Discharging Inductors and Capacitors with Superconductivity, Analyzed with Duality of Charge

Circuit theory is well established for inductors and capacitors, but becomes problematic in extreme cases of zero resistance, such as in superconductivity. The concept of duality has been extended to power circuits, switching, semiconductors, superconductivity, and other varied fields. However, the concept of duality of charge has rarely been explored and applied. This paper develops the concept of the dual of charge, and uses it in multiple inductances discharging through a resistor. Attempts to calculate individual inductor currents are either tedious, or impossible in the limiting case of zero resistance. Duality concepts are used for discharging inductors, where other methods are either tedious or impossible. Discharging through zero resistance, as in superconductivity, violates the law of conservation of energy, as there is a loss of energy without a resistor to absorb the loss. The law of conservation of momentum during mechanical collisions implies an inexplicable loss of kinetic energy, and is seen to be analogous to the laws of conservation of charge and conservation of flux linkage. The analysis also helps to handle situations of zero resistance, arising from superconductivity.