Final answer:
A wire with the same material and either half the length or √2 times the diameter of the original would have half the resistance, resulting in 0.15 ohms.
Step-by-step explanation:
The student asked which wire of the same material as the original 40 cm long and 2.0 mm diameter wire with a resistance of 0.30 ohms would have a resistance of 0.15 ohms.
To find the required dimensions of the new wire, we can use the relationship between resistance (R), resistivity (ρ), length (L), and cross-sectional area (A) of the wire, given by the equation R = ρ * (L/A).
Because the resistance is halved and the material is the same (hence, resistivity is constant), either the length must be halved or the area must be doubled.
Doubling the area can be achieved by increasing the diameter by a factor of √2.
Therefore, a wire that is either 20 cm long with a diameter of 2.0 mm or 40 cm long with a diameter of approx 2.83 mm (2.0 mm * √2) would have the desired resistance of 0.15 ohms, assuming the same environmental conditions and that the wire has a uniform cross-section and is made of the same material.