5.6.SUMMARY117To be consistent, we need a complementary measure representing the reciprocal of impedance.The name for this measure is admittance. Admittance is measured in (guess what?) the unit ofSiemens, and its symbol is “Y”. Like impedance, admittance is a complex quantity rather thanscalar. Again, we see a certain logic to the naming of this new term: while impedance is a measureof how much alternating current is impeded in a circuit, admittance is a measure of how much currentis admitted.Given a scientiﬁc calculator capable of handling complex number arithmetic in both polar andrectangular forms, you may never have to work with ﬁgures of susceptance (B) or admittance (Y).Be aware, though, of their existence and their meanings.5.6SummaryWith the notable exception of calculations for power (P), all AC circuit calculations are based onthe same general principles as calculations for DC circuits. The only signiﬁcant diﬀerence is thatfact that AC calculations use complex quantities while DC calculations use scalar quantities. Ohm’sLaw, Kirchhoﬀ’s Laws, and even the network theorems learned in DC still hold true for AC whenvoltage, current, and impedance are all expressed with complex numbers. The same troubleshootingstrategies applied toward DC circuits also hold for AC, although AC can certainly be more diﬃcultto work with due to phase angles which aren’t registered by a handheld multimeter.Power is another subject altogether, and will be covered in its own chapter in this book. Becausepower in a reactive circuit is both absorbed and released – not just dissipated as it is with resistors– its mathematical handling requires a more direct application of trigonometry to solve.When faced with analyzing an AC circuit, the ﬁrst step in analysis is to convert all resistor,inductor, and capacitor component values into impedances (Z), based on the frequency of the powersource. After that, proceed with the same steps and strategies learned for analyzing DC circuits,using the “new” form of Ohm’s Law: E=IZ ; I=E/Z ; and Z=E/IRemember that only the calculated ﬁgures expressed in polar form apply directly to empiricalmeasurements of voltage and current. Rectangular notation is merely a useful tool for us to addand subtract complex quantities together. Polar notation, where the magnitude (length of vector)directly relates to the magnitude of the voltage or current measured, and the angle directly relatesto the phase shift in degrees, is the most practical way to express complex quantities for circuitanalysis.5.7ContributorsContributors to this chapter are listed in chronological order of their contributions, from most recentto ﬁrst. See Appendix 2 (Contributor List) for dates and contact information.Jason Starck (June 2000): HTML document formatting, which led to a much better-lookingsecond edition.