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Did I do the nodal analysis right?

  1. Feb 18, 2013 #1
    can someone confirm i did this rite:

    1. The problem statement, all variables and given/known data
    Find I(x)
    1zgxh14.png

    2. Relevant equations
    see the next part plz

    3. The attempt at a solution
    16jhp47.png
    using nodal analysis method i have 2 nodes and these are the equations i got for each, after simplification:

    V1: (5/2)V1-V2=21
    V2: (5/2)V2-V1=10.5

    Using cramer's law, this is matrix i got when i plugged in above equations:

    | 5 -2 | |V1| = |42|
    | -2 5 | |V2| = |21|

    V1=[(42*5)-(21*-2)/(5*5)-(-2*-2)]=12V
    V2=[(5*21)-(-2*42)/(5*5)-(-2*-2)]=9V

    now recognize that I(x)=V2/10, i got I(x)=0.9A.

    so my question is two-part: 1st, did i do this rite? 2nd, is there easier way to solve for I(x)?
     
  2. jcsd
  3. Feb 18, 2013 #2

    gneill

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    Staff: Mentor

    Re: did i do nodal analysis rite??

    I think you'll want to check the polarity of the 10.5V source, then verify your equations.

    With only two equations in two unknowns it may be faster to solve by substitution rather than fire up the Cramer's Rule machinery :smile:
     
  4. Feb 18, 2013 #3
    yeah your rite, i didnt see that. since the sign of the 10.5 is opposite all i have to do is negate the 21 in the matrix. so solving i get V1=8 and V2=-1. so I(x)=-0.1A?


    and btw i did do substitution to check my answer but i wanted to try out cramer's rule to see that i could do it correctly. and in my 1st try i did get the same answers for both methods.
     
  5. Feb 18, 2013 #4

    gneill

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    Staff: Mentor

    That looks better :smile:
    Well that's fine then.
     
  6. Feb 19, 2013 #5
    my teacher wants me to solve I(x) with mesh analysis so i can prove i can use another method to get the same answer, however i'm having trouble. would apreciate if u could tell me what i am doing wrong:

    mesh 1: 15(I1)-10(I2)=21
    mesh 2: -10(I1)+25(I2)-10(I3)=0
    mesh 3: -10(I2)+15(I3)=10.5

    i am going under the assumption that I(x) is equal to -I3. my matrix is:

    |15 -10 0| |I1)=|21|
    |-10 25 -10| |I2|=|0|
    |0 -10 15| |I3|=|10.5|

    but when i solve this, i get a weird answer, 1.9A for I3. and I know I(x) is supposed to be -0.1A. can u tell me what i am doing wrong??
     
    Last edited: Feb 19, 2013
  7. Feb 19, 2013 #6

    gneill

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    Staff: Mentor

    It would appear that the problem lies with your assumption about Ix; Ix is comprised of a suitable sum of the two mesh currents that flow through it.
     
  8. Feb 20, 2013 #7
    thanks your rite, i got it. I(x)=I2-I3=1.8-1.9=-0.1A
     
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