What is the diameter, in inches, of 2,000 kcmil wire?
The Correct Answer and Explanation is:
To find the diameter of a 2,000 kcmil (thousand circular mils) wire, we can use the relationship between the area (in circular mils) and the diameter of a wire.
Step-by-Step Process:
- Understanding Circular Mils:
- The unit “circular mil” (kcmil) is a measure of cross-sectional area used in the wire industry. One circular mil is the area of a circle with a diameter of one mil (1/1000 of an inch).
- The cross-sectional area in circular mils (CM) is given by the formula:
[
A = D^2
]
where (A) is the area in circular mils and (D) is the diameter of the wire in mils.
- Relating the Kcmil to Circular Mils:
- 1 kcmil = 1,000 circular mils. Therefore, 2,000 kcmil = 2,000,000 circular mils.
- Formula for Diameter:
- To find the diameter of a wire, we rearrange the area formula:
[
D = \sqrt{A}
]
where (D) is the diameter in mils and (A) is the area in circular mils.
- Substitute the Area:
- For a 2,000 kcmil wire, the area is 2,000,000 circular mils:
[
D = \sqrt{2,000,000} = 1414.21 \text{ mils}
]
- Converting Mils to Inches:
- Since 1 inch = 1,000 mils, we convert the diameter to inches:
[
D = \frac{1414.21}{1,000} = 1.414 \text{ inches}
]
Final Answer:
The diameter of a 2,000 kcmil wire is approximately 1.414 inches.
Explanation:
This calculation follows from the principle that the area of a circular wire cross-section (in circular mils) is proportional to the square of its diameter. By using the standard formula for the area of a circle and converting the result from circular mils to inches, we arrive at the diameter of a 2,000 kcmil wire. This is a useful measurement in various industries, including electrical engineering, where wire sizes are typically specified in kcmil.