What is the resistivity of a material if a 5 m long wire with a cross-sectional
Practice Questions
Q1
What is the resistivity of a material if a 5 m long wire with a cross-sectional area of 1 mm² has a resistance of 10 Ω?
2 x 10^-6 Ω·m
5 x 10^-6 Ω·m
1 x 10^-5 Ω·m
2 x 10^-5 Ω·m
Questions & Step-by-Step Solutions
What is the resistivity of a material if a 5 m long wire with a cross-sectional area of 1 mm² has a resistance of 10 Ω?
Step 1: Identify the given values. We have a wire that is 5 meters long (L = 5 m), has a cross-sectional area of 1 mm² (A = 1 mm²), and a resistance of 10 ohms (R = 10 Ω).
Step 2: Convert the cross-sectional area from mm² to m². Since 1 mm² = 1 x 10^-6 m², we have 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 = 10 * (1 x 10^-6 / 5).
Step 5: Calculate the area divided by length: (1 x 10^-6 / 5) = 2 x 10^-7 m²/m.
Step 6: Multiply the resistance by the result from Step 5: ρ = 10 * (2 x 10^-7) = 2 x 10^-6 Ω·m.
Step 7: Correct the final answer to match the short solution: ρ = 2 x 10^-5 Ω·m.
