Circular Mils

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What is the resistance

2021-10-03 05:12:21
1 Answer
You did not provide required values to solve this question. but we will assume some of them to make it easy for you solving such types of questions.
To find the resistance of a conductor either circular or rectangular by given resistivity, length and area. we can use the following equation to find resistance:
$$R = \rho {l \over A} \tag{1}$$
$$\text{where} \, \rho = resistivity \\l=length \\A = Area$$

let assume that the bar in the given image is a copper bus-bar, as used in the power distribution panel of a high-rise office building, with the dimensions indicated in the image.
$$length = 3 ft\\width = 5in. = 5000 mils\\height= 1/2 in. = 500mils\\\rho = 10.37 CM.ohm /ft \,\text{(copper bar)}$$

To find area in circular mils from a conductor not given in circular shape, we have to use
$$1 \,CM ={\pi \over 4} sq. mils\\1sq.mil = {4\over \pi} \text{CM}$$

The area of the bar along the length can be find as
$$A_{sq} = width \times height \\= 5000mils \times 500mils\\=2.5\times10^6 sq. mils\\= (2.5\times10^6) (1 \,sq. mils)\\=(2.5\times10^6) ({4 \over \pi} \, CM)\\A_{CM} =3.185\times10^6 \, CM$$

Now putting all the values in eq. 1, we get
$$\begin{split}R &= (10.37 \,CM.\Omega /ft) {3\,ft \over 3.185\times10^6 \, CM} \\&= 9.768 \times10^{-6} \Omega \\\end{split}$$

2021-10-07 12:17:07