Signals and Networks: Inductor

An inductor is a passive component which resists changes in electric current passing through it. When a current flows through it, energy is stored temporarily in a magnetic field in the coil. When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor, according to Faraday’s law of electromagnetic induction, which opposes the change in current that created it.

Inductors have values that typically range from 1 µH (10⁻⁶H) to 1 H.

Inductance (L) results from the magnetic field around a current-carrying conductor; the electric current through the conductor creates a magnetic flux. Inductance is determined by how much magnetic flux φ through the circuit is created by a given current i,

L = {\phi \over i}

Inductors that have ferromagnetic cores are nonlinear; the inductance changes with the current, in this more general case inductance is defined as

L = {d\phi \over di} \,

Any change in the current through an inductor creates a changing flux, inducing a voltage across the inductor. By Faraday's law of induction, the voltage induced by any change in magnetic flux through the circuit is

v = {d\phi \over dt} \,

v = {d \over dt}(Li) = L{di \over dt} \,

The dual of the inductor is the capacitor, which stores energy in an electric field rather than a magnetic field.

The ratio of the peak voltage to the peak current in an inductor energised from a sinusoidal source is called the reactance and is denoted X_L.

X_\mathrm L = \frac {V_\mathrm P}{I_\mathrm P} = \frac {2 \pi f L I_\mathrm P}{I_\mathrm P}

X_\mathrm L = 2 \pi f L

Reactance is measured in the same units as resistance (ohms) but is not actually a resistance. A resistance will dissipate energy as heat when a current passes. This does not happen with an inductor; rather, energy is stored in the magnetic field as the current builds and later returned to the circuit as the current falls.

Parallel and series connection

$\frac{1}{L_{parallel}}=\frac{1}{L_1}+\frac{1}{L_2}+...+\frac{1}{L_n}$

$L_{series}=L_1+L_2+...+L_n$