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An easy way to deal with these inherent inductances in circuit analysis is by using a lumped element model to express each physical component as a combination of an ideal component and a small inductor in series, the inductor having a value equal to the inductance present in the non-ideal, physical device.
Kinetic inductance is the manifestation of the inertial mass of mobile charge carriers in alternating electric fields as an equivalent series inductance. Kinetic inductance is observed in high carrier mobility conductors (e.g. superconductors ) and at very high frequencies.
In the most general case, inductance can be calculated from Maxwell's equations. Many important cases can be solved using simplifications. Where high frequency currents are considered, with skin effect , the surface current densities and magnetic field may be obtained by solving the Laplace equation .
Capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance.However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series with a resistance; this resistance is defined as the equivalent series resistance (ESR) [1].
Series RL, parallel C circuit with resistance in series with the inductor is the standard model for a self-resonant inductor. A series resistor with the inductor in a parallel LC circuit as shown in Figure 4 is a topology commonly encountered where there is a need to take into account the resistance of the coil winding and its self-capacitance.
These include resistors in series, resistors in parallel and the extension to series and parallel circuits for capacitors, inductors and general impedances. Also well known are the Norton and Thévenin equivalent current generator and voltage generator circuits respectively, as is the Y-Δ transform .
Self Inductance: L: Two equivalent definitions are possible: = ... DC Circuit equations AC Circuit equations Series circuit equations RC circuits:
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.