The Charge Non-Conservation Paradox Implied by Loss Free Resistors

Ivo Barbi, Sigmund Singer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The purpose of this paper is to investigate a paradox in which electrical charges appear not to be conserved when two identical capacitors with unequal initial electrical charges are connected by a loss free resistor (LFR). The theoretical analyses were based on the basic LFR model, the results of that analysis were verified by experimentation of a circuit in which the loss free resistor was realized by means of a PWM converter operated in the DCM mode. The paradox presentation, its solution and rectification by the remodeling of the real capacitive element, applying a new, extended formula for its charge calculation are some of the novelties included in the paper. Use of power conservative two port networks in systems such as capacitive converters, regenerative voltage clamping circuits and capacitive energy storage systems for efficiency increase is the practical implication of the research results. Since operation of that systems implies such paradox, its rectification removes all doubt regarding their functioning.

Original languageEnglish
Pages (from-to)2623-2631
Number of pages9
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number6
StatePublished - 1 Jun 2024


  • Charge conservation law
  • charge non conservation paradox
  • dc-dc converter
  • discontinuous-conduction mode
  • loss-free resistor (LFR)
  • power conservation two port networks
  • series loss-free resistor (SLFR)


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