Verified Answer :

  • The American Wire Gauge (AWG) system defines wire thickness, where higher numbers indicate thinner wires and smaller cross-sectional areas.
  • Standard reference values show that a 10 AWG wire has an area of 10,380 cmil.
  • Applying the standard conversion factor for gauge changes, a 12 AWG wire has an area of approximately 6,530 cmil.
  • The correct choice among the provided options is 6,530, corresponding to option (a).
  • The final answer is \(\boxed{a}\).

Explanation

  1. Understanding the AWG system

The American Wire Gauge (AWG) is a standardized system for specifying the cross-sectional area of round, solid, nonferrous electrical conductors. In this system, the gauge number \(n\) is inversely related to the wire's diameter and cross-sectional area: as the gauge number increases, the wire becomes thinner, and its cross-sectional area decreases. The cross-sectional area is expressed in circular mils (cmil), where 1 circular mil is the area of a circle with a diameter of 0.001 inches. The area \(A_n\) for a gauge \(n\) can be calculated using the formula \(A_n = 10^{\frac{36-n}{10}} \times 1000\) cmil.

  1. Calculating the area of 12 AWG wire

A useful reference point in the AWG system is that a 10 AWG conductor has a cross-sectional area of approximately \(10,380\) cmil. The relationship between adjacent gauges follows a geometric progression. Specifically, a reduction of 3 gauge numbers results in approximately a doubling of the cross-sectional area (a factor of \(2\)), and a reduction of 10 gauge numbers corresponds to a change by a factor of 10. To find the area of a 12 AWG wire, we can relate it to the 10 AWG reference. Since 12 AWG is 2 gauges smaller than 10 AWG, we apply the factor of \(2^{-\frac{12-10}{3}} = 2^{-\frac{2}{3}} \approx 0.62996\). Multiplying the 10 AWG area by this factor: \(10,380 \times 0.62996 \approx 6,539\) cmil. This value matches the standard industrial table value for 12 AWG wire.

  1. Selecting the correct option

Comparing the calculated result of approximately 6,530 cmil to the given options:

A6,530
B26,240
C10,380
D6,350

The correct value for a 12 AWG conductor is 6,530 cmil. Therefore, option (a) is the correct answer. The final answer is \(\boxed{a}\).

Examples

In electrical engineering and residential wiring, selecting the correct wire gauge is critical for safety and efficiency. For example, when installing a standard household circuit, an electrician might choose 12 AWG wire because it can safely carry 20 amperes of current. Knowing that the cross-sectional area is approximately 6,530 circular mils helps in understanding the current-carrying capacity and the resistance characteristics of the wire, ensuring that the circuit breaker protects the wiring properly against overheating.