Are these resistors in series or parallel?

[ainster31]

Homework Statement

Ignore the wires that go out of the image.

Homework Equations

The Attempt at a Solution

At first I thought they were in series because they're all lined up. But why can't the 4 kilo-ohm resistor and 12 kilo-ohm resistor be in parallel with the 6 kilo-ohm resistor where A and B are the two nodes? Does it depend on the polarity of the resistors?

 

[tiny-tim]

hi ainster31!

Ignore the wires that go out of the image.

sorry, but that's virtually impossible …

in particular, we need to know whether there's something important attached to that sticky-out line between the 4 kΩ and the 12 kΩ

At first I thought they were in series because they're all lined up.

the equation for being in series depends on them all having the same current through them, in the same direction

how can that happen here? (with no battery in that loop)

 

[CWatters]

At first I thought they were in series because they're all lined up. But why can't the 4 kilo-ohm resistor and 12 kilo-ohm resistor be in parallel with the 6 kilo-ohm resistor where A and B are the two nodes?

Assuming the lines that go off the image go nowhere then...

If A and B are the two nodes of concern then they ARE exactly as you describe. The 4K and 12K are in series with each other and the pair are in parallel with the 6k.

Does it depend on the polarity of the resistors?

No.

Two components are in series if they share one (and only one) node with each other and no other component. For example the 4k and 12K share a common node (the one between them) with each other and no other component (you said to ignore the line going off the image).

Components are in parallel if they share two nodes.

 

[phinds]

Does it depend on the polarity of the resistors?

Just FYI, passive resistors such as are shown in your diagram don't HAVE a polarity.