Kirchhoff's Law Can Be Exact

Abstract

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.

Version 4, December 5, 2022. Updated to cite new work. Version 3: Expanded treatment of continuity equation

References in corpus (6)

• Chiral Quantum Optics
• Simulation of gating currents of the Shaker K channel using a Brownian model of the voltage sensor
• What Current Flows Through a Resistor?
• The pedagogical value of the four-dimensional picture II: Another way of looking at the electromagnetic field
• Updating Maxwell with Electrons, Charge, and More Realistic Polarization
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Cited by in corpus (2)

• Updating Maxwell with Electrons, Charge, and More Realistic Polarization
• Electrodynamics Correlates Knock-on and Knock-off: Current is Spatially Uniform in Ion Channels