Answer:
A.
Step-by-step explanation:
The resistance of a wire is given by the formula:
R = ρL/A
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
Since the wires are all aluminum, ρ cancels out:
R ~ L/A
Cross-sectional area is π*radius^2, but since we're given diameter,
A = π*(diameter/2)^2 = (π/4)*diameter^2
π/4 is a constant, so it's same across all four wires, leaving:
R ~ L/d^2
Looking at our choices:
A) an aluminum wire 10 cm in length and 3 cm in diameter
R ~ 10/(3^2) --> R ~ 10/9≈1.1
B) an aluminum wire 5 cm in length and 3 cm in diameter
R ~ 5/(3^2) --> R ~ 5/9≈0.56
C) an aluminum wire 10 cm in length and 5 cm in diameter
R ~ 10/(5^2) --> R ~ 10/25≈0.40
D) an aluminum wire 5 cm in length and 5 cm in diameter
R ~ 5/(5^2) --> R ~ 5/25≈0.20
Greatest resistance is found in the wire described by choice A.