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Given this circuit, we want to find V(t) or the equivalent D node circled.

circuit

I set up the nodal analysis equations in the phasor domain as follows, with a super node at the dependent source.

system of equations for the circuit

However, Wolfram Alpha shows no solutions. There is something wrong with the set up of my equations I believe, but I am having trouble figuring out where.

https://www.wolframalpha.com/input/?i=solve+(5-a)%2F2%2B(5-c)%2F4%3D0,2*i%3Db-a,(a-5)%2F2%2B(b-c)%2F2%3D0,(c-b)%2F2%2B(c-5)%2F4%2B(c-d)%2F3%3D0,+(d-c)%2F3%2Bd%2F(0.5*10*root(-1))%3D0,(c-d)%2F3%3Di&rawformassumption=%22i%22+-%3E+%22Variable%22

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  • \$\begingroup\$ It is in the phasor domain, so we use the impedances of the passive components instead of differentials or integrals. \$\endgroup\$
    – user1106340
    Commented May 9, 2017 at 1:59
  • \$\begingroup\$ I missed that. Sorry. \$\endgroup\$
    – jonk
    Commented May 9, 2017 at 2:05
  • \$\begingroup\$ You want the voltage at node D relative to what reference node? \$\endgroup\$
    – The Photon
    Commented May 9, 2017 at 4:06
  • \$\begingroup\$ The ground which would be after the inductor and before the voltage source. \$\endgroup\$
    – user1106340
    Commented May 9, 2017 at 4:23

1 Answer 1

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Not really sure why, but it seems that I included one too many equations.

After removing the first equation on that list (maybe because that node is already given through the source?), the equation becomes solvable and the answers end up being correct.

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