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.
Best Answer
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