Basics of Inductors and Inductance

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Any conductor possesses a characteristic called inductance. Inductance is the ability to store energy in the form of a magnetic field. Inductance is symbolized by the capital letter L and is measured in the unit of the Henry (H). Some of the symbols for an inductor in an electric circuit are:
Circuit symbols for inductors
Inductance is a non-dissipative quantity. Unlike resistance, a pure inductance does not dissipate energy in the form of heat; rather, it stores and releases energy from and to the rest of the circuit.

Inductors are devices expressly designed and manufactured to possess inductance. They are typically constructed of a wire coil wound around a ferromagnetic core material. Inductors have current ratings as well as inductance ratings. Due to the effect of magnetic saturation, inductance tends to decrease as current approaches the rated maximum value in an iron-core inductor.

Inductance of an Inductor
Concept of Inductance in a Coil
An inductor’s inductance depends on the magnetic permeability of the core material (μ), the number of turns in the wire coil (N), the cross-sectional area of the coil (A), and the length of the coil (l):

L= μN2A/L

We can deduce the following from the above formula:
(a) Inductance (L) increases as the relative permeability μr of the core material increases.
(b) Inductance increases as the square of the number of turns N of wire around the core increases.
(c) Inductance increases as the area A enclosed by each turn increases. Since the area is a function of the square of the diameter of the coil, inductance increases as the square of the diameter.
(d) Inductance decreases as the length l of the coil increases (assuming the number of turns remains the constant)

Inductors in Series and Parallel Connection
Inductance adds when inductors are connected in series. It diminishes when inductors are connected in parallel:
L(series) = L1 + L2 + ….+ Ln
L(parallel) = 1/[1/L1 + L2 + … +1/Ln]

Flow of DC Current through an Inductor
When DC source is connected across a pure inductor, the flow of current creates a magnetic field which acts in such a manner as to oppose the change in current. The relationship between voltage and current for an inductor is given by:

V = LdI/dt

Inductors oppose changes in current over time by dropping a voltage. This behavior makes inductors useful for stabilizing current in DC circuits. One way to think of an inductor in a DC circuit is as a temporary current source, always “wanting” to maintain current through its coil at the same value.

Energy Stored in an Inductor
When DC current flows through an inductor, it stores energy in the form of a magnetic field. This stored energy is given by the formula:
E = 1/2LI2 

E = Energy stored
L = Inductance of inductor
I = Current flowing through inductor

Flow of Alternating Current (AC) through an Inductor.
When AC current flows through an inductor, it creates a magnetic field which varies continuously. In fact, the magnetic field will expand and contract as the current increases and decreases. The changing magnetic field will induce a voltage and a current in the inductor. This induced voltage is in a direction so as to oppose the supply voltage and is called a counter-EMF or back-EMF. 
The net effect of this back-EMF is to oppose the change of current due to the alternating voltage. This opposition to current flow causes the voltage to lead the current by 90°as indicated in the waveform below:

Inductive Reactance
Inductive reactance, is the opposition to AC current due to the inductance in the circuit. The unit of inductive reactance is the ohm. The formula for inductive reactance is given by:
XL = 2πfL

XL = Inductive reactance
f    = frequency
L   = Inductance