I am confused with this?

Question

The resistance of a wire is R. It is bent at the middle by 180 degrees and both the ends are twisted together to make a shorter wire. The resistance of the new wire is?

 

a. R/2

b. R/4

c. R/8

d. 2R

Answer 1

Another way to look at this:

 

Consider the formula

R = ρL/A,

where

ρ = resistivity
L = length
A = cross sectional area

 

When you combine ends, L is reduced to L/2 and A is increased to 2A.  Then

 

R' = ρ(L/2)/(2A) = (1/4)(ρL/A) = R/4

Answer 2

Resistance of a wire is proportional to length, so each half has resistance R/2.  We then effectively connect these in parallel, cutting resistance in half again for a result of R/4.