# Node-voltage method to find current

**1. The problem statement, all variables and given/known data**

Use the node-voltage method to find i_0 in the figure (Figure 1) if v = 29.0V.

**2. Relevant equations**

G = 1/R

[itex]\sum[/itex]G connected to node 1 * v_1 – [itex]\sum[/itex]G between node 1 and 2 * v_2 = Current source into node 1

[itex]\sum[/itex]G connected to node 2 * v_2 – [itex]\sum[/itex]G between node 1 and 2 * v_1 = Current source into node 2

**3. The attempt at a solution**

Labels: Top node = 1, left node = 2, right node = 3, bottom node = 4

v_1 = 29, v_4 = 0

Node 1:

0 = 29*(1/2000+1/5000) – v_2*(1/2000) – v_3*(1/5000) – 0

Node 2:

-i_0 = -29*(1/2000) + v_2*(1/2000+1/5000+1/30000) – v_3*(1/5000) – 0

Node 3:

i_0 = -29*(1/5000) – v_2*(1/5000) + v_3*(1/5000+1/5000+1/1000) – 0

Node 4:

0 = 0 – v_2*(1/30000) – v_3*(1/1000) + 0

Solving, I get i_0 = -0.0160 which isn’t right. Thoughts?

http://ift.tt/1eP6MfN

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