The real value of the permittivity or dielectric constant e is determined from the ratio (553) where C represents the measured capacitance in F and C is the equivalent capacitance in vacuo, which is calculated for the same specimen geometry from Co=E, Ald; here E, denotes the permittivity in vacuo and is equal to 8.854 X 10-4Fcm-(8.854 X 10-2F m-in SI units)or more conveniently to unity in the Gaussian CGS system. In practice, the value of E, in free space is essentially the same as that for a gas (e. g, for air, a 000536). The majority of liquid and solid dielectric materials, presently in use, have dielectric constants extending from approximately 2 to 10. 55.2 Dielectric losses Under ac conditions dielectric losses arise mainly from the movement of free charge carriers(electrons and ns),space charge polarization, and dipole orientation [ Bartnikas and Eichhorn, 1983]. Ionic, space charge, values of o and e. This necessitates the introduction of a complex permittivity e defined in the measured and dipole losses are temperature- and frequency-dependent, a dependency which is reflected where e"is the imaginary value of the permittivity, which is equal to o/o. Note that the conductivity o determined under ac conditions may include the contributions of the dipole orientation, space charge, and onic polarization losses in addition to that of the drift of free charge carriers(ions and electrons)which determine its dc value ohase angle difference 8 between the d and E vectors, then in complex notation d and E may be expressed as D exp [(of-8)] and E, expliot), respectively, where o is the radial frequency term, t the time, and Do and E, the respective magnitudes of the two vectors. From the relationship between D and E, it follows that E It is cu the magnitude of loss of of its dissipation factor, tan8; it is apparent from Eqs.(55.5)and (55.6), that ans Examination of Eq (55.7)suggests that the behavior of a dielectric material may also be described of an equivalent electrical circuit. It is most commonplace and expedient to use a parallel circuit repre consisting of a capacitance C in parallel with a large resistance R as delineated in Fig. 55. 1. Here C© 2000 by CRC Press LLC The real value of the permittivity or dielectric constant e¢ is determined from the ratio (55.3) where C represents the measured capacitance in F and Co is the equivalent capacitance in vacuo, which is calculated for the same specimen geometry from Co = eo A/d; here eo denotes the permittivity in vacuo and is equal to 8.854 3 10–14 F cm–1 (8.854 3 10–12 F m–1 in SI units) or more conveniently to unity in the Gaussian CGS system. In practice, the value of eo in free space is essentially the same as that for a gas (e.g., for air, eo = 1.000536). The majority of liquid and solid dielectric materials, presently in use, have dielectric constants extending from approximately 2 to 10. 55.2 Dielectric Losses Under ac conditions dielectric losses arise mainly from the movement of free charge carriers (electrons and ions), space charge polarization, and dipole orientation [Bartnikas and Eichhorn, 1983]. Ionic, space charge, and dipole losses are temperature- and frequency-dependent, a dependency which is reflected in the measured values of s and e¢. This necessitates the introduction of a complex permittivity e defined by e = e´ – je² (55.4) where e² is the imaginary value of the permittivity, which is equal to s/w. Note that the conductivity s determined under ac conditions may include the contributions of the dipole orientation, space charge, and ionic polarization losses in addition to that of the drift of free charge carriers (ions and electrons) which determine its dc value. The complex permittivity, e, is equal to the ratio of the dielectric displacement vector D to the electric field vector E, i.e., e = D/E. Since under ac conditions the appearance of a loss or leakage current is manifest as a phase angle difference d between the D and E vectors, then in complex notation D and E may be expressed as Do exp [j (vt – d)] and Eo exp[jvt], respectively, where v is the radial frequency term, t the time, and Do and Eo the respective magnitudes of the two vectors. From the relationship between D and E, it follows that (55.5) and (55.6) It is customary under ac conditions to assess the magnitude of loss of a given material in terms of the value of its dissipation factor, tand; it is apparent from Eqs. (55.5) and (55.6), that (55.7) Examination of Eq. (55.7) suggests that the behavior of a dielectric material may also be described by means of an equivalent electrical circuit. It is most commonplace and expedient to use a parallel circuit representation, consisting of a capacitance C in parallel with a large resistance R as delineated in Fig. 55.1. Here C represents e¢ = C Co e d ¢ = D E o o cos e d ¢¢ = D E o o sin tand e e s w e = ¢¢ ¢ = ¢