So we know from using nodal analysis and

Kirchhoff's current laws that what we're looking for are the nodal voltages.

So typically with Kirchhoff's current law,

we would sum up the currents about each of our nodes, and we have

a simultaneous set of equations which have a certain number of unknowns.

In our case, this would have two unknowns, V sub 1 and V sub 2 for

the different nodes and we would then solve our two equations or

our two unknowns to find V sub 1 and V sub 2.

But in the approach that we've just taken, we've introduced another unknown.

We've introduced the current through the 6 volt source as an unknown as well

because we have no way of determining that current through the 6 volt source.

So this approach is not going to work for us in this problem and the reason for

it is because we have a voltage source, an independent voltage source which is

between two nodes, but neither of those nodes are the ground node.

So we don't have a reference voltage for

the 6 volt source from one node to another node.

So ultimately if we were to continue writing these equations,

we'd have two equations and we'd three unknowns and it would be unsolvable.

So the way we get around this is we introduce the concept of a super node.

And what this super node allows us to do is it allows us to kind of block off

that independent voltage source which is

floating up in the circuit between node 1 and node 2.

And if we do this, then we'll be able to then write our two equations about

our nodes and then we'll also be able to, actually we're going to write one

equation around a super-node and then we're going to have a second equation

which relates the nodal voltages to that 6 volt source.

So let's do this and see if we can figure out how to do this problem.