Final answer:
To find the resistance of a 22.0 m long copper wire with a 2.05 mm diameter, calculate the cross-sectional area and use the resistivity of copper to compute the resistance, which in this case, would be approximately 1.123 ohms.
Step-by-step explanation:
To calculate the resistance of a piece of copper wire with a given length and diameter, we use the formula for resistance of a conductor: R = ρL/A. In this formula, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
The resistivity (ρ) of copper at room temperature is typically about 1.68 × 10⁻⁸ Ω·m. The diameter (d) of the wire is 2.05 mm, which gives a radius (r) of 1.025 mm or 1.025 × 10⁻³ m. The area (A) can be calculated using the formula for the area of a circle: A = πr². Thus, the resistance for a 22.0 m long copper wire can be calculated as follows:
Calculate the cross-sectional area: A = π(1.025 × 10⁻³ m) ²
= 3.1416 × (1.050625 × 10⁻¶ m²)
= 3.301 × 10⁻¶ m²
Calculate the resistance: R = 1.68 × 10⁻⁸ Ω·m × 22.0 m / 3.301 × 10⁻¶ m²
= 1.123 Ω