Answer:
A. 20
Explanation:
The AWG rating of the wire can be determined by applying the formula;
[tex]d_{i}[/tex] = 0.005 x [tex]92^{\frac{(36 - s)}{39}} }[/tex]
where [tex]d_{i}[/tex] is the diameter of wire in inches, and s is the diameter of wire in AWG.
Given that [tex]d_{i}[/tex] = 0.032 inches, then;
0.032 = 0.005 x [tex]92^{\frac{(36 - s)}{39}} }[/tex]
[tex]\frac{0.032}{0.005}[/tex] = [tex]92^{\frac{(36 - s)}{39}} }[/tex]
6.4 = [tex]92^{\frac{(36 - s)}{39}} }[/tex]
Find the log of both sides to have,
log 6.4 = log [tex]92^{\frac{(36 - s)}{39}} }[/tex]
log 6.4 = [tex](\frac{36 -s}{39})[/tex] log 92
[tex]\frac{log 6.4}{log92}[/tex] = [tex](\frac{36 -s}{39})[/tex]
0.410523 = [tex](\frac{36 -s}{39})[/tex]
36 - s = 0.410523 x 39
= 16.0104
⇒ s = 36 - 16.0104
= 19.9896
s = 20
Therefore, the AWG of the wire is 20.
