inductors.md

Inductors

A typical inductor is given in the figure below:

The voltage and current relation of an inductor is:

\(V = L \frac{di}{dt}\)

or in integral form:

\(I = \frac{1}{L} \int_0^t V(t) dt\)

An inductor opposes to the change of current. The unit of inductance is Henry (H).

The inductance of an inductor can be written as:

\(L = \frac{N^2 \mu A}{l}\)

where \(N\) is the number of turns, \(\mu\) is the permeability of the core, \(A\) is the cross-section area, \(l\) is the mean length of the magnetic flux.

Energy stored in an inductor is:

\(w = \frac{1}{2} L I^2\)

####DC Response

• An inductor behaves like short-circuit under DC
• Inductor current cannot be change instantenously as this means infinite voltage.

Inductor Connections

Series Connection

Equivalent inductance of series connected inductors are the sum of inductances:

\(L_{eq} = L_1 + L_2 + L_3 ... L_N\)

Parallel Connection

Parallely connected N inductors are shown in the figure below:

Equivalent inductance in parallel connection is:

\(\frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} ... \frac{1}{L_N}\)