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

*Here in this Chapter the verification of newly developed formula of charge storage in capacitor as q = c*v, in RC circuit, is carried out in order to get validation for ideal loss less capacitor as well as fractional order capacitors for charging and discharging cases. This new formula is generalization of charge storage mechanism in capacitors dielectric relaxations (with and without memory effect), which 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 the RC circuits to verify the results that are obtained via classical circuit theory, for a case of classical ideal loss less capacitor as well as for case for fractional capacitor. The use of this formulation is suited for super-capacitors, Constant Phase Elements (CPE), and for dielectric relaxations that show memory effect 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 get clarity in usage of this new formula in the RC circuit examples. This Chapter validates the new formula of charge storage q = c*v, in capacitor, for circuital usage.*

**For more information contact author**

**Shantanu Das**

Scientist Reactor Control Division, E&I Group BARC, Mumbai-400085, India.

Department of Physics, Jadavpur University, Kolkata-700032, India.

E-mail: shantanu@barc.gov.in, shantanu.das@live.com

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Books convolution operation fractional capacitor fractional derivative ideal loss-less capacitor Laplace transform memory effect. Mittag-Leffler function Science self-discharging super-capacitor time varying capacity function