When I first saw this problem my initial reaction was to solve using a supernode since we have a voltage source between two non-reference nodes. Then I figured that you're probably not allowed to have another component in series within a supernode.
So I defined a new node between the 2Ω resistor and voltage source and approached the problem this way:
(I've included ground as Vg and try to show all my work and make it as clear as possible)
I'm slightly worried about my statement of equality for i1. I know current across a resistor in series is the same but I'm not sure where else I could've gone wrong. I know the solution can be obtained through regular nodal analysis like as I've show below, but I don't understand where I went wrong in the method above and why it doesn't work.
Maybe I'm over-thinking things, but I want to try to understand these concepts as thoroughly as possible. Any input is appreciated!!
So I defined a new node between the 2Ω resistor and voltage source and approached the problem this way:
(I've included ground as Vg and try to show all my work and make it as clear as possible)
I'm slightly worried about my statement of equality for i1. I know current across a resistor in series is the same but I'm not sure where else I could've gone wrong. I know the solution can be obtained through regular nodal analysis like as I've show below, but I don't understand where I went wrong in the method above and why it doesn't work.
Maybe I'm over-thinking things, but I want to try to understand these concepts as thoroughly as possible. Any input is appreciated!!