Finding Req - Understanding Professor's Solution

[zr95]

Homework Statement

Homework Equations

Series: Req = r1 + r2...
Parallel: 1/req = 1/r1 + 1/r2...

The Attempt at a Solution

This is my professors solution for the problem and of course without any explanation it doesn't make sense to me. Under what principle can he justify immediately adding 10 + 8?

For my solution I redrew the circuit and did:
5||20 = 4
10+4 = 14

3 || 6 = 2
2+8 = 10

10+14 = 24

Another question: Had I not redrawn the circuit I still would've gotten 14 and 10 but I would've thought they would be in parallel with each other with the way its drawn out?

I understand redrawing it is the easiest way to make sure I have it correct but there won't be enough time unless I immediately recognize what it looks like.

 

[gneill]

Under what principle can he justify immediately adding 10 + 8?

Is there any path that you can draw between a and b (following circuit pathways of course) that does not pass through both the 10 and 8 Ohm resistors? If not, they must be in series between a and b.

Another question: Had I not redrawn the circuit I still would've gotten 14 and 10 but I would've thought they would be in parallel with each other with the way its drawn out?

I understand redrawing it is the easiest way to make sure I have it correct but there won't be enough time unless I immediately recognize what it looks like.

The trick is to look at the nodes that are bridged by a short circuit. In this circuit nodes c and f are connected together via a wire. That means you are free to move all the connections at one of those nodes to the other node. Symmetry also helps here, as you can put nodes c and f together by "folding" the circuit along a line passing through d-a-b-e. Once you make that fold you've got your parallel resistor connections that you and your professor found, while the two series resistors are left at the fold.