3.5.INDUCTOR QUIRKS71EIVoltsAmpsOhmsZRLTotal5 + j05 ∠ 0o0 + j3.76993.7699 ∠ 90o10 + j010 ∠ 0o10 + j010 ∠ 0o10 + j010 ∠ 0o0 - j2.65262.6526 ∠ -90o2 + j02 ∠ 0o2 - j2.65263.322 ∠ -52.984o1.8122 + j2.40353.0102 ∠ 52.984oOhm’sLaworRule of parallelcircuits:Ztotal =ZRZL1+11Z =EI• REVIEW:• 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 inductors 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.3.5Inductor quirksIn an ideal case, an inductor acts as a purely reactive device. That is, its opposition to AC currentis strictly based on inductive reaction to changes in current, and not electron friction as is the casewith resistive components. However, inductors are not quite so pure in their reactive behavior. Tobegin with, they’re made of wire, and we know that all wire possesses some measurable amountof resistance (unless it’s superconducting wire). This built-in resistance acts as though it wereconnected in series with the perfect inductance of the coil, like this: (Figure 81,3.15)Consequently, the impedance of any real inductor will always be a complex combination ofresistance and inductive reactance.Compounding this problem is something called the skin eﬀect, which is AC’s tendency to ﬂowthrough the outer areas of a conductor’s cross-section rather than through the middle. Whenelectrons ﬂow in a single direction (DC), they use the entire cross-sectional area of the conductor