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# Reactance of Wire

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#### Cookie

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What is behind the none linear drop in conductor reactance? Is it the stranding of manufacturing variants between gauges? Or something else?

For example 8 gauge and 1 gauge wire goes up in reactance, and #6 while having a lower reactance than #8 is still higher than #10

#### Lucien Nunes

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Inductive reactance (which dominates at 50Hz) is proportional to inductance. The inductance per unit length of a circuit comprising two parallel wires is proportional to arccosh(S/D) where S is the distance between centres and D the effective diameter. Constructional factors affecting these parameters include, as you mention, stranding and layup, departures from circularity and radial thickness of insulation. With real cables in real conduits, the spacing is variable so the reactance is an average anyway.

With insulation of zero thickness S=D so the inductance should follow a parabolic curve w.r.t diameter (note that gage numbers increase diameter geometrically, not arithmetically). I suspect the upwards jumps in reactance as conductor size increases correspond to steps in the insulation thickness or stranding features that locally increase S/D. They may occur in different places for cables of different voltage rating or construction.

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#### Cookie

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Best reply ever!

Question- why does reactance increase when wires are further apart, but decrease as they come closer together?

#### static zap

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Advent Win
@Lucien Nunes
So the environment the cable is in is making it's
calculated reactance vary
compared to a "neighbour" on the chart ?

..Our brains hate broken patterns..

#### Cookie

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@Lucien Nunes
So the environment the cable is in is making it's
calculated reactance vary
compared to a "neighbour" on the chart ?

..Our brains hate broken patterns..

If it helps to clarify these values are from the National Electrical Code.

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#### Lucien Nunes

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Well, the environment would make a difference, yes, but the jumps in the chart relative to AWG# will be about the manufacturing differences between one size of cable and the next that affect the spacing only, or diameter and spacing in a non-proportional way. For example, shaped conductor stranding decreases the diameter (and hence spacing, but not proportionally) relative to circular stranding, without altering the CSA.

#### Cookie

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Thats probably it. Would this table help in any way?

#### Cookie

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Well, the environment would make a difference, yes, but the jumps in the chart relative to AWG# will be about the manufacturing differences between one size of cable and the next that affect the spacing only, or diameter and spacing in a non-proportional way. For example, shaped conductor stranding decreases the diameter (and hence spacing, but not proportionally) relative to circular stranding, without altering the CSA.

I just want to say you were correct as validated by this, reactance is less of a dominating factor with smaller wire sizes at 50/60Hz:

https://www.mikeholt.com/img/product/pdf/1038225525sample.pdf

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