Nodal analysis independent and dependent voltage source and current source

circuit analysiscurrent-sourcevoltage measurementvoltage-source

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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

Best Answer

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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