Obtain the equivalent resistance at the terminals a-b

[FBS]

Homework Statement

[PLAIN]http://img593.imageshack.us/img593/6015/251a.png

Homework Equations

for combining resistors in series: R1 + R2
for combining resistors in parallels: R1R2/(R1 + R2)

The Attempt at a Solution

I've tried redrawing the circuit many times trying to make it easier to see which are in series and which are in parallel but I cannot arrive at the answer 9.231 ohms. I think? that the 20 ohm resistor in the upper right is in series with the 10 ohm in between the two 20s, but I'm not even sure about that.

 

[tiny-tim]

Hi FBS!

Hint: which way is the current flowing thorugh that "horizontal" 10 Ω ?

 

[FBS]

I am not so sure. It looks like it could be flowing in both directions. :( Would it be flowing to the right because the 20 ohm resistor "resisted" more of the current than the 10 ohm one did?

 

[tiny-tim]

Hint2: symmetry.

 

[FBS]

I think I feel more confused than ever. I'm not sure how symmetry affects the current unless you mean the current on the opposite side of the circuit should be identical? But they all seem different to me, maybe I'm not understanding some basic principle...

[PLAIN]http://img638.imageshack.us/img638/6015/251a.png

 

[berkeman]

Think about the voltage dividers and the symmetry as tim has suggested.

When you have a voltage across two 10 Ohm resistors, what is the voltage at the midpoint? Like, if you have 2V across two 10 Ohm resistors in series, how much voltage drop is there across each? What if they were 20 Ohm resistors, would the midpoint voltage be any different?

And if you have a voltage across a resistor that is 100 Ohms, would anything be different it you made that 100 Ohm resistor out of two 50 Ohm resistors?

 

[FBS]

So it turns out I couldn't figure it out because I hadn't learned delta-wye conversions yet. D'oh. I was able to get the right answer by converting the three 10 ohm resistor Y to a triangle of 30 ohms which then let me parallel the two 20 ohm resistors with two 30s and then parallel the remaining two 30s.

[PLAIN]http://img857.imageshack.us/img857/5959/251p.png

Was Delta-Wye what you guys meant by symmetry?

 

[tiny-tim]

So it turns out I couldn't figure it out because I hadn't learned delta-wye conversions yet.

nooo … you didn't need it

Was Delta-Wye what you guys meant by symmetry?

no

let's see … now you have the equivalent resistance, can you say how much of the current goes through that "horizontal" 10 Ω resistor, and which way?