Effective Resistance if bent in the form a circle

[logearav]

Homework Statement

A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?

Homework Equations

I have attached the image and my attempt to solve it as told by my teacher.

Homework Equations

The Attempt at a Solution

But I don't know why the reciprocal formula is used. Please help.

 

[Stonebridge]

It's because it is equivalent to having two resistors in parallel.
The current entering at A has a choice of 2 directions.
Both involve taking a path that is 4R. That is, half the resistance of the complete wire. (Round half the circumference to B.)
So to find the combined resistance, you need to add 4R and 4R in parallel.

 

[logearav]

Thanks a lot stonebridge. Your help is very much appreciated