Solving Nodal Analysis: Find V1 and i1

[J.live]

Homework Statement

Find V1 and i1 using nodal analysis

The Attempt at a Solution

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?

 

[d-rock]

There is only two nodes, and no nodes are being ignored.

A node is not always just a "point" connecting two circuit parts. It is any part of a circuit that connects two OR MORE circuit elements.

Therefore, Node 1 is the wire that the 3 ohms, 2 A, and 1 ohm elements share at the top left.

Node 2 is the wire that the 1 ohm, both of the 6 ohms, 4 A, and the 2 ohms elements share at the top right.