There seems to be a typo in the question. The question asks to find the resistivity, instead of resistance. Resistivity is a property of the wire and does not change when its physical dimensions change.
Answer:
(A) doubles
Explanation:
The resistivity of a wire is defined by
[tex]\rho=\dfrac{RA}{l}[/tex]
R is the resistance, A is the cross-sectional area and l is the length of the wire.
[tex]R = \dfrac{\rho l}{A}[/tex]
It follows that
[tex]R\propto\dfrac{l}{A}[/tex]
Assuming a circular cross section, the area is given by
[tex]A =\pi \dfrac{D^2}{4}[/tex]
where D is the diameter.
Then
[tex]R\propto\dfrac{l}{D^2}[/tex]
[tex]R=k\dfrac{l}{D^2}[/tex]
k is an arbitrary constant
When l and D are halved, the new resistance, R1 is
[tex]R_1=k\dfrac{0. 5l}{(0.5D)^2} =2k\dfrac{l}{D^2} = 2R[/tex]
Hence, the resistance is doubled.
