Theoretical Verification of Formula for Charge Function in Time q = c * v in RC Circuit for Charging/Discharging of Fractional & Ideal Capacitor

Abstract

Objective of this paper is verification of newly developed formula of charge storage in capacitor as   q = c*v, in RC circuit, to get validation for ideal loss less capacitor as well as fractional order capacitors for charging and discharging cases. This new formula is different to usual and conventional way of writing capacitance multiplied by voltage to get charge stored in a capacitor   i.e. q = cv. We use this new formulation i.e.   q = c*v in RC circuits to verify the results that are obtained via classical circuit theory, for a case of classical loss less capacitor as well as fractional capacitor. The use of this formulation is suited for super-capacitors, as they show fractional order in their behavior. This new formula is used to get the ‘memory effect’ that is observed in self-discharging phenomena of super-capacitors-that memorizes its history of charging profile. Special emphasis is given to detailed derivational steps in order to clarity in usage of this new formula in the RC circuit examples. This paper validates  the new formula of   charge   storage  in  capacitor i.e. q = c*v.