Nodal Analysis Problem help (Double Supermesh)

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SUMMARY

The discussion focuses on the Nodal Analysis problem involving a Supernode with a 12V branch. The current calculated as (V2-V3)/2 is internal to the supernode and does not affect the overall nodal equations, confirming that the provided solution is correct. The user initially questioned the validity of the solution due to the omission of this current in the equations. However, it was clarified that the current cancels out when considering the supernode's boundaries.

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IonizingJai
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Homework Statement
We are required to find the Node Voltages in the given circuit.
Relevant Equations
Why is the Node current b/w node 1 and 3, I = (V2-V3)/2 , not included in the KCL at Supernode -1,3, which is the equation 1.
That is, for Supernode -1,3 (12V branch) , we do Nodal Analysis and we have (V2-V3)/2 , over the 2 ohm branch.
But this current is not included in the Equation 1 in the solution I have attached(Which is my only source to cross check answers/solution right now.)
Is the solution wrong?

Thanks for help.
 

Attachments

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The current I = (V2-V3)/2 doesn't come into play because it's internal to the supernode. It enters node 2 and leaves node 3, so it cancels as far as its effect on the supernode. The given solution is correct.
 

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