Editing Series and parallel circuits (section)

===Inductors <span class="anchor" id="Lseries"></span>===
[[Inductor]]s follow the same law, in that the total [[inductance]] of non-coupled inductors in series is equal to the sum of their individual inductances:

[[File:Inductors in series.svg|A diagram of several inductors, connected end to end, with the same amount of current going through each.|border|center|x100px]]
<math display="block">L = \sum_{i=1}^n L_i = L_1 + L_2 + L_3 \cdots + L_n.</math>

However, in some situations, it is difficult to prevent adjacent inductors from influencing each other as the magnetic field of one device couples with the windings of its neighbors. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.

When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which is termed self-inductance or simply inductance. For three coils, there are six mutual inductances <math>M_{12}</math>, <math>M_{13}</math>, <math>M_{23}</math> and <math>M_{21}</math>, <math>M_{31}</math> and <math>M_{32}</math>. There are also the three self-inductances of the three coils: <math>M_{11}</math>, <math>M_{22}</math> and <math>M_{33}</math>.

Therefore
<math display="block">L = \left(M_{11} + M_{22} + M_{33}\right) + \left(M_{12} + M_{13} + M_{23}\right) + \left(M_{21} + M_{31} + M_{32}\right)</math>

By reciprocity, <math>M_{ij}</math> = <math>M_{ji}</math> so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.