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'Resistivity' is usually considered to be a property of a substance, not a structure.

In the normal unit of resistivity, the length and cross-section area are divided out,

so they don't affect the 'resistivity.

In the case of your piece of wire, the only characteristic that it seems reasonable

to discuss is just plain good old 'resistance'.

I think the point of this question is to investigate the relative effects ... of a change

in length compared to the same change in diameter ... on the initial resistance of a

piece of wire.

Length:

The resistance of the sample is directly proportional to its length.

Diameter:

The resistance of the sample is inversely proportional to the cross-sectional area,

which is the same as saying 'inversely proportional to the square of the diameter'.

So, let's look at the choices listed in the question:

Change length to 1/2:

Resistance changes to 1/2 .

Change length and diameter both to1/2 :

Resistance changes by factor of 1/2 x 4 = 2

Length doubles, diameter 1/2:

Resistance changes by factor of 2 x 4 = 8 times

Length doubled, diameter doubled:

Resistance changes by factor of 2 x 1/4 = 1/2

The first and last choices both reduce the resistance.

The others both increase the resistance.

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Q: How do you reduce resistivity of a wire length and diameter should be equal or length should be halve or both should be halved or length should b doubled and diameter should be halved or diameter doub?
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