Effective Resistance if bent in the form a circle

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The problem involves calculating the effective resistance of a circular wire with a resistance of 8R between the ends of a diameter. The wire can be viewed as having two parallel paths, each with a resistance of 4R. To find the total resistance, the parallel resistance formula is applied, combining the two 4R resistances. This results in an effective resistance of 2R between points A and B. The discussion emphasizes understanding the use of the reciprocal formula in parallel resistor calculations.
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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.

 

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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.
 
Thanks a lot stonebridge. Your help is very much appreciated
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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