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After spending quite a few hours I am stumped with this problem while trying to solve for Vo, which is supposed to 0.5V and this was confirmed through PSpice. I have no idea what I am doing wrong or if I missed a step. So here is what I have so far since I have 5 nodes and a reference node as labeled on top based on what I have I have made V5 = Vo and V4 = Vx. Here are my 5 equations when not reduced:

  1. (V1-V2)/1k + (V1-V3)/1k + (V1-V4)/1k + (V1-V5)/1k = 0 From V1

  2. (V2-V1)/1k + (V3-V1)/1k + (V4-V1)/1k - 4ma + V3/2k + V4/2k = 0 When treating V2,V3,V4 as a supernode.

  3. (V5-V4)/2k + (V5-V1)/1k + V5/1k = 0 from V5

  4. V3-V2 = 2Vx where Vx = V4

  5. V4-V3 = 12V

When reduced the equations become: 1. 4V1/1k -V2/1k - V3/1k - V4/1k - V5/1k = 0

  1. -3V1/1K + V2/1K + 3V3/2K + 5V4/2k - V5/1k = 4ma

  2. -V1/1k + 0V2 + 0V3 - V4/2k + 5V5/2k = 0

  3. 0V1 + 0V2 - V3 + V4 + 0V5 = 12

  4. 0V1 - V2 + V3 - 2V4 + 0V5 = 0

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You forgot the contribution from \$(V_5-V_4)/2k\$ from the supernode. The reduced system is

$$4V_1-V_2-V_3-V_4-V_5=0\\ -3V_1+V_2+3V_3/2+2V_4-V_5/2=4\\ -V_1-V_4/2+5V_5/2=0\\ -V_2+V_3-2V_4=0\\ -V_3+V_4=12$$

which results in

$$V_1=-3.5V\\ V_2=-21.5V\\ V_3=-2.5V\\ V_4=9.5V\\ V_5=0.5V$$

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  • \$\begingroup\$ So in order to make the supernode work I have to include V5? \$\endgroup\$ – user40699 Apr 24 '14 at 7:41
  • \$\begingroup\$ @user2881196 You don't need to include V5 in the supernode, but if V2, V3 and V4 is your supernode you need to consider all currents going in or out of this node, and the current through the 2k resistor between V4 V5 is one of them. \$\endgroup\$ – Matt L. Apr 24 '14 at 7:44
  • \$\begingroup\$ Oh I see what you are saying so I was in the right track I just was missing one piece of information for my equation then. Well thanks anyways though I feel bad I did not catch that error after so much time lost. \$\endgroup\$ – user40699 Apr 24 '14 at 7:52
  • \$\begingroup\$ Yeah, in principle everything was OK, you just forgot to include one current contribution. \$\endgroup\$ – Matt L. Apr 24 '14 at 7:53

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