View source for Dielectric complex reluctance

'''Dielectric complex reluctance''' is a scalar measurement of a passive dielectric circuit (or element within that circuit) dependent on sinusoidal [[voltage]] and sinusoidal electric induction flux, and this is determined by deriving the ratio of their complex ''effective'' amplitudes. The units of dielectric complex reluctance are <math>F^{-1}</math> (inverse [[Farads]] - see [[Daraf]]) [Ref. 1-3].

: <math>Z_\epsilon = \frac{\dot U}{\dot Q} = \frac{\dot {U}_m}{\dot {Q}_m} = z_\epsilon e^{j\phi}</math>  

As seen above, dielectric complex reluctance is a [[phasor]] represented as ''uppercase Z epsilon'' where:
: <math>\dot U</math> and <math>\dot {U}_m</math> represent the voltage (complex effective amplitude)
: <math>\dot Q</math> and <math>\dot {Q}_m</math> represent the electric induction flux (complex effective amplitude)
: <math>z_\epsilon</math>, ''lowercase z epsilon'', is the real part of dielectric reluctance

The "lossless" [[dielectric reluctance]], ''lowercase z epsilon'', is equal to the [[Absolute value#Complex numbers|absolute value]] (modulus) of the dielectric complex reluctance. The argument distinguishing the "lossy" dielectric complex reluctance from the "lossless" dielectric reluctance is equal to the natural number <math>e</math> raised to a power equal to:

: <math>j\phi = j\left(\beta - \alpha\right)</math>

Where:
*<math>j</math> is the [[imaginary unit]]
*<math>\beta</math> is the phase of voltage
*<math>\alpha</math> is the phase of electric induction flux
*<math>\phi</math> is the phase difference

The "lossy" dielectric complex reluctance represents a dielectric circuit element's resistance to not only electric induction flux but also to ''changes'' in electric induction flux.  When applied to harmonic regimes, this formality is similar to [[Ohm's Law]] in ideal AC circuits. In dielectric circuits, a dielectric material has a dielectric complex reluctance equal to:

:<math>Z_\epsilon = \frac{1}{\dot {\epsilon} \epsilon_0} \frac{l}{S}</math>

Where:
*<math>l</math> is the length of the circuit element
*<math>S</math> is the cross-section of the circuit element
*<math>\dot {\epsilon} \epsilon_0</math> is the ''complex dielectric permeability''

==See also==
*[[Dielectric]]
*[[Dielectric reluctance]] — Special definition of dielectric reluctance that does not account for energy loss

==References==
# Hippel A. R. Dielectrics and Waves. – N.Y.: JOHN WILEY, 1954.
# Popov V. P.  The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian).
# [[Karl Küpfmüller|Küpfmüller K.]] Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.

[[Category:Electric and magnetic fields in matter]]