4.5.CAPACITOR QUIRKS93• Impedances (Z) are managed just like resistances (R) in parallel circuit analysis: parallelimpedances diminish to form the total impedance, using the reciprocal formula. Just be sureto perform all calculations in complex (not scalar) form! ZT otal = 1/(1/Z1 + 1/Z2 + . . .1/Zn)• Ohm’s Law for AC circuits: E = IZ ; I = E/Z ; Z = E/I• When resistors and capacitors are mixed together in parallel circuits (just as in series circuits),the total impedance will have a phase angle somewhere between 0o and -90o. The circuitcurrent will have a phase angle somewhere between 0o and +90o.• Parallel AC circuits exhibit the same fundamental properties as parallel DC circuits: voltage isuniform throughout the circuit, branch currents add to form the total current, and impedancesdiminish (through the reciprocal formula) to form the total impedance.4.5Capacitor quirksAs with inductors, the ideal capacitor is a purely reactive device, containing absolutely zero resistive(power dissipative) eﬀects. In the real world, of course, nothing is so perfect. However, capacitorshave the virtue of generally being purer reactive components than inductors. It is a lot easier todesign and construct a capacitor with low internal series resistance than it is to do the same withan inductor. The practical result of this is that real capacitors typically have impedance phaseangles more closely approaching 90o (actually, -90o) than inductors. Consequently, they will tendto dissipate less power than an equivalent inductor.Capacitors also tend to be smaller and lighter weight than their equivalent inductor counterparts,and since their electric ﬁelds are almost totally contained between their plates (unlike inductors,whose magnetic ﬁelds naturally tend to extend beyond the dimensions of the core), they are lessprone to transmitting or receiving electromagnetic “noise” to/from other components. For thesereasons, circuit designers tend to favor capacitors over inductors wherever a design permits eitheralternative.Capacitors with signiﬁcant resistive eﬀects are said to be lossy, in reference to their tendency todissipate (“lose”) power like a resistor. The source of capacitor loss is usually the dielectric materialrather than any wire resistance, as wire length in a capacitor is very minimal.Dielectric materials tend to react to changing electric ﬁelds by producing heat. This heatingeﬀect represents a loss in power, and is equivalent to resistance in the circuit. The eﬀect is morepronounced at higher frequencies and in fact can be so extreme that it is sometimes exploited inmanufacturing processes to heat insulating materials like plastic! The plastic object to be heated isplaced between two metal plates, connected to a source of high-frequency AC voltage. Temperatureis controlled by varying the voltage or frequency of the source, and the plates never have to contactthe object being heated.This eﬀect is undesirable for capacitors where we expect the component to behave as a purelyreactive circuit element. One of the ways to mitigate the eﬀect of dielectric “loss” is to choose adielectric material less susceptible to the eﬀect. Not all dielectric materials are equally “lossy.” Arelative scale of dielectric loss from least to greatest is given in Table 103,4.2.Dielectric resistivity manifests itself both as a series and a parallel resistance with the purecapacitance: (Figure 103,4.15)