==== Calculator of inductance of a straight rectangular non-magnetic wire ====
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| {{/calculator/icon_calc.png?60&nolink}} | //[[user/Stan Zurek]], Calculator of inductance of a straight rectangular non-magnetic wire, Encyclopedia Magnetica//, \\ https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_rectangular_wire, {accessed: @YEAR@-@MONTH@-@DAY@} |
| {{/wiki/logo.png?20&nolink}} //See more: [[/Calculators of inductance]]// ||
Definition of the dimensions of a **straight rectangular wire**
[[/file/inductance_of_straight_rectangular_wire_png|{{/inductance_of_straight_rectangular_wire.png}}]]
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[[/Inductance]] of a [[/straight wire]] or conductor with a rectangular or square cross-section can be calculated withe the equations as specified below.
//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 its sides (a,b << l), otherwise the calculation errors might be excessive. 3) The medium and the wire are assumed to be non-magnetic with μr ≡ 1. 3) The current is uniformly distributed inside the wire (no [[/skin effect]]). 4) The equations were converted here to be consistent with [[/SI units]].//
^ Inductance of a straight rectangular 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// ^^^
| **(1a)** \\ //Rosa [1], full eq. (21), p. 315// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{a+b} \right) + \frac{1}{2} + \frac{0.2235⋅(a+b)}{l} \right) $$ | (H) |
| **(1b)** \\ //Rosa [1], simplified eq. (21), p. 315// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{a+b} \right) + \frac{1}{2} \right) $$ | (H) |
^ //[2] Source: F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570// ^^^
| **(2a)** \\ //Grover [2], full eq. (9), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{a+b} \right) + \frac{1}{2} - G(a,b) \right) $$ | (H) |
| **(2b)** \\ //Grover [2], simplified eq. (9), p. 35// | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{2⋅l}{a+b} \right) + \frac{1}{2} - G_{half} \right) $$ | (H) |
| where: $μ_0$ - [[/permeability of vacuum]] (H/m), $l$ - wire length (m), $a$ and $b$ - side lengths (m) of the rectangular cross-section, $G(a,b)$ - Grover function of Table 3 [2] (unitless) approximated here with 6th degree polynomial as listed below, $G_{half} = 0.00125 $ - a constant set to half of the peak value of the Grover function of Table 3 (unitless), the Grover function depends on the ratio $r = a/b$ or $r = b/a$ (whichever ratio gives the result between 0 and 1), and is approximated here with the following 6th degree polynomial with the intercept forced to 0, just for ease of implementation (rather than using the full Grover's look-up table): |||
| $G(a,b) = -0.15627 ⋅ r^6 +0.54511 ⋅ r^5-0.75699 ⋅ r^4+0.53460 ⋅ r^3-0.20147 ⋅ r^2+0.03677 ⋅ r + 0 $ || (unitless) |
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{{tag>Calculators Inductance_of_straight_rectangular_wire Inductance_of_straight_rectangular_conductor Inductance_of_straight_square_wire Inductance_of_straight_square_conductor}}