Find the CSA of a wire with a diameter of 17/1,000 inch. ...

Name: Problem 13, Chapter 8: Electricity 1: Devices, Circuits and Materials
Uploaded: 2019-07-23T01:43:29-08:00
Duration: 5 min 40 s
Channel: Zachary Warner
Description: Find the CSA of a wire with a diameter of 17/1,000 inch.

Find the CSA of a wire with a diameter of 17/1,000 inch. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

Find the CSA of a wire with a diameter of 17/1,000 inch.
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Key Concepts

Area Calculation of a Circle

The area of a circle is calculated using the formula A = ?r², where r is the radius of the circle. This formula is fundamental in geometry and is used to determine the CSA of circular shapes, such as the cross-section of a wire.

Relationship Between Diameter and Radius

The radius of a circle is defined as half of its diameter. When a wire's diameter is provided, this relationship is used to convert the diameter to the radius, which is then substituted into the area formula to calculate the cross-sectional area.

Cross-Sectional Area (CSA) of a Wire

The cross-sectional area (CSA) of a wire represents the area of the cut face of the wire, which is typically circular. This measurement is crucial in fields such as electrical engineering and material science because it directly influences properties like resistance and current-carrying capacity.

Transcript

00:01 Our question says that the united states national electric code sets maximum safety currents for insulated copper wires of various diameters.

00:09 It is given in part in the table, and it wants us to plot the safe current density as a function of diameter, and it wants to know which wire gauge has the maximum safe current density.

00:21 And as an aside, gauge is a way of identifying wire diameter, and one mil is equal to 10 to the minus 3 inches.

00:29 So if i'd write down that's what we're given here.

00:31 1 mil is 10 to minus 3 inches.

00:33 Okay.

00:34 And we can express the magnitude of current density vector in si units by converting the diameter value in mills to inches with that conversion.

00:42 And then to put it in si units, we can convert it from inches to meters.

00:46 So let's write down with that conversion in as well.

00:50 So 1 inch is equal to 0 .025 meters.

01:08 Okay, and we can also use the fact that the current density here, j is equal to the current divided by the area, which is equal to the current divided by pi r squared.

01:28 Now let's write a better pi here.

01:37 Okay, which is equal to four times i divided by pi times the diameter squared.

01:49 So now we have a relationship between the current density, and the diameter.

01:55 So for example, the gauge 14 wire has a diameter of 64 mils, and using the conversion above, diameter is 64 mils, which using the conversion above is equal to 0 .0016 meters.

02:24 And i got that by dividing 64 mils by 1 ,000 inches, and then multiplying that by 0 .025 meters.

02:33 And then we can plot the values of j in si units versus their diameter in mills.

02:42 We'll plot that over here, and it looks something like this...

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