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Calculator of inductance of a straight round non-magnetic wire
 See more: Calculators of inductance. |
 This section is an interactive calculator. |
Inductance of a straight wire or conductor with round (circular) 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 it radius (r « l), and for r ≈ l 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 Calculator of inductance of a magnetic straight round wire. 4) The current is uniformly distributed inside the wire (no skin effect, apart from the simplified eq. (3b)). For high-frequency inductance see Calculator of inductance of a straight round wire at high frequency. 5) The equations were converted here to be consistent with SI units.
| [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. 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. | ||