 1/(3.58w)
So I still need the angular frequence and I don't know where to get it from.

Maybe everything I did is wrong and those functions only work with LRC circuits. If that's true then I'm in a big problem =S

Please any help will be welcome and thanks in advance.

 

[Irid]

The equations are correct. However, since the value of capacity always goes in combination with the frequency $$X_C = \frac{1}{\omega C}$$, you can't deduce any of these separately. In this case I would just assume that the frequency is 50 Hz, unless stated otherwise.