A cylindrical conductor has a length of 1 m and a radius of 0.01 m. If its resistivity is 2 x 10^-8 Ω·m, what is its resistance?

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Q: A cylindrical conductor has a length of 1 m and a radius of 0.01 m. If its resistivity is 2 x 10^-8 Ω·m, what is its resistance?

Solution: Resistance R = ρ * (L / A) = 2 x 10^-8 * (1 / (π * (0.01)²)) = 0.02 Ω.

Steps: 8

Step 1: Identify the given values. The length (L) of the cylindrical conductor is 1 meter, the radius (r) is 0.01 meters, and the resistivity (ρ) is 2 x 10^-8 Ω·m.
Step 2: Calculate the cross-sectional area (A) of the cylinder using the formula A = π * r². Substitute r = 0.01 m into the formula.
Step 3: Calculate A = π * (0.01)². This gives A = π * 0.0001 m².
Step 4: Use the value of π (approximately 3.14) to calculate A. So, A ≈ 3.14 * 0.0001 = 0.000314 m².
Step 5: Now, use the formula for resistance R = ρ * (L / A). Substitute ρ = 2 x 10^-8 Ω·m, L = 1 m, and A = 0.000314 m² into the formula.
Step 6: Calculate R = 2 x 10^-8 * (1 / 0.000314).
Step 7: Calculate 1 / 0.000314, which is approximately 3184.6.
Step 8: Multiply 2 x 10^-8 by 3184.6 to find R. This gives R ≈ 0.02 Ω.