Question :

Find V1 and i1 using nodal analysis


Attempt

I know i1 is 0 because of a circuit break.

But, I am not able to figure out how many nodes there are in this circuit?

I thought there are four nodes connected to the reference point but the book only considers two.

Or is it because we are only looking for V1 so we ignore the other nodes?

 

Yes - I1=0

There are effectively three nodes including the common or reference 'rail'. You can ignore the 2Ω and I1 for the purposes of finding V1.

 

but why does the book considers the first two nodes which are VA and VB in order to find V1? The last one with
6 ohms is ignored I don't understand why.

 

I'd consider the nodes as shown in attachment.

 

That's what my question is. How can Node b be a combination 3 nodes? I don't know how to identify that.

 

Is there anything located between those "three nodes"? No, and therefore you can view them as a single node. Since there is a short circuit between those points, they all have the same voltage and can be treated as a single point.

 

Yeah, very true. Thanks once again, Georacer.