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 12.2 m, a width of 1.8 mm, and a thickness of 0.11 mm. The wire is connected to the car's 12.0 V battery and draws 7.5 A. What is the resistivity of the wire material?

Answer is given below.

Explanation:

resistance = voltage / current

R = V/I

= 12 / 7.5 = 1.6 ohm

R = pL/A

where p = resistivity

L = length, A = cross sectional area

1.6 = p*12.2 / (1.6*10^-3*0.11*10^-3)

p = 2.3*10^-8 ohm - m

so the resistivity of the material is 2.3*10^-8 ohm - m

Answer: 2.6*10^-8 Ωm

Explanation:

given

Length of the wire, l = 12.2 m

width of the wire, w = 1.8 mm

thickness of the wire, T = 0.11 mm

Potential difference of the battery, v = 12 V

Current in the battery, I = 7.5 A

Remember, Ohms law says, V = IR.

So that, R = V/I

R = 12/7.5 = 1.6 Ω

Resistivity if a material is

ρ = RA/l

ρ = [1.6 * 1.8*10^-3 * 0.11*10^-3] / 12.2

ρ = (3.168*10^-7) / 12.2

ρ = 2.596*10^-8

Therefore, the resistivity of the wire is 2.60*10^-8 Ωm