8. Electric circuits#
Electrical circuits in irrotational regions. Electric circuits are discussed here first for regions of space with no time-varying magnetic fields, \(\partial_t \vec{b} = \vec{0}\). From Faraday’s law, this condition implies \(\nabla \times \vec{e} = \vec{0}\) and that the electric field can be expressed as the gradient of the potential \(\phi\), interpreted as voltage. Under these assumptions, Kirchhoff laws for electric circuits, and constitutive equations of elementary components of electric circuits are derived from equations of electromagnetism.
Electromagnetic induction in electrical circuits. Electromagnetic induction is discussed in electromagnetic systems modelled with circuit approximation: electromagetic induction in sections of a circuit is governed by Faraday’s law, and thus produced by time-varying flux of the magnetic field, produced as an example by (a) time-varying magnetic field, (b) moving sections of the circuit.
Operating regimes. Some characteristic regimes are discussed: steady regime (DC), transient dynamics, periodic regime (AC).