Final answer:
The resistance to the flow of electricity in a wire varies inversely to the square of the diameter of the wire.
Step-by-step explanation:
The statement is true: the resistance to the flow of electricity in a wire varies inversely to the square of the diameter of the wire.
According to Ohm's Law, the resistance (R) of a wire is directly proportional to its length (L) and resistivity (ρ), and inversely proportional to its cross-sectional area (A).
Mathematically, R = (ρ * L) / A. Since the diameter of a wire is directly related to its cross-sectional area (A = π * (d/2)^2), doubling the diameter of a wire would result in halving its cross-sectional area, and vice versa. Therefore, the resistance to the flow of electricity in a wire varies inversely to the square of the diameter of the wire.