Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws (see also Kirchhoff's laws for other meanings of that term).
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Labels show the currents in the various branches as found using a combination of Ohm's law and Kirchhoff's laws.
If all the terms in f(x', y) can be neglected except for the terms in x and y, we have the Fraunhofer diffraction equation.
Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n.
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It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.
The MNA uses the element's Branch Constitutive Equations or BCE, i.e., their voltage - current characteristic and the Kirchhoff's circuit laws.
With Kirchhoff, he collaborated in the publication of Die umbrischen Denkmäler (Umbrian memorials, 1849–51).
In this situation, Kirchhoff's law of equality of radiative emissivity and absorptivity and the Helmholtz reciprocity principle are in play.