Final answer:
Resistance of a wire is influenced by its length and cross-sectional area. If the diameter is doubled while keeping the length constant, the new resistance will be one-fourth of the original. However, more details are needed to answer the initial question on the resistance of a wire loop of radius b.
Step-by-step explanation:
The student's question is about the resistance of concentric circular loops of radii b and 2b, made of the same type of wire. Since the question is related to circular wire loops and their electrical properties, it falls within the realm of Physics which often involves calculations related to electric circuits and electromagnetism.
For a wire of a given material, the resistance is directly proportional to the length and inversely proportional to the cross-sectional area. When the diameter is doubled, the cross-sectional area becomes four times larger because area is proportional to the square of the diameter for a circular cross-section. Consequently, if the original resistance is R, the new resistance will be R/4.
However, to address the student's initial question regarding the total resistance of the wire loop of radius b, more information is needed regarding the properties of the wire such as its resistivity and length to accurately determine resistance using the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.