Final answer:
To find the smallest radius of copper wire that can be used in the extension cord, we need to calculate the power dissipated in the cord and compare it to the manufacturer's recommendation. Using the information provided, we can calculate the power dissipation per meter length of the cord and find the smallest radius of the copper wire.
Step-by-step explanation:
To find the smallest radius of copper wire that can be used in the extension cord, we need to calculate the power dissipated in the cord. The power dissipated can be found using the formula P = I^2 * R, where P is the power, I is the current, and R is the resistance.
In the given problem, it is not specified what the length of the extension cord is. Therefore, we cannot directly calculate the power dissipated in the cord. We can only calculate the power dissipation per meter length of the cord.
Using the information provided in Conceptual Example 7, we can calculate the power dissipation per meter length of the cord as follows: (a) P = I^2 * R = (5.00 A)^2 * 0.0600 Ω = 1.50 W/m; (b) P = I^2 * R = (5.00 A)^2 * 0.300 Ω = 75.00 W/m.
Therefore, the manufacturer's recommendation is to have a maximum power dissipation of 2.00 W/m. So, to find the smallest radius of copper wire that can be used, we need to calculate the resistance per meter length of the wire using the formula R = ρ * (L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire.
Since the resistivity of copper is known (1.68 × 10^-8 Ω·m), we can rearrange the formula to solve for A: A = ρ * (L/R). Substituting the values for ρ, L, and R, we get A = (1.68 × 10^-8 Ω·m) * (1 m) / (2.00 W/m) = 8.40 × 10^-9 m^2. Finally, we can find the radius using the formula of the area of a circle: A = π * r^2. Rearranging the formula, we get r = √(A/π) = √((8.40 × 10^-9 m^2)/π) ≈ 1.54 × 10^-4 m.