How Do Resistors and Nodes Function in a Parallel Circuit?

[07jfortune]

Homework Statement

http://img487.imageshack.us/img487/2263/physicsqh1.png
Shot at 2007-07-23

Homework Equations

I=V/R
V=IR
R=V/I
P=VI
P=(I^2)(R)
P=(V^2)/R

The Attempt at a Solution

Just a Quick Question, are both of the 3 Ohms parallel?? as well as the 6hom and the 12 Ohm?

Also what exactly do nodes do (there should be little dots on the corners of the top and bottom diagonals "\/" and the "^"

 

[Homo sapiens sapiens]

The two 3ohm resistors aren't connected in parallel, in order to have two resistors in parallel their terminal must be the same, that is they must be connected between the same two nodes. A node is a portion of the circuit were the electric potential is the same everywhere, that is a wire were there isn't a potential difference. To analyze this circuit you could associate the left 3ohm resistor with the 6ohm resistor and replace it by an equivalent 3+6=9ohm resistor, because they are in series, and you could associate the 12ohm and the right 3ohm resistor too, the same way. Then you would get three resistors in parallel.