Editing Series and parallel circuits (section)

===Inductors<span class="anchor" id="Lparallel"></span>===
[[Inductor]]s follow the same law, in that the total [[inductance]] of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
[[File:Inductors_in_parallel.svg|alt=A diagram of several inductors, side by side, both leads of each connected to the same wires.|border|center|x120px]]
<math display="block">L = \left(\sum_{i=1}^n{1\over L_i}\right)^{-1} = \left({1\over L_1} + {1\over L_2} + {1\over L_3} + \dots + {1\over L_n}\right)^{-1}.</math>

If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is {{mvar|M}}, the equivalent inductor is:
<math display="block">L = \frac{L_1L_2 - M^2}{L_1 + L_2 - 2M}</math>

If <math>L_1 = L_2</math>
<math display="block"> L = \frac{L + M}{2}</math>

The sign of <math>M</math> depends on how the magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of every single coil. If the polarity of one coil is reversed so that {{mvar|M}} is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. It is assumed in the "tightly coupled" case {{mvar|M}} is very nearly equal to {{mvar|L}}. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of {{mvar|M}}, which can cause problems.

More than three inductors become more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances <math>M_{12}</math>, <math>M_{13}</math> and <math>M_{23}</math>. This is best handled by matrix methods and summing the terms of the inverse of the <math>L</math> matrix (3×3 in this case).

The pertinent equations are of the form:
<math display="block">v_{i} = \sum_{j} L_{i,j} \frac{di_j}{dt} </math>