Inductance L (H) is the proportionality constant between the current flow I (A) through the wire and the linkage flux Φ, and the relation is expressed as follows: Φ = LI (Wb) (6.1) Here L is the value of inductance. When an inductor is used as a circuit component, it is usually constructed by winding a wire into a coil. This case, inductance is expressed as follows:

L = n/Rm (H) (6.2) Here, n is the number of turns and Rm is the magnetic reluctance (A/Wb). Magnetic reluctance, Rm, is given by Rm = l/(μS) (A/Wb) (6.3) Here, l is the average magnetic path length (m), μ is the permeability (H/m), and S is the cross-sectional area of the magnetic path (m2). Using Eqs. 6.2 and 6.3, the value of magnetic reluctance is determined from the required inductance; the reluctance determines the required permeability, which in turn determines the required characteristics and shape of the core material. In an ideal inductor, the phase of the current flowing through the inductor lags 90° behind the voltage across its terminals. The energy stored in the inductor due to a current flow of I (A) is given by

W = 1 2

2LI (6.4)

Inductors are constructed by winding a wire on an iron core. The material and form of the iron core are determined by the required inductor characteristics and inductance. Usually small inductors have ring-shaped cores; medium-sized inductors use two C-shaped cores, E-I shaped cores, or E-E shaped cores. Multiple block-type cores are used to construct large inductors. Here we will restrict this discussion to inductors used in electronic circuits and omit discussion of the various types of laminated-core inductors used in power systems.