A research team is characterizing a sample wire whose dimensions and resistance have been measured with the following results:
• Length: l=1.50±0.01m
• Diameter: d=0.800±0.005mm
• Resistance: R=5.00±0.05Ω
Potential materials under consideration are listed below with their accepted room-temperature resistivities:
• Stainless steel: 7.2×10−7Ωm
• Nichrome: 1.1×10−6Ωm
• Constantan: 4.9×10−7Ωm
(a) Compute the cross-sectional area of the wire and its absolute uncertainty, clearly stating any assumptions you make about the propagation of uncertainty.
(b) Determine the resistivity of the sample and its uncertainty, propagating the quoted uncertainties in l, d, and R through your calculation.
(c) Using your result from part (b) and the material data provided, indicate which of the listed materials are consistent with the experimental value within the calculated uncertainty range. Explain your reasoning and suggest one additional measurement that could narrow the identification further.