Answer: Resistance = (1.7 x 10⁻⁸ ohm-meters) x (450 ft x 0.3048 meters/ft) / (A)
Step-by-step explanation:
To find the resistance of a wire, we can use the formula:
Resistance = (Resistivity x Length) / Cross-sectional Area
1. First, let's find the cross-sectional area of the 2 AWG copper conductor. The AWG (American Wire Gauge) system is a standard for wire sizes. For a 2 AWG wire, the diameter is approximately 0.2576 inches.
2. The cross-sectional area (A) of a wire can be calculated using the formula for the area of a circle: A = πr², where r is the radius. The radius (r) is half of the diameter.
r = 0.2576 inches / 2 = 0.1288 inches
A = π(0.1288 inches)²
3. Now we have the cross-sectional area in square inches. To convert it to square feet, we divide by 144 (since there are 144 square inches in a square foot):
A = π(0.1288 inches)² / 144 square inches/square foot
4. Next, we need to find the resistivity of copper. The resistivity of a material is a measure of its resistance to electrical current. For copper, the resistivity is approximately 1.7 x 10⁻⁸ ohm-meters.
5. Now we can calculate the resistance using the formula:
Resistance = (Resistivity x Length) / Cross-sectional Area
Resistance = (1.7 x 10⁻⁸ ohm-meters) x (450 ft x 0.3048 meters/ft) / (A)
Make sure to use the correct units for length (feet to meters) to match the resistivity unit.
6. Substitute the value of A into the formula:
Resistance = (1.7 x 10⁻⁸ ohm-meters) x (450 ft x 0.3048 meters/ft) / (A)
7. Finally, calculate the resistance using the values obtained:
Resistance = (1.7 x 10⁻⁸ ohm-meters) x (450 ft x 0.3048 meters/ft) / (A)
Remember to substitute the value of A that we calculated earlier.
This calculation will give you the resistance of the 2 AWG copper conductor.