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I have this circuit which I have to solve for Io using nodal analysis. Everything seems easy but I am confused about the nodal equation for V2 given below in the solution. They seemed to ignore the part of the node that goes from V2 to ground, through the 2 1-ohm resistors? In other words, shouldn't there be another term that looks like: $$\frac {V_2}{2}$$

Can you please clarify this? Thank you.

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  • \$\begingroup\$ The only components connected to V2 are R3, the capacitor, and the 4A current source. \$\endgroup\$ – sherrellbc Apr 11 '15 at 0:40
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The voltage at the node to the left of R3 is V1, hence current away from the V2 node and through R3 is (V2-V1)/R3. Note that R2 and R3 are NOT in series as there is another resistor (R1), and a current generator connected to their junction.

Similarly the current through the capacitor and away from the V2 node is (V2-0)/-j

The sum of the above two currents must equal the current flowing towards the V2 node, which is 4 Amps from the current generator.

Note that the two blobs of solder between R1 and R3 do not constitute two nodes - there is only one node betwen these two resistors and that is V1

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