Final answer:
To find the resistance of 27.2 m of copper wire with a 2.05 mm diameter, you must calculate the cross-sectional area and then use the resistivity of copper along with the length of the wire to calculate the resistance using the formula R = ρ(L/A).
Step-by-step explanation:
We are asked to find the resistance of a 27.2-meter length of copper wire with a diameter of 2.05 mm. The formula to calculate resistance is R = ρ(L/A), where ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
First, we convert the diameter (d) of the wire to meters to get a radius (r = d/2), then we calculate the cross-sectional area (A) using the formula A = πr². With the cross-sectional area known, we use the length of the wire and the resistivity of copper (ρ = 1.72×10⁻⁸ Ω·m) to find the resistance.
Here is the step-by-step calculation:
- Convert the diameter to meters: d = 2.05 mm = 0.00205 m
- Calculate the radius: r = d/2 = 0.001025 m
- Calculate the cross-sectional area: A = πr²
- Calculate the resistance: R = (1.72×10⁻⁸ Ω·m)(27.2 m) / (π(0.001025 m)²)
After carrying out these calculations, you will arrive at the resistance of the wire in ohms (Ω).