3.3.SERIES RESISTOR-INDUCTOR CIRCUITS61OppositionFor an inductor:90o0o90o(XL)EIFigure 3.9: Current lags voltage by 90o in an inductor.Mathematically, we say that the phase angle of an inductor’s opposition to current is 90o, meaningthat an inductor’s opposition to current is a positive imaginary quantity. This phase angle of reactiveopposition to current becomes critically important in circuit analysis, especially for complex ACcircuits where reactance and resistance interact. It will prove beneﬁcial to represent any component’sopposition to current in terms of complex numbers rather than scalar quantities of resistance andreactance.• REVIEW:• Inductive reactance is the opposition that an inductor oﬀers to alternating current due to itsphase-shifted storage and release of energy in its magnetic ﬁeld. Reactance is symbolized bythe capital letter “X” and is measured in ohms just like resistance (R).• Inductive reactance can be calculated using this formula: XL = 2πfL• The angular velocity of an AC circuit is another way of expressing its frequency, in units ofelectrical radians per second instead of cycles per second. It is symbolized by the lower-caseGreek letter “omega,” or ω.• Inductive reactance increases with increasing frequency. In other words, the higher the fre-quency, the more it opposes the AC ﬂow of electrons.3.3Series resistor-inductor circuitsIn the previous section, we explored what would happen in simple resistor-only and inductor-onlyAC circuits. Now we will mix the two components together in series form and investigate the eﬀects.Take this circuit as an example to work with: (Figure 71,3.10)The resistor will oﬀer 5 Ω of resistance to AC current regardless of frequency, while the inductorwill oﬀer 3.7699 Ω of reactance to AC current at 60 Hz. Because the resistor’s resistance is a realnumber (5 Ω0o, or 5 + j0 Ω), and the inductor’s reactance is an imaginary number (3.7699Ω90o, or 0 + j3.7699 Ω), the combined eﬀect of the two components will be an opposition tocurrent equal to the complex sum of the two numbers. This combined opposition will be a vectorcombination of resistance and reactance. In order to express this opposition succinctly, we need a