# Curie–von Schweidler law

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[1] and Egon Ritter von Schweidler.[2]

### Overview

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

${\displaystyle I\left(t\right)\propto t^{-n},}$

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

${\displaystyle I\left(t\right)=at^{b}+c,}$

where ${\displaystyle a}$ is a constant of proportionality, ${\displaystyle b}$ is the decay constant (i.e., ${\displaystyle b=-n}$), and ${\displaystyle c}$ 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, ${\displaystyle \tau }$, according to:

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

The Curie–von Schweidler behavior has been observed in many instances such as those shown by Andrzej Ka Johnscher[3] and Jameson et al.[4] 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:

${\displaystyle t^{-n}={\frac {1}{\Gamma \left(n\right)}}\int _{0}^{\infty }\tau ^{-\left(n+1\right)}e^{-t/\tau }d\tau ,}$

where ${\displaystyle \Gamma \left(n\right)}$ is the Gamma function. Effectively, this relationship shows the power law expression to be composed of an infinite weighted sum of Debye responses.

### References

1. ^ Curie, Jaques (1889). "Recherches sur le pouvoir inducteur spécifique et sur la conductibilité des corps cristallisés". Annales de Chimie et de Physique. 17: 384–434.
2. ^ Schweidler, Egon 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.