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RC network

The questions below are due on Wednesday April 15, 2020; 11:59:00 PM.
 
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For the RC circuit shown in the figure above, assume R1=R2=R and C1=C2=C, determine the transfer H(j\omega) = \dfrac{V_{OUT}}{V_{IN}}, where the real parts of V_{OUT} and V_{IN} represent the output and input voltages.

Please note \omega is the Greek letter "omega" and should be entered as such.

H(j\omega) =

What is the resonant frequency of the circuit \omega_0 =
Now assume V_{IN} = V_{0}sin(\omega t), V_{OUT} = V_{1}sin(\omega t + \phi). Use V0 for V_{0}.
Express V_{1} in terms of V_{0}, R and C at \omega = \omega_0
Express \phi in terms of V_{0}, R and C at \omega = \omega_0

Express V_{1} in terms of V_{0}, R and C in the limit as \omega approaches 0
Express \phi in terms of V_{0}, R and C in the limit as \omega approaches 0

Express V_{1} in terms of V_{0}, R and C in the limit as \omega approaches \infty
Express \phi in terms of V_{0}, R and C in the limit as \omega approaches \infty