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A material is formed into a long rod with a square cross-section 0.50 cm on each side. When a 176 V voltage is applied across a 20-m length of the rod, a 4.0 A current is carried. Part A) What is the resistivity of the material? Part B) Is the material a conductor, an insulator, or a semiconductor?

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Answer:

Step-by-step explanation:

Part A:

The resistance of the rod can be calculated using Ohm's law:

R = V/I = 176 V / 4.0 A = 44 Ω

The resistance of a cylindrical conductor can be calculated using the formula:

R = ρL/A

where ρ is the resistivity of the material, L is the length of the rod, and A is the cross-sectional area of the rod. For a square cross-section, the area is given by A = (0.50 cm)^2 = 0.25 cm^2.

Substituting the given values, we get:

44 Ω = ρ (20 m) / 0.25 cm^2

Simplifying, we get:

ρ = (44 Ω x 0.25 cm^2) / (20 m) = 0.55 x 10^-6 Ω·m

Therefore, the resistivity of the material is 0.55 x 10^-6 Ω·m.

Part B:

Whether the material is a conductor, an insulator, or a semiconductor depends on its resistivity. A material with a resistivity less than about 10^-4 Ω·m is considered a conductor, while a material with a resistivity greater than about 10^8 Ω·m is considered an insulator. Materials with resistivities in between are considered semiconductors.

In this case, the resistivity of the material is 0.55 x 10^-6 Ω·m, which is much smaller than 10^-4 Ω·m. Therefore, the material is a conductor.

User Guillaume Esquevin
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