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AC Characteristics of Dielectrics
Equations 265 and 267 show that current in an ideal capacitor [Fig. 225(a)] leads the applied voltage, if sinusoidal, by an angle of 90° as shown in Fig. 225. In liquid dielectrics such as insulating oils and other liquids used in capacitors, transformers, and highvoltage cables, as well as in solid dielectrics, the current leads the voltage by an angle that is somewhat smaller than 90°. This departure from 90° results from dielectric energy losses that show up in the form of heat. In the case of ac fields the dipoles undergo rotation, which is opposed, to some extent, by a sort of molecular friction, and as a result the current associated with the charges induced by the dipoles leads the voltage by an angle of less than 90°. Other losses result from conduction currents in the dielectric. The phasor diagram of Fig. 225(d) shows the relationships between the components of current resulting from the free charges, induced charges, and conduction in a capacitor with an imperfect dielectric. In Fig. 225 let I_{0} = charging current from the free charge
The current I_{0} is the current that would result if the dielectric were free space. The dielectric power factor is
Dissipation factor is a term commonly used in connection with dielectric losses and the symbol for it is DF
At small values of d the difference between the power factor cos Θ or sin δ and the dissipation factor tan δ is negligible. For example when the power factor, i.e., sin δ is 0.1000 the dissipation factor tan δ is 0.1004. The value of dissipation factor is about 0.005 or less for dielectrics used in highvoltage cable, liquidimpregnated capacitors, and other applications where dielectric losses must be kept at low values. The angle δ shown in Fig. 225(d) is much larger than is normal for a good dielectric. The quality factor Q is another term used in connection with capacitors; it is the reciprocal of the dissipation factor, i.e.
The equivalent circuit for an imperfect capacitor is shown in Fig, 225(e), which shows the loss component of current I tan δ to flow through an equivalent resistance and the outofphase current I cot δ to flow through an equivalent ideal capacitance. This equivalent circuit greatly oversimplifies the actual conditions. In a given dielectric the dielectric constant and consequently the capacitance C of Fig. 225(e) varies with frequency and temperature. The dielectric losses are also functions of frequency and temperature so that the shunt resistance R is also a variable. Nevertheless, the equivalent circuit of Fig. 225(e) is quite useful for certain kinds of analyses.


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