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Calculator of inductance of a straight rectangular non-magnetic wire
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 | Stan Zurek, Calculator of inductance of a straight rectangular non-magnetic wire, Encyclopedia Magnetica, http://e-magnetica.pl/doku.php/calculator/inductance_of_straight_round_strands_on_circle, {accessed: 2025-03-14} |
 See more: Calculators of inductance |
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S. Zurek, E-Magnetica.pl, CC-BY-4.0
Inductance of a several identical parallel straight wires or conductors, connected in parallel, without current return path can be calculated with the equations as below.
Equations
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 other dimensions (a,d,D « 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 re-arranged and converted here to be consistent with SI units, and making use of diameter rather than radius. 5) The calculations may fail for large N (e.g. N > 150), due to limitations of raising to such a large power value.
| Inductance of a several round wires or conductors distributed equally on a circle | |||
|---|---|---|---|
| [1] Source: F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570 | |||
| (The equations listed below are based on [1] but were rearranged by S. Zurek to make use of diameter rather than radius, and for SI units.) | |||
| for N wires (uniformly spaced, regular polygon) | (1) [1], full eq. (14), p. 37 | $$ L = \frac{μ_0 ⋅ l}{2⋅π} ⋅ \left( ln \left( \frac{4 ⋅ l}{\sqrt[N]{d ⋅ N ⋅ D^{N-1} }} \right) +\frac{1}{4⋅N} - 1 \right) $$ | (H) |
| for N = 3 wires (equilateral triangle) | (2) [1], full eq. (13), p. 37 | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{\sqrt[3]{d ⋅ D^2}} \right) - \frac{11}{12} \right) $$ | (H) |
| for 2 wires (one on each side of the circle) | (3) [1], full eq. (12), p. 37 | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{\sqrt{d ⋅ D}} \right) - \frac{7}{8} \right) $$ | (H) |
| for N = 1 wire (single wire, for comparison only) | (4) [1], full eq. (7), p. 35 | $$ L = \frac{μ_0 ⋅ l}{2⋅π} ⋅ \left( ln \left( \frac{4 ⋅ l}{d} \right) - \frac{3}{4} \right) $$ | (H) |
| where: $μ_0$ - permeability of vacuum (H/m), $l$ - wire length (m), $d$ - diameter (m) of the wire, $D$ - diameter (m) of the circle, $a = D ⋅ sin(π/N) $ - side length (m) of a the N-sided polygon. | |||
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