If the resistivity of a material is 2 x 10^-8 Ω·m and the wire has a length of 3

If the resistivity of a material is 2 x 10^-8 Ω·m and the wire has a length of 3 m and a cross-sectional area of 0.5 mm², what is the resistance?

If the resistivity of a material is 2 x 10^-8 Ω·m and the wire has a length of 3 m and a cross-sectional area of 0.5 mm², what is the resistance?

Correct Answer: 0.12 Ω

Step 1: Identify the given values. The resistivity (ρ) is 2 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 A = 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 = 2 x 10^-8 * (3 / (0.5 x 10^-6)).
Step 5: Calculate the value inside the parentheses: 3 / (0.5 x 10^-6) = 3 / 0.5 x 10^-6 = 6 x 10^6.
Step 6: Now multiply: R = 2 x 10^-8 * 6 x 10^6.
Step 7: Perform the multiplication: R = 12 x 10^-2 = 0.12 Ω.

Ohm's Law and Resistance Calculation – The question tests the understanding of how to calculate resistance using the formula R = ρ * (L / A), where ρ is resistivity, L is length, and A is cross-sectional area.
Unit Conversion – The question requires converting the cross-sectional area from mm² to m² to ensure consistent units in the calculation.