54 lines
1.3 KiB
Markdown
54 lines
1.3 KiB
Markdown
# Circular Mil
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> A [**circular mil**](https://en.wikipedia.org/wiki/Circular_mil)
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> is a unit of area, equal to the area of a circle with a diameter of one mil
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> (one thousandth of an inch or 0.0254 mm).
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> It is equal to π/4 square mils...
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>
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> The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula:
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>
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> $$
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> A_{\rm{cmil}} = ( d_{\rm{mil}} )^{2}
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> $$
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> In square mils, the area of a circle with a diameter of 1 mil is:
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>
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> $$
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> \begin{align}
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> A &= \pi r^{2} \\
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> &= \pi \left( \frac{d}{2} \right)^{2} \\
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> &= \frac{\pi d^{2}}{4} \\
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> &= \frac{ \pi \times (1~\rm{mil})^{2} }{4} \\
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> &= \frac{\pi}{4}~\rm{mil}^{2} \\
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> &\approx 0.7854~\rm{mil}^{2} \\
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> \end{align}
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> $$
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>
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> By definition, this area is also equal to 1 circular mil, so
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>
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> $$
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> \rm{ 1~cmil = \frac{\pi}{4}~mil^{2} }
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> $$
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>
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> The conversion factor from square mils to circular mils is therefore 4/π cmil per square mil:
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>
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> $$
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> \rm{ 1~mil^{2} = \frac{4}{\pi} }~cmil
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> $$
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> The formula to calculate the area in circular mil
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> for any given AWG (American Wire Gauge) size
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> is as follows.
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> $A_{n}$ represents the area of number $n$ AWG.
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>
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> $$
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> A_{n}=\left( 5 \times 92^{(36-n)/39} \right)^{2}
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> $$
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>
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> For example, a number 12 gauge wire would use $n=12$:
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>
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> $$
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> \left( 5 \times 92^{(36-12)/39} \right)^{2}
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> = 6530~\rm{cmil}
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> $$
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