In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 10 m long wire with a cross-sectional area of 1 mm²?
Practice Questions
1 question
Q1
In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 10 m long wire with a cross-sectional area of 1 mm²?
0.02 Ω
0.2 Ω
2 Ω
20 Ω
Resistance R = ρ(L/A) = 2 x 10^-8 * (10 / (1 x 10^-6)) = 0.2 Ω.
Questions & Step-by-step Solutions
1 item
Q
Q: In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 10 m long wire with a cross-sectional area of 1 mm²?
Solution: Resistance R = ρ(L/A) = 2 x 10^-8 * (10 / (1 x 10^-6)) = 0.2 Ω.
Steps: 7
Step 1: Identify the given values. The resistivity (ρ) is 2 x 10^-8 Ω·m, the length (L) of the wire is 10 m, and the cross-sectional area (A) is 1 mm².
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 resistance: R = ρ(L/A).
Step 4: Substitute the values into the formula: R = (2 x 10^-8) * (10 / (1 x 10^-6)).
Step 5: Calculate the value inside the parentheses: 10 / (1 x 10^-6) = 10,000,000.
Step 6: Multiply the resistivity by the result from Step 5: R = (2 x 10^-8) * 10,000,000.
Step 7: Calculate the final resistance: R = 0.2 Ω.
