Origin of the Curie–von Schweidler law and the fractional capacitor from time-varying capacitance

On the test of novel constitutive relation of capacitor for electrical circuit analysis: a fractal calculus-based approach

“…In this work, we originally test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor (Pandey, 2022). The associated responses of RL, RC, LC and RLC circuits defined on the fractal set have been derived by means of the fractal calculus and fractal Laplace transformation.…”

“…Definition 1 (Pandey, 2022): The constitutive relation of arbitrary capacitor can be given by: where c ( t ) denotes the capacitance and * is the convolution operator. Such variation with time of the capacitance is caused by the capacitor’s memory effect (Pandey, 2022).…”

“…where c(t) denotes the capacitance and * is the convolution operator. Such variation with time of the capacitance is caused by the capacitor's memory effect (Pandey, 2022).…”

“…Also for ceteris paribus , we assume the circuit parameters with linear time variations like Pandey (2022). Thus, we let: …”

“…Despite its compliance with the impedance analyzers (Allagui et al , 2021b) and accuracy in the calculation of capacitance of any electrochemical energy storage device (Allagui et al , 2021a), it has been found by Banchuin that this revisited relationship fails to properly analyze the electrical circuits (Banchuin, 2022c). Later, a novel constitutive relationship of capacitor defined by the convolution of capacitance and derivative of the applied voltage has been proposed by Pandey for serving as the deriving basis of Curie–von Schweidler law without any inconsistency (Pandey, 2022). To the best of our knowledge, the capability to properly analyze the electrical circuits of this novel relationship has never been verified.…”