What is the resistivity of a material if a wire of length 2 m and cross-sectional area 1 mm² has a resistance of 4 ohms?
Correct Answer: 4 x 10^-6 Ω·m
- Step 1: Identify the given values. We have a wire with a length (L) of 2 meters, a cross-sectional area (A) of 1 mm², and a resistance (R) of 4 ohms.
- Step 2: Convert the cross-sectional area from mm² to m². 1 mm² = 1 x 10^-6 m², so A = 1 x 10^-6 m².
- Step 3: Use the formula for resistivity (ρ): ρ = R * (A / L).
- Step 4: Substitute the values into the formula: ρ = 4 * (1 x 10^-6 / 2).
- Step 5: Calculate the area divided by length: 1 x 10^-6 / 2 = 0.5 x 10^-6.
- Step 6: Multiply by the resistance: ρ = 4 * (0.5 x 10^-6) = 2 x 10^-6.
- Step 7: Write the final answer: The resistivity of the material is 2 x 10^-6 Ω·m.
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