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1. Homework Statement
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. Homework 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 doublepole, 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?
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. Homework 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 doublepole, 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?
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