Does the resistance change with the length of the wire?
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How would the resistance of a wire change if the length …
But if we're looking at skin effect, the picture changes. The cross-sectional area is practically irrelevant because the "skin depth" is next to nothing. Instead of cross-sectional area, loss to resistance is going to be inversely proportional to the amount of copper through which the signal actually passes--that is, it's going to be inversely proportional to the cable's surface area--or, speaking in cross-sectional terms, its perimeter. A 24 AWG wire has a diameter of .0201 inch, and a 22 AWG wire has a diameter of .0253 inch. Since the perimeters are simply these numbers each multiplied by pi, we can see the ratio of perimeters without doing that multiplication. The 22 AWG is "bigger" than the 24 by .0253/.0201, or a factor of 1.259. When we were concerned with area of the cross-section rather than perimeter, the ratio of circular mils was much steeper: 640.4/404, making the 22 AWG "bigger" by a factor of 1.585. Instead of the use of 22 AWG dropping resistance to about 63% of the 24 AWG wire's resistance, as happens at DC, it drops resistance only to about 80% of the 24 AWG's value.
What is American Wire Gage (AWG), and Why Does it …
In long interconnection runs, the attenuation which results from, among other things, the resistance of the center conductor, will eventually become sufficient to harm signal quality; but for runs of moderate length, this is rarely a concern. Consequently, wire gage has some significance to signal quality, but is not the primary consideration. As with analog audio, however, there is a secondary sense in which wire gage is relevant to cable design; the cable's characteristic impedance is tied to its inductance and capacitance, and wire gage affects both of these because the center conductor must be in proper proportion to the other physical dimensions of the cable. If we stick a 16 AWG conductor into the center of an RG-6 cable where an 18 AWG conductor belongs, we wind up with our characteristic impedance too low; if we stuck a 20 AWG conductor in that same spot, characteristic impedance would be too high. So, while there may be no strong consideration affecting the specific choice of wire gage in most applications, it is nonetheless important that all of the cable's internal dimensions be in the right proportions to one another, and that includes the gage of the center conductor.
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