Dielectric complex reluctance

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 F − 1 (inverse Farads - see Daraf) [Ref. 1-3].

Z_\epsilon = \frac{\dot U}{\dot Q} = \frac{\dot {U}_m}{\dot {Q}_m} = z_\epsilon e^{j\phi}

As seen above, dielectric complex reluctance is a phasor represented as uppercase Z epsilon where:

\dot U and \dot {U}_m represent the voltage (complex effective amplitude)
\dot Q and \dot {Q}_m represent the electric induction flux (complex effective amplitude)
z_\epsilon, lowercase z epsilon, is the real part of dielectric reluctance

The "lossless" dielectric reluctance, lowercase z epsilon, is equal to the 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 e raised to a power equal to:

j\phi = j\left(\beta - \alpha\right)

Where:

  • j is the imaginary number
  • β is the phase of voltage
  • α is the phase of electric induction flux
  • ϕ 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:

Z_\epsilon = \frac{1}{\dot {\epsilon} \epsilon_0} \frac{l}{S}

Where:

  • l is the length of the circuit element
  • S is the cross-section of the circuit element
  • \dot {\epsilon} \epsilon_0 is the complex dielectric permeability

See also

References

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

Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Dielectric reluctance — is a scalar measurement of a passive dielectric circuit (or element within that circuit) dependent on voltage and electric induction flux, and this is determined by deriving the ratio of their amplitudes. The units of dielectric reluctance are… …   Wikipedia

  • Magnetic reluctance — Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating magnetic energy it stores magnetic energy. In likeness to the …   Wikipedia

  • Permeability (electromagnetism) — Magnetic Circuits Conventional Magnetic Circuits Magnetomotive force Magnetic flux Φ Magnetic reluctance Phasor Magnetic Circuits Complex reluctance Zμ …   Wikipedia

  • Constitutive equation — Many defining equations are in the form of a constitutive equation, since parameters of a property or effect associated matter are characteristic to the substance in question. A large number of other defining equations not specifically… …   Wikipedia

  • Business and Industry Review — ▪ 1999 Introduction Overview        Annual Average Rates of Growth of Manufacturing Output, 1980 97, Table Pattern of Output, 1994 97, Table Index Numbers of Production, Employment, and Productivity in Manufacturing Industries, Table (For Annual… …   Universalium

  • Oliver Heaviside — Heaviside redirects here. For other uses, see Heaviside (disambiguation). Oliver Heaviside Portrait by Francis Edwin Hodge …   Wikipedia

  • electromagnetic radiation — Physics. radiation consisting of electromagnetic waves, including radio waves, infrared, visible light, ultraviolet, x rays, and gamma rays. [1950 55] * * * Energy propagated through free space or through a material medium in the form of… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”