A wire of length L and diameter D has a resistance R.
If BOTH the length and the diameter of the same wire are decreased to half of their original values, the resistivity of the new wire:

A. doubles.
B. drops to half its original value.
C. quadruples
D. drops to one quarter its original value.
E. remains the same.

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.

(A) doubles

Explanation:

The resistivity of a wire is defined by

R is the resistance, A is the cross-sectional area and l is the length of the wire.

It follows that

Assuming a circular cross section, the area is given by

where D is the diameter.

Then

k is an arbitrary constant

When l and D are halved, the new resistance, R1 is

Hence, the resistance is doubled.

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explanation:

electrical power