calculator:inductance_of_straight_round_wire
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Calculator of inductance of a straight round wire
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Inductance of a straight wire or conductor with round (circular) cross-section can be calculated withe the equations as specified below.
| [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 | ||
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| (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 μr ≡ 1 (for magnetic wire see Calculator of inductance of a magnetic straight round wire), 3) the current is uniformly distributed (no skin effect, for high-frequency inductance see Calculator of inductance of a straight round wire at high frequency). The equations were converted here to be consistent with SI units. | ||
calculator/inductance_of_straight_round_wire.1736343250.txt.gz · Last modified: 2025/01/08 14:34 by stan_zurek