Are the 10 ohm and 20 ohm resistors in this circuit truly parallel?

[breez]

So there is a circuit in my physics book which looks like

[img=http://img177.imageshack.us/img177/4127/circuitcz2.th.gif]

The problem asks for the current in the interconnecting wire between the 2 wires with the 2 resistors.

I solved this using loop rules, but the book shows a shortcut by using equivalent resistance. The book states the top 10 ohm and 20 ohm resistors are parallel and the bottom two are in parallel as well. However, I am confused as how this is possible. There are other paths between the start and end node points of the 10 and 20 ohm resistors. How can they be in parallel?

I was thinking this was a special case maybe, because normally they shouldn't be parallel, but the symmetry of the arrangement means the voltage at end points of the resistor pairs are the same, hence making them essentially parallel.

 

[f95toli]

Yes, they are parallel.
I suspect that it is the horizontal line that is bothering you, but the lines connecting the resistors do not "exist", is it just a way of drawing the schematic and they merely indicate how the components are connected together. Both pairs of resistors share a common "in"- and "output" which means that they are connected in parallel.

 

[breez]

but it looks that they don't share a common out? The top 10 ohm resistor has a split in its path.

 

[mikelepore]

If one is connected between some point A and some point B, and the other is also connected between point A and point B, then they are in parallel, regardless of anything else. The same voltage is across them at all times.

You have ((the top 10 ohms in parallel with the top 20 ohms) in series with (the bottom 20 ohms in parallel with the bottom 10 ohms)).