### How to Calculate the Inductance of an Electric Cable

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The inductance, L , per core of a 3-core cable or of three single-core cables comprises two parts namely the self-inductance of the conductor and the mutual inductance with other cores.

The formula for calculating the Inductance of a cable is given by:

$L = K + 0.2Log_e{\frac{2S}{d}}$                    (Hm/Km)

Where:
L  =  Inductance of cable in (Hm/Km)
K  =  a constant relating to the conductor formation (see table below)
S  =  axial spacing between conductors within the cable (mm) or axial spacing between
Conductors of a trefoil group of single core cables (mm) or
=  1.26 x phase spacing for a flat formation of three single-core cables (mm)
d =  conductor diameter or for shaped designs the diameter of an equivalent circular
conductor (mm)

For 2-core, 3-core and 4-core cables, the inductance obtained from the formula should be multiplied by 1.02 if the conductors are circular or sector-shaped, and by 0.97 for 3-core oval conductors.

Typical Values for K for Different Stranded Conductors (at 50Hz)

 Number of Wires in Conductor K 3 0.0778 9 0.0642 7 0.0554 37 0.0528 61 and Over 0.0514 1 (Solid) 0.0500 Hollow core conductor, 12mm duct 0.0383