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Kirchhoff's Current Law is an essential tool in the design of circuits thatoperate very quickly, faster than nanoseconds. But Kirchhoff's current is oftenidentified as the flow of particles. The continuity equation or theMaxwell-Ampere law shows that the sum of displacement current $\textbf{plus}$particle current is conserved by Maxwell's equations and Kirchhoff's law.Kirchoff included the displacement current in the current of his law, fromearly on. This Kirchhoff current (including the displacement current) does notvary with spatial location in the ionic channels of biology. Electroniccircuits switching in nanoseconds are analyzed using the Bohm representation ofquantum mechanics including particle and displacement current.

Kirchhoff's Current Law with Displacement Current