Node Analysis with frequency domain circuit...Help

Discussion in 'Homework Help' started by bserrato86, Apr 19, 2009.

  1. bserrato86

    Thread Starter New Member

    Apr 18, 2009
    2
    0
    I need some help understanding where I messed up on an assessment problem I was doing. I took a pic with my phone but it didn't come out so well.

    Is=10cosωτ
    Vs=100sinωτ

    R(next to current source on the left)=5Ω
    C=9μF
    L=100μH
    R(next to voltage source on the right)=20Ω

    ω=50κ
    --------------------------------------------------------
    1st) I changed everything to it's proper form...

    Is=10 angle(0°)
    Vs=100 angle(-90°)
    R=5Ω
    C=-j2.2
    L=j5
    R=20Ω
    ---------------------------------------------------------
    2nd) I got the equation for node analysis...

    V-[100 angle(-90)] + V + V + V - 10 = 0
    20 j5 -j2.2 5

    ----------------------------------------------------------
    3rd) Did some math...

    V + V + V + V -10-[5 angle(-90)]= 0
    20 j5 -j2.2 5

    .05s + (-j.2)s + (j.45)s => .05s + (j.25)s => [.26 angle(78.7)]s =>

    3.84 angle(-78.7) = Z

    so............

    I=V => 15 angle(-90) = ______v______
    Z 3.84 angle(-78.7)

    V= 57.6 angle(168.7)
    ------------------------------------------------------------
    Problem...

    the answer is:

    31.62 angle(−71.57◦)
    v = 31.62 cos(50,000t − 71.57◦)V

    Where did I go wrong? Also it has to be nodal analysis.
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Your attachment is extremely fuzzy. Can you provide a clearer image?

    hgmjr
     
  3. PRS

    Well-Known Member

    Aug 24, 2008
    989
    35
    I hope this helps. Using < for the angle, I would write the nodal equation like this:

    (V-100<0)/20 + V/j5 + V/-j2.22 +V/5 = 10<0

    This is the current through the 20ohm resistor plus the current through the inductor plus the current through the capacitor plus the current through the 5 ohm resistor equals the current from the current source.

    Good luck! :)
     
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