How to Find Vout/Vin vs. Frequency in a Voltage Divider Circuit

[phrygian]

Homework Statement

The problem deals with a circuit that has a voltage divider composed of an inductor L and a capacitor C in series connected to a node, one end is an open circuit with the output voltage and the other end is connected to a resistor R that is connected to ground.

Find the response ( Vout/Vin ) versus frequency.

Homework Equations

The Attempt at a Solution

I found the amplitude of V out by finding V out = (Zr / (Zr + Zc + Zl) )*Vin and multiplying V out by its complex conjugate and taking the square root. This got me to |Vout| = R * Vin / ( R^2 + (wL-1/wC)^2)^.5

From that equation I see that V out is 0 at 0 frequency, and then also 0 at infinite frequency but don't know anything about the middle. Am I even on the right track?

Thanks for the help

 

[Jhero]

!

Thank you for your post. It seems like you are on the right track with your solution. However, there are a few things that you may want to consider in order to fully answer the question.

Firstly, you have correctly identified that the output voltage, Vout, is dependent on the input voltage, Vin, and the impedances of the circuit components. However, it would be helpful to also consider the phase difference between Vout and Vin, as this will affect the overall response of the circuit.

Secondly, you may want to consider using the concept of reactance, which takes into account the frequency of the input voltage, to simplify your equation. This will give you a better understanding of the behavior of the circuit at different frequencies.

Lastly, it would be helpful to plot the response (Vout/Vin) versus frequency to get a visual representation of the circuit's behavior. This will give you a better understanding of how the output voltage changes with respect to the input voltage at different frequencies.

I hope this helps guide you in the right direction. If you have any further questions or need clarification, please do not hesitate to ask. Good luck with your problem!