# Curie–von Schweidler law

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The Curie–von Schweidler law refers to the response of dielectric material to the step input of a direct current (DC) voltage first observed by Jacques Curie  and Egon Ritter von Schweidler. A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

## Overview

According to this law, the current decays according to a power law:

$I\left(t\right)\propto t^{-n},$ where $I\left(t\right)$ is the current at a given charging time, $t$ , and $n$ is the decay constant such that $0 . Given that the dielectric has a finite conductance, the equation for current measured through a dielectric under a DC electrical field is:

$I\left(t\right)=at^{b}+c,$ where $a$ is a constant of proportionality, $b$ is the decay constant (i.e., $b=-n$ ), and $c$ is the intrinsic conductance of the dielectric. This stands in contrast to the Debye formulation, which states that the current is proportional an exponential function with a time constant, $\tau$ , according to:

$I\left(t\right)\propto \exp \left\{-t/\tau \right\}$ .

The Curie–von Schweidler behavior has been observed in many instances such as those shown by Andrzej Ka Johnscher  and Jameson et al.  It has been interpreted as a many-body problem by Jonscher, but can also be formulated as an infinite number of resistor-capacitor circuits. This comes from the fact that the power law can be expressed as:

A resistor–capacitor circuit, or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.

$t^{-n}={\frac {1}{\Gamma \left(n\right)}}\int _{0}^{\infty }\tau ^{-\left(n+1\right)}e^{-t/\tau }d\tau ,$ where $\Gamma \left(n\right)$ is the Gamma function. Effectively, this relationship shows the power law expression to be composed of an infinite weighted sum of Debye responses. In mathematics, the gamma function is one of the extensions of the factorial function with its argument shifted down by 1, to real and complex numbers. Derived by Daniel Bernoulli, if n is a positive integer,

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1. Curie, Jaques (1889). "Recherches sur le pouvoir inducteur specifique et la conductibilite des corps cristallises". Annales de Chimie et de Physique. 17: 384–434.
2. Schweidler, Ergon Ritter von (1907). "Studien über die Anomalien im Verhalten der Dielektrika (Studies on the anomalous behaviour of dielectrics)". Annalen der Physik. 329 (14): 711–770. Bibcode:1907AnP...329..711S. doi:10.1002/andp.19073291407.
3. Jonscher, Andrzej Ka (1983), Dielectric Relaxation in Solids, Chelsea Dielectrics Press Limited, ISBN   978-0-9508711-0-3
4. Jameson, N. Jordan; Azarian, Michael H.; Pecht, Michael (2017). Thermal Degradation of Polyimide Insulation and its Effect on Electromagnetic Coil Impedance. Proceedings of the Society for Machinery Failure Prevention Technology 2017 Annual Conference.