The topic of this problem is nodal analysis.

The problem is to determine the nodal equations for

each node in the circuits drawn.

In the circuits that we have,

we have a 12 volt source on the left hand side of the circuit and

a series of parallel or resisters through out the rest of the circuit.

So when we're doing nodal analysis the first thing we do is we identify

all the nodes in the circuit.

Remember that a node is a connection between two elements in the circuit.

So we have a node 1 at the left hand side of the circuit,

we have a node 2 at the top we have a node 3 at the top, a node 4 at the top,

and we always have kind of our ground node at the bottom of

the circuit which we know the voltage for already, it's 0V.

So whenever we're doing nodal analysis we have to first of all acknowledge that

when we're doing nodal analysis that we're finding the nodal voltage and

we're going to use these equations these nodal equations ultimately to

find the nodal voltages associated with a circuit.