Resistance of this circuit containing a Circular section

[Aristarchus_]

Homework Statement

A piece of wire has resistance R. The wire is cut into three parts of equal length and connected
together as shown in the figure. What will be the resistance between A and B?

Relevant Equations

Solution is 1/12 + 2/3 = 3/4ohm.

I understand that the two separate parts make 2/3, but where is 1/12 ohm coming from?

 

[haruspex]

How did R turn into $1\Omega$?
Call the two points where the straight sections meet the circle C, D. There are two parallel paths (electrically speaking) from C to D. What is the resistance of each?

 

[Aristarchus_]

How did R turn into $1\Omega$?
Call the two points where the straight sections meet the circle C, D. There are two parallel paths (electrically speaking) from C to D. What is the resistance of each?

But would we calculate then resitance in parallel(1/6 and 1/6)?

 

[Delta2]

Yes exactly, what total resistance you get if you connect two resistors of 1/6 in parallel?

 

[Aristarchus_]

Yes exactly, what total resistance you get if you connect two resistors of 1/6 in parallel?

right! Hmm... However, it is hard to picture the circuit in the way you described it. I could not come up with that sketch on my own...

 

[Delta2]

right! Hmm... However, it is hard to picture the circuit in the way you described it. I could not come up with that sketch on my own...

Yes agreed from the image of the wire with the circle in the middle your mind just doesn't think the corresponding lumped model of the two resistors of 1/3 in series with the two resistors of 1/6 which are in parallel.