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Node Volt Analysis

  1. Feb 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Find [tex]\frac{V_o}{V_i}[/tex]

    for

    http://img685.imageshack.us/img685/8658/nodevoltage.png [Broken]

    2. Relevant equations

    [tex]s=σ+jω[/tex], where σ=real component & jω=imaginary component

    3. The attempt at a solution

    Solution is
    [tex]\frac{V_o}{V_i}=\frac{1}{s+2}[/tex]

    Solution manual says:
    [tex]\frac{V_o-V_i}{s}+\frac{V_o}{s}+V_o=0[/tex]

    I don't know where that comes from. I don't understand why there are 2 s's
    Shouldn't it be;

    [tex]\frac{V_L-V_i}{R}+\frac{V_L-0}{Ls}+\frac{V_L-V_o}{R}=0[/tex]

    where [tex]V_L=V_o[/tex]

    so

    [tex]\frac{V_o-V_i}{R}+\frac{V_o-0}{Ls}+\frac{V_o-V_o}{R}=0[/tex]
    [tex]\frac{V_o-V_i}{R}+\frac{V_o-0}{Ls}=0[/tex]

    That won't give me an s+2 in the denominator...
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 18, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    You seem to be using V_o for ground, whereas the diagram shows V_o = V_L.
    You're close, fix that up, & shoot again.
    You should call ground (the bottom node voltage) zero like everybody else does! :smile:
     
    Last edited by a moderator: May 5, 2017
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