==== Calculator of inductance of a straight round non-magnetic wire ====
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| {{/calculator/icon_calc.png?60&nolink}} | //[[user/Stan Zurek]], Calculator of inductance of a straight round non-magnetic wire, Encyclopedia Magnetica//, \\ https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_round_wire, {updated: ~~LASTMOD~~, accessed: @YEAR@-@MONTH@-@DAY@} |
| {{/wiki/logo.png?20&nolink}} //See more: [[/Calculators of inductance]]// ||
Definition of the dimensions of a **straight round wire**
[[/file/inductance_of_straight_round_wire_png|{{/inductance_of_straight_round_wire.png}}]]
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[[/Inductance]] of a [[/straight wire]] or conductor with round (circular) cross-section can be calculated with the equations as specified below. This calculations is for a hypothetical single wire in isolation, without considering the return conductor.
//Note: Several assumptions are made for all these equations: 1) The return path is **not** considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than it radius (r << l), otherwise the calculation errors might be excessive. 3) The medium and the wire are assumed to be non-magnetic with μr ≡ 1. For magnetic wire see [[inductance_of_straight_round_magnetic_wire|Calculator of inductance of a straight round magnetic wire]]. 4) The current is uniformly distributed inside the wire (no [[/skin effect]], apart from the simplified eq. (3b)). For high-frequency inductance see [[inductance_of_straight_round_wire_vs_frequency|Calculator of inductance of a straight round wire with frequency effects]]. 5) The equations were converted here to be consistent with [[/SI units]].//
^ [[/Inductance]] of a straight round non-magnetic wire or conductor ^^^
^ //[1] Source: Edward B. Rosa, The self and mutual inductance of linear conductors, Department of Commerce and Labor, Bulletin of the Bureau of Standards, Volume 4, 1907-8, Washington, 1908// ^^^
| **(1)** \\ //Rosa [1], eq. (9), p. 305// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{r}{l} \right) $$ | (H) |
^ //[2] Source: F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570// ^^^
| **(2)** \\ //Grover [2], eq. (7), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - \frac{3}{4} \right) $$ | (H) |
^ //[3] Source: C.R. Paul. Inductance: Loop and Partial, Wiley-IEEE Press, 2009, New Jersey, ISBN 9780470461884// ^^^
| **(3a)** \\ //Paul [3], full eq. (5.18b), p. 208// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( asin \left( \frac{l}{r} \right) - \sqrt{1+ \left (\frac{r}{l} \right)^2} + \frac{r}{l} \right) $$ | (H) |
| **(3b)** \\ //Paul, [3] simplified eq. (5.18c), p. 208 (for r << l) \\ and for high-frequency (skin depth δ ≈ 0) // | $$ L ≈ \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 \right) $$ | (H) |
^ //[4] Source: Aebischer H.A., Aebischer B., Improved formulae for the inductance of straight wires. Advanced electromagnetics. 2014 Sep 8;3(1):31-43// ^^^
| **(4a)** \\ //King & Prasad [4] eq. (28), p. 34// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 + \frac{r}{l} \right) $$ | (H) |
| **(4b)** \\ //Meinke & Gundlach [4], eq. (29), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{10⋅l}{4⋅r} \right) - 1 \right) $$ | (H) |
| **(4c)** \\ //Aebischer & Aebischer [4], eq. (34), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{0.905415⋅r}{l} \right) $$ | (H) |
| where: $μ_0$ - [[/permeability of vacuum]] (H/m), $l$ - wire length (m), $r$ - wire radius (m) |||
| //Note: All these equations are based on the radius r of the wire, and in some other on-line calculators this is mistakenly assumed to be the diameter. In this interactive calculator the correct dimensions are taken into account (diameter in input, radius in calculations).// |||
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{{tag>Calculators Inductance_of_straight_round_wire Inductance_of_straight_round_conductor Circular_conductor Circular_wire}}