How to detect if resistors are in parallel or series? Some circuits are easier to see which resistors are in parallel or series.  However, when faced with a more complex circuit, I can't figure out which ones are in series or parallel.
I am currently facing the following problem:

I am instructed to find the equivalent resistance; but I do not know how to determine which are in parallel or series.  Is there a particular method to do so?
 A: The trick is to look at the nodes in the circuit. A node is a junction in the circuit. Two resistor are in parallel if the nodes at both ends of the resistors are the same. If only one node is the same, they are in series. So, R1 and R2 are in parallel and R3 is in series with R1||R2.
A: Basically, you simplify, simplify, simplify. For instance, your $R_1$ and $R_2$ are simply in parallel, so you can replace them with a single resistor. Then, depending on which terminals you're measuring from, the merged resistor and $R_3$ will be in parallel or series.
A: Sometimes a bit of visualization can help, either as a mental exercise or using real objects. Picture the resistors as, lets say, ping-pong balls and the wires as stretchy string (e.g. bungee cord). Pick any two terminals, pull on them and see what happens; repeat for a different pair, etc.. You find that:


*

*The bottom terminals are the same node, because no resistor is on the path between them

*R1 and R2 are in parallel because they will end up side-by-side for at least one pair of terminals and never in line with each other.

*R3 is in series with R1/R2 because they will end up in line for at least one pair of terminals and R3 will never end up side by side with either R1 or R2.

A: The easiest method to determine series vs parallel connectivity is to do the following:
1.  If one end of R1 is connected to one end of R2 and the other end of R1 is connected to the other end of R2, then the resistors are in parallel. R1 & R2 are in parallel.
2.  If only 1 end of R2 is connected to 1 end of R3 and the other end of each resistor is not connected then R3 is in series with the parallel pair R2&R1.
