Nodal Analysis questions

Discussion in 'Homework Help' started by Digit0001, Mar 13, 2011.

  1. Digit0001

    Thread Starter Member

    Mar 28, 2010
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    0
    Hi

    The two questions i am having trouble getting the correct equations.
    View attachment tut2qns.doc
    Can someone tell me where is my mistake?

    Question 1
    SuperNode
    5 = i2 + i3 + i4

    Node 1
    i1 = i2 + i6 + i5

    KVL
    6 + V3 - V1 = 0


    Question 2

    For SuperNode
    i1 + i3 + i2 + i - i3 = 0

    For Node V3
    i4 + i3 = i

    For KVL
    2i + V2 + V1 =0

    P.S
     
    Last edited: Mar 13, 2011
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    782
    In question 1 the 3A source to the left side is translated in the circuit to the right as a 6V equivalent source. The equivalent circuit shown on the right is incorrect, as the 6V source should have a series resistance of 2Ω. This is not a supernode example.
     
  3. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    It would have been "nice" if you had acknowledged the fact that you had made a mistake in the schematic attached with your original post, rather than just correcting the problem and leaving my post in no-man's land.

    In any case there are several errors in your equations as well.

    This is the set ...

    i2+i5+i6=5

    i6-i3-i7=0

    i4+i5+i7=0

    i2=V1/4

    i3=V2/2

    i4=(12-V3)/8

    i5=(V1-V3-6)/2

    i6=(V1-V2)/8

    i7=(V2-V3)/4
     
  4. Digit0001

    Thread Starter Member

    Mar 28, 2010
    89
    0
    i have done Question 2 again and these are the equations i get but the answer is incorrect.

    supernode V1-V2
    i1 + i2 + i3 + i4 = 0

    Node V3
    i3 + i4 = i

    KVL Supernode
    2i + V1 - V2 = 0
     
  5. peter_morley

    Member

    Mar 12, 2011
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    Can you make v2 and v3 also a supernode? I am also learning nodal analysis and number 2 is a problem I have never come across...quite a mess.
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    782
    This was my attempt at a solution for the second problem. Interesting challenge although I didn't specifically use supernode approach.
     
  7. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,281
    326
    To solve problem 1, it's better not to convert the 3A current source in parallel with the 2 Ω resistor into a voltage source. Rather, convert the 12 volt source in series with the 8 Ω resistor into a 1.5A current source in parallel with an 8 Ω resistor. Then there is no supernode and a nodal solution is straightforward.

    ----------------------------------------------------------

    A supernode solution for problem 2 goes like this:

    All three nodes comprise the supernode, so the three currents from the supernode to ground must add to zero: I1 + I2 + i = 0

    That becomes a nodal equation:

    Eq 1: V1/4 + V2/1 + V3/4 = 0

    The next 2 equations are constraint equations for the two sources:

    Eq 2: V1 - V3 = 12

    Given that 2*i = 2*(V3/4) = V3/2, we have:

    Eq 3: V1 - V2 = V3/2

    Solving these three equations gives us:

    V1 = -3
    V2 = 9/2
    V3 = -15
     
    Digit0001 and t_n_k like this.
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