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## Inductors Basics

Any conductor possesses a characteristic called inductance: 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).

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. Here are some schematic symbols for inductors:

**L = (μN2A) / l**

Inductance adds when inductors are connected in series. It diminishes when inductors are connected in parallel:

**L _{series} = L_{1} + L_{2} + ・ ・ ・L_{n}**

**L _{parallel} = 1 / ((1 / L_{1}) + (1 / L_{2}) + ・ ・ ・( 1 / L_{n}))**

The relationship between voltage and current for an inductor is as follows:

**V = L ( dI/ dt)**

As such, 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.

The amount of potential energy (Ep, in units of joules) stored by an inductor may be determined by altering the voltage/current/inductance equation to express power (P = IV ) and then applying some calculus (recall that power is defined as the time-derivative of work or energy, P = *d*W / *d*t = *d*E / *d*t ):

**V = L ( dI/ dt)**

**P = IV = LI ( dI / dt )**

*d*Ep / dt = LV ( *d*I / *d*t )

**( dEp / dt) / dt = LI dV**

**∫ ( dEp / dt) / dt = ∫ LI dI**

∫

∫

*d*Ep = L ∫*d*I**Ep = (1/2 ) LI ^{2}**

In an AC circuit, the amount of inductive reactance (XL) offered by an inductor is directly proportional to both inductance and frequency:

**X _{L} = 2πfL**

This means an AC signal finds it “harder” to pass through an inductor (i.e. more ohms of reactance) at higher frequencies than at lower frequencies.

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