If the resistivity of a material is 1.5 x 10^-8 Ω·m, what is the resistance of a

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Question: If the resistivity of a material is 1.5 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 0.5 mm²?

Options:

Correct Answer: 0.18 Ω

Solution:

Resistance R = ρ(L/A) = (1.5 x 10^-8)(3)/(0.5 x 10^-6) = 0.09 Ω.

If the resistivity of a material is 1.5 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 0.5 mm²?

If the resistivity of a material is 1.5 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 0.5 mm²?

Correct Answer: 0.09 Ω

Step 1: Identify the given values. The resistivity (ρ) is 1.5 x 10^-8 Ω·m, the length (L) of the wire is 3 m, and the cross-sectional area (A) is 0.5 mm².
Step 2: Convert the cross-sectional area from mm² to m². Since 1 mm² = 1 x 10^-6 m², we have 0.5 mm² = 0.5 x 10^-6 m².
Step 3: Use the formula for resistance: R = ρ(L/A).
Step 4: Substitute the values into the formula: R = (1.5 x 10^-8)(3) / (0.5 x 10^-6).
Step 5: Calculate the numerator: (1.5 x 10^-8) * 3 = 4.5 x 10^-8.
Step 6: Calculate the denominator: (0.5 x 10^-6) = 0.5 x 10^-6.
Step 7: Now divide the numerator by the denominator: R = (4.5 x 10^-8) / (0.5 x 10^-6).
Step 8: Perform the division: R = 4.5 / 0.5 x 10^-8 / 10^-6 = 9 x 10^(-8 + 6) = 9 x 10^-2 = 0.09 Ω.

Resistivity and Resistance – Understanding the relationship between resistivity, length, cross-sectional area, and resistance in a conductor.
Unit Conversion – Converting units of area from mm² to m² to ensure consistency in calculations.