  Kirchhoff's current law is thought to describe the translational movement of
charged particles through resistors. But Kirchhoff's law is widely used to
describe movements of current through resistors in high speed devices. Current
at high frequencies/short times involves much more than the translation of
particles. Transients abound. Augmentation of the resistors with ad hoc 'stray'
capacitances is often used to introduce transients into models like those in
real resistors. But augmentation hides the underlying problem, rather than
solves it: the location, value and dielectric properties of the stray
capacitances are not well determined. Here, we suggest a more general approach,
that is well determined. If current is redefined as in Maxwell's equations,
independent of the properties of dielectrics, Kirchhoff's law is exact and
transients arise automatically without ambiguity. The transients in a
particular real circuit-a high density integrated circuit for example-can then
be described by measured constitutive equations together with Maxwell's
equations without the introduction of arbitrary circuit elements.
