Electric charge flow in linear circuits

Abstract

This paper deals with a fundamental property of circuits that can simplify certain analysis, bring new methods of measurements and possibly other applications, which has apparently passed unnoticed until now. It shows that the net charge injected by an arbitrary source into a linear circuit is divided among the circuit branches (including transmission lines) in the same proportion as the charge would divide among the same branches, if the circuit was replaced by its equivalent circuit at direct current (DC). The DC equivalent circuit alone will govern the exact sharing of the net charge, despite current oscillations caused by reactive elements or propagation effects of transmission lines. In this paper, this property is demonstrated analytically and proved by computer simulations and laboratory experiments. The paper also exemplifies its application in the calculation of the net charge distribution among the conductors of an installation struck by lightning. Finally, the paper forecasts other possible applications for the new circuit property.