Question

A rear window defroster consists of a long, flat wire bonded to the inside surface of the window. When current passes through the wire, it heats up and melts ice and snow on the window. For one window the wire has a total length of 12.0 m, a width of 1.8 mm, and a thickness of 0.12 mm. The wire is connected to the car's 12.0 V battery and draws 12.0 A. What is the resistivity of the wire material?

Answer 1

Given

Length of wire, \(1=12 \mathrm{~m}\)

Area of wire, \(\mathrm{A}=1.8 \times 10^{-3} \times 0.12 \times 10^{-3}=0.216 \times 10^{-6} \mathrm{~m}^{2}\)

Voltage, \(\mathrm{V}=12 \mathrm{~V}\)

Current, \(\mathrm{I}=12 \mathrm{~A}\)

Resistivity

$$ \rho=R \frac{A}{l}=\frac{V A}{I} \frac{12 V \times 0.216 \times 10^{-6} \mathrm{~m}^{2}}{12 A \times 12 \mathrm{~m}}=1.8 \times 10^{-8} \Omega m $$