A New Analysis and Derivations of Properties of Ideal and Fractional Capacitors by Application of New Generalized Formula of Charge Function q(t) = c(t)*v(t)

Abstract

This chapter is continuation of application of a newly developed generalized formula for capacitor i.e. charge as a function of time, which is convolution operation of a time varying capacity function and a time-varying voltage function (different from capacitance multiplied by voltage to get charge stored in a capacitor). This chapter gives a theoretical validity test i.e. analytically obtained in several applications for this new formulation. This chapter will be useful in various super-capacitor studies, dielectric relaxation experiments, and impedance spectroscopy for various material developments for electrical energy storage missions. This new generalized formula is also verified experimentally. Here we use this new expression and apply to various types of input excitation voltages those are-sinusoidal, constant step, ramp voltage We analyze and interpret the effects, like the charge, the current, the loss-tangent and the memory effects, memorizing shape of input voltage and extend this to evaluate impedance function of a classical capacitor as well as a fractional capacitor. We also derive by using this new formula to get value of equivalent Farads for a fractional capacitor having units in fractional order elaborated on the Nyquist’s diagram.  However, this concept is yet to be used to its full potential.