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## Homework Statement

http://i.imgur.com/HTGycr8.png?1

[tex]f = 248 Hz\Rightarrow \omega = 1558.23r/s\\ L = 34 mH\\R = 7\Omega\\\alpha = -6°\\C=? [/tex]

Alpha is the angle between current and voltage (V - I).

[tex]X_L=\omega\times L=1558.23 * 34 * 10^-3 = 52.9798 \Omega[/tex]

## Homework Equations

[tex]\arctan{\frac{R}{X}} = \alpha[/tex]

## The Attempt at a Solution

Basically I tried combining everything into one impedance, then I would find real and imaginary part:

[tex]\frac{\Re{Z}}{\Im{Z}} = \tan{\alpha}[/tex]

but I can't get past some maths and I know this is probably a problem; so far (jX_L = L, -jX_C = C):

[tex]\frac{RL(C+R)}{(C+R)(R+L)+RL}[/tex] now if I were to plug everything in I would get something very complicated... Now I need to get this denominator to something simple, but I don't know how to do it the easy way... it's too tedious... is there a simpler way?

Also, if the problem stated that current and voltage were in phase, I could combine R and L that are separate (in first and last branch) in one branch (a series) then use this formula: [tex]\omega_0 = \frac{1}{\sqrt{LC}} \times\sqrt{\frac{R_C^2 - L/C}{R_L^2 - L/C}}[/tex]? I tried to do that exactly and it didn't work, I checked several times with the given result...

Thanks in advance.

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