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Finding angular frequency in electric circuit

  1. Mar 29, 2008 #1
    1. The problem statement, all variables and given/known data
    At a certain angular frequency, the phase difference between [tex]U_{2}[/tex] and [tex]U_{1}[/tex] is [tex]180^{\circ}[/tex].
    a) Calculate this angular frequency
    b) Calculate [tex]U_{2}[/tex] at this angular frequency

    See the attachment for circuit configuration.


    2. Relevant equations
    Ohms law: [tex]U = Z \cdot I[/tex]
    Voltage: [tex]U = \hat{U} cos(\omega t + \alpha) [/tex]


    3. The attempt at a solution
    I can't seem to find the relation between phase difference and angular frequency.

    I've tried to compute the equivalent double-pole, separating the coil with voltage [tex]U_2[/tex] from the rest och the circuit, with the following result:

    Idle current:
    [tex]U_t = \frac{\omega^2 L^2 + Rj\omega L}{R^2 + \omega^2 L^2} U_1[/tex]

    Equivalent impedance:
    [tex]Z_0 = \frac{\omega^2 RCL - R - j\omega L}{\omega^2 LC - j\omega RC}[/tex]

    And from this I've calculated [tex]U_{2}[/tex]:
    [tex]U_{2} = \frac{j\omega L}{Z_0 + j\omega L} U_t[/tex]

    But as stated, I can't find the relation between angular frequency and phase difference. How do I use the phase difference?
     

    Attached Files:

    Last edited: Mar 29, 2008
  2. jcsd
  3. Apr 3, 2008 #2
    I'm stuck here. Does anyone have a suggestion?
     
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