- #1

rohanprabhu

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## Homework Statement

Q] The figure below shows a typical circuit for a low-pass filter. An AC input [itex]V_i~=~10~mV[/itex] is applied at the left end and the output [itex]V_o[/itex] is received at the right end. Find the output voltage as a function of [itex]\nu~(\textrm{frequency})[/itex]

http://img252.imageshack.us/img252/3724/lowpassfilterrb2.jpg

## Homework Equations

well.. maybe:

[tex]

Z = \sqrt{R^2 + (X^2_C - X^2_L)}

[/tex]

[tex]

i = i_o sin(\omega t + \phi)

[/tex]

[tex]

\phi = tan^{-1}\left(\frac{X_C - X_L}{R}\right)

[/tex]

## The Attempt at a Solution

Well.. I'm just thinking that the voltage across the capacitor will be the output voltage. I found out the current in the circuit using the equations and it is coming to be:

[tex]

i = i_o sin\left(\omega t + tan^{-1}\left(\frac{10^6}{2\pi \nu}\right)\right)

[/tex]

This is the current in the first loop. I thought of using Kirchoff's law first.. but i have no idea how to do this in this case as the current will split at the resistor-capacitor junction.

Any help is appreciated. Thanks.

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