A student investigates an unmarked

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

A student investigates an unmarked, uniform cylindrical wire at 20 ∘ ⁣C20\,^{\circ}\!\text{C}. The wire is l=2.00 ml = 2.00\,\text{m} long and has a diameter of d=1.20 mmd = 1.20\,\text{mm}. With a digital multimeter, the student measures the resistance of the wire to be R=1.28  ΩR = 1.28\;\Omega. A table of room-temperature resistivity values for several common metals is provided: • Copper: 1.68×10−8  Ω m1.68\times10^{-8}\;\Omega\,\text{m} • Aluminum: 2.82×10−8  Ω m2.82\times10^{-8}\;\Omega\,\text{m} • Brass: 6.0×10−8  Ω m6.0\times10^{-8}\;\Omega\,\text{m} • Nichrome: 1.10×10−6  Ω m1.10\times10^{-6}\;\Omega\,\text{m} (a) Calculate the cross-sectional area of the wire. (b) Determine the resistivity of the metal using the measured quantities. (c) Using the data table, identify the most likely metal and justify your choice quantitatively.

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