A cylindrical wire has a length of 1 m and a radius of 0.5 mm. If its resistivity is 1.68 x 10^-8 Ω·m, what is its resistance?

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Q: A cylindrical wire has a length of 1 m and a radius of 0.5 mm. If its resistivity is 1.68 x 10^-8 Ω·m, what is its resistance?

Solution: Resistance R = ρ(L/A) = 1.68 x 10^-8 * (1 / (π(0.5 x 10^-3)²)) = 0.0424 Ω.

Steps: 7

Step 1: Identify the given values. The length (L) of the wire is 1 meter, the radius (r) is 0.5 mm, and the resistivity (ρ) is 1.68 x 10^-8 Ω·m.
Step 2: Convert the radius from millimeters to meters. 0.5 mm = 0.5 x 10^-3 m.
Step 3: Calculate the cross-sectional area (A) of the wire using the formula A = πr². Substitute r = 0.5 x 10^-3 m into the formula.
Step 4: Calculate A = π(0.5 x 10^-3)². This gives A ≈ 7.854 x 10^-7 m².
Step 5: Use the formula for resistance R = ρ(L/A). Substitute ρ = 1.68 x 10^-8 Ω·m, L = 1 m, and A = 7.854 x 10^-7 m² into the formula.
Step 6: Calculate R = (1.68 x 10^-8) * (1 / (7.854 x 10^-7)).
Step 7: Perform the calculation to find R ≈ 0.0424 Ω.