  Most dielectrics of practical purpose exhibit memory and are described by the
century-old Curie-von Schweidler law. Interestingly, the Curie-von Schweidler
law is the motivation behind an unconventional circuit component called
fractional capacitor which due to its power-law property is extensively used in
the modeling of complex dielectric media. Unfortunately, the empirical nature
of the Curie-von Schweidler law plagues the applications of the fractional
capacitor. Here, we derive the Curie-von Schweidler law from a series
combination of a resistor and a capacitor with a linear time-varying
capacitance. This may possibly be its first derivation from physical
principles. However, this required a modification of the classical
charge--voltage relation of a capacitor to account for the time-varying
capacitance. The limitation of the classical charge-voltage relation and its
subsequent modification are justified using appropriate circuit modeling.
Consequently, the parameters of the Curie-von Schweidler law and the fractional
capacitor gain physical interpretation. The Debye response of dielectrics
emerges naturally from the limiting case of the power-law response at short
timescales. The obtained results are validated by matching them with the
published experimental reports.
