Editing Inductance (section)

====Practical formulas====
For derivation of the formulas below, see Rosa (1908).<ref name=Rosa1908>{{cite journal |first=E.B. |last=Rosa |title=The self and mutual inductances of linear conductors |journal=Bulletin of the Bureau of Standards |volume=4 |issue=2 |year=1908 |page=301 ff |publisher=[[U.S. Bureau of Standards]]|doi=10.6028/bulletin.088 |doi-access=free }}</ref>
The total low frequency inductance (interior plus exterior) of a straight wire is:

<math display=block>L_\text{DC} = 200\text{ }\tfrac{\text{nH}}{\text{m}}\, \ell \left[\ln\left(\frac{\,2\,\ell\,}{r}\right) - 0.75 \right]</math>

where 
* <math>L_\text{DC}</math> is the "low-frequency" or DC inductance in nanohenry (nH or 10<sup>&minus;9</sup>H),
* <math>\ell</math> is the length of the wire in meters,
* <math>r</math> is the radius of the wire in meters (hence a very small decimal number),
* the constant <math>200\text{ }\tfrac{\text{nH}}{\text{m}}</math> is the [[Vacuum permeability|permeability of free space]], commonly called <math>\mu_\text{o}</math>, divided by <math>2 \pi</math>; in the absence of magnetically reactive insulation the value 200 is exact when using the classical definition of ''μ''<sub>0</sub> = {{val|4|end=π|e=-7|u=H/m}}, and correct to 7 decimal places when using the [[2019 revision of the SI|2019-redefined SI value]] of ''μ''<sub>0</sub> = {{val|1.25663706212|(19)|e=-6|u=[[Henry (unit)|H]]/m}}.

The constant 0.75 is just one parameter value among several; different frequency ranges, different shapes, or extremely long wire lengths require a slightly different constant ([[#current_distribution_parameter_Y|see below]]). This result is based on the assumption that the radius <math>r</math> is much less than the length {{nowrap|<math>\ell</math>,}} which is the common case for wires and rods. Disks or thick cylinders have slightly different formulas.

For sufficiently high frequencies skin effects cause the interior currents to vanish, leaving only the currents on the surface of the conductor; the inductance for alternating current, <math>L_\text{AC}</math> is then given by a very similar formula:

<math display=block>L_\text{AC} = 200\text{ }\tfrac{\text{nH}}{\text{m}}\, \ell \left[\ln\left(\frac{\,2\,\ell\,}{r}\right) - 1 \right]</math>
where the variables <math>\ell</math> and <math>r</math> are the same as above; note the changed constant term now 1, from 0.75 above.

For example, a single conductor of a lamp cord {{val|10|u=m}} long, made of 18&nbsp;[[American wire gauge|AWG]] ({{val|1.024|u=mm}}) wire, would have a low frequency inductance of about {{val|19.67|u=µH}}, at k=0.75, if stretched out straight.