If the resistivity of copper is 1.68 x 10^-8 Ω·m, what is the resistance of a copper wire of length 100 m and diameter 1 mm?

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Q: If the resistivity of copper is 1.68 x 10^-8 Ω·m, what is the resistance of a copper wire of length 100 m and diameter 1 mm?

Solution: Resistance R = ρ * (L / A) = 1.68 x 10^-8 * (100 / (π * (0.5 x 10^-3)²)) = 0.168 Ω.

Steps: 7

Step 1: Identify the given values. The resistivity (ρ) of copper is 1.68 x 10^-8 Ω·m, the length (L) of the wire is 100 m, and the diameter is 1 mm.
Step 2: Convert the diameter from mm to meters. 1 mm = 1 x 10^-3 m.
Step 3: Calculate the radius of the wire. The radius (r) is half of the diameter, so r = 0.5 x 10^-3 m.
Step 4: Calculate the cross-sectional area (A) of the wire using the formula A = π * r². Substitute r = 0.5 x 10^-3 m into the formula.
Step 5: Calculate A = π * (0.5 x 10^-3)². This gives you the area in square meters.
Step 6: Use the resistance formula R = ρ * (L / A). Substitute the values of ρ, L, and A into the formula.
Step 7: Perform the calculation to find the resistance R.