Differences

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--- calculator:inductance_of_straight_round_wire [2025/01/08 14:34] – stan_zurek
+++ calculator:inductance_of_straight_round_wire [2025/02/08 17:13] (current) – stan_zurek
@@ Line 1: / Line 1: @@
-==== Calculator of inductance of a straight round wire ====
+==== Calculator of inductance of a straight round non-magnetic wire ====
-{{page>insert/todo}}
+<box 100% #efffef>
+|< 100% 10% 90% >|
+|  {{/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]]//  ||
+</box>
-{{page>insert/calc}}
-<WRAP lo right>//[[https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_round_wire|[open]]]//</WRAP>
+<box 30% right #f0f0f0>
+Definition of the dimensions of a **straight round wire**
+[[/file/inductance_of_straight_round_wire_png|{{/inductance_of_straight_round_wire.png}}]]
+{{page>insert/by_SZ}}
+</box>
-[[/Inductance]] of a [[/straight wire]] or conductor with round (circular) cross-section can be calculated withe the equations as specified below.
+[[/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.
 <HTML>
@@ Line 123: / Line 130: @@
            <OPTION value="1e-2">(cm)</OPTION>
            <OPTION value="1e-3" selected>(mm)</OPTION>
-        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><br>
@@ Line 162: / Line 169: @@
            <OPTION value="1e6" selected>(μH)</OPTION>
            <OPTION value="1e9">(nH)</OPTION>
-        </SELECT> <i>Paul, eq. (3a)</i><br>
+        </SELECT> <i>Paul, full eq. (3a)</i><br>
 <b><i>L</i></b> = <input type="text" name="result3b" size="10" maxlength="10">
@@ Line 170: / Line 177: @@
            <OPTION value="1e6" selected>(μH)</OPTION>
            <OPTION value="1e9">(nH)</OPTION>
-       </SELECT>  <i>Paul, eq. (3b)</i><br>
+       </SELECT>  <i>Paul, simplified eq. (3b)</i><br>
 <b><i>L</i></b> = <input type="text" name="result4a" size="10" maxlength="10">
@@ Line 202: / Line 209: @@
            <OPTION value="1e6" selected>(μH)</OPTION>
            <OPTION value="1e9">(nH)</OPTION>
-        </SELECT> <b>Average of all above</b> <br><br>
+        </SELECT> <b>Average of all above</b>
  </form>
@@ Line 211: / Line 218: @@
 <WRAP lo>
-^  [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  ^^^
+//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 μ<sub>r</sub> ≡ 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]].//
-|  **(1)** \\ //Rosa [1], eq. (9), p. ??//  |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{r}{l}  \right) $$  |  (H)  |
-^  //[2] Source: F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570//  ^^^
-|  **(2)** \\ //Grover [2], eq. (7), p. ??//  |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - \frac{3}{4} \right) $$  |  (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. ??//   |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( asin \left( \frac{l}{r} \right) - \sqrt{1+ \left (\frac{r}{l} \right)^2} + \frac{r}{l} \right) $$  |  (H)  |
-|  **(3b)** \\ //Paul, [3] simplified eq. (5.18c), p. ?? \\ for r << l \\ and for very high-frequency (infinitely thin skin depth) //  |  $$ L_{wire,round} ≈ \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 \right) $$  |  (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. ??//  |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{r} \right) - 1 + \frac{r}{l} \right) $$  |  (H)  |
-|  **(4b)** \\ //Meinke & Gundlach [4], eq. (29), p. ??//  |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{10⋅l}{4⋅r} \right) - 1 \right) $$  |  (H)  |
-|  **(4c)** \\ //Aebischer & Aebischer [4], eq. (34), p. ??//  |  $$ L_{wire,round} = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{l+\sqrt{l^2 + r^2}}{r} \right) + \frac{1}{4} - \frac{\sqrt{l^2 + r^2}}{l} + \frac{0.905415⋅r}{l}  \right) $$  |  (H)  |
-| where: $μ_0$ - [[/permeability of vacuum]] (H/m), $l$ - wire length (m), $r$ - wire radius (m)   |||
-| //Note: Several assumptions are made for  all these equations: 1) the length of the wire is significantly longer than it radius, 2) the medium and the wire are assumed to be non-magnetic with μ<sub>r</sub> ≡ 1 (for magnetic wire see [[inductance_of_magnetic_straight_round_wire|Calculator of inductance of a magnetic straight round wire]]), 3) the current is uniformly distributed (no [[/skin effect]], for high-frequency inductance see [[inductance_of_straight_round_wire_at_high-frequency|Calculator of inductance of a straight round wire at high frequency]]). The equations were converted here to be consistent with [[/SI units]].//   |||
 </WRAP>
+^  [[/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).//   |||
+<box 100% #efffef>↑</box>
+{{page>insert/paypal}}
-{{tag>Calculators Inductance_of_straight_wire Inductance_of_straight_conductor}}
+{{tag>Calculators Inductance_of_straight_round_wire Inductance_of_straight_round_conductor Circular_conductor Circular_wire}}