Dielectrics in alternating electric fields

The discussion so far has been concerned with dielectrics in steady electric fields more commonly they are in fields that change with time, usually sinusoidally. This is clearly the case for capacitors in most ordinary circuit applications, but there are less obvious instances. For example, because electromagnetic waves have an electric field component it would be the case for dielectric resonators in microwave devices and also for fight passing through a transparent material. Fortunately, no matter how the field may vary with time, the variation can be 

The earlier discussion can be extended by considering a capacitor to which a sinusoidal voltage is applied (Fig. 2.29). At a time when the voltage is U, the charge on C is Q = UC and, since the current Ic = Q, it follows that 

with the usual notation, if the voltage is described by C/osin( ut) then the current is UoCtocos(tot) and leads U by 90°. Since the instantaneous power drawn from the voltage source is Ic U, the time average power dissipated is P where 

If there is to be a net extraction of power from the source, there must be a component I of /in phase with U, as shown in Fig. 2.31 I leads to power loss, whereas the capacitative component Ic does not. Therefore the time average power loss is 

It can be seen from Eq. (2.95) that sin 5 (or cos r/ ) represents the fraction of the current-voltage product that is dissipated as heat. It is termed the power factor . From Eq. (2.96) the dissipation factor tan S is the fraction of the product of the capacitive current (the component 90° out of phase with the voltage) and the voltage, dissipated as heat. In most cases of interest 5 is small enough for sin 5 = tan 5. 

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The behaviour of dielectrics in alternating electric fields may be treated in the framework of forced harmonic oscillation. The displacement is then given by... 

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