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If the resistivity was restored to its original value and instead the length of the conductor decreased by a factor of 4, what would the value of the new resistance be, in ohms?

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The resistance would decrease by a factor of 4.

What is the resistance?

We know that the resistance is directly proportional to the length of the wire and inversely proportional to the cross sectional area of the wire.

Thus;

R = ρl/A

R= resistance

ρ = resistivity

l = length

A = area

When we decrease the length by a factor of 4

R2 =  ρl/4/A

Then;

R2/R1 = ρl/4/A/ ρl/A

R2/R1 =A/ρl * ρl/4A

R2/R1 = 1/4

Hence, the resistance would decrease by a factor of 4.

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