Series R, L, and C

Chapter 5.2 Series R, L, and C

Lessons In Electric Circuits Volume II – AC Book
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Lessons In Electric Circuits Volume II – AC Book

  • 98CHAPTER 5. REACTANCE AND IMPEDANCE – R, L, AND Calternating current goes through an impedance, a voltage drop is produced that is somewhere be-tween 0o and 90o out of phase with the current. Impedance is mathematically symbolized by theletter “Z” and is measured in the unit of ohms (Ω), in complex form.Perfect resistors (Figure 107,5.1) possess resistance, but not reactance. Perfect inductors and perfectcapacitors (Figure 107,5.1) possess reactance but no resistance. All components possess impedance,and because of this universal quality, it makes sense to translate all component values (resistance,inductance, capacitance) into common terms of impedance as the first step in analyzing an ACcircuit.Resistor100 ΩR = 100 ΩX = 0 ΩZ = 100 Ω ∠ 0oInductorR = 0 Ω159.15 Hz100 mHX = 100 ΩZ = 100 Ω ∠ 90oCapacitor 10 µF159.15 HzR = 0 ΩX = 100 ΩZ = 100 Ω ∠ -90oFigure 5.1: Perfect resistor, inductor, and capacitor.The impedance phase angle for any component is the phase shift between voltage across thatcomponent and current through that component. For a perfect resistor, the voltage drop and currentare always in phase with each other, and so the impedance angle of a resistor is said to be 0o. Foran perfect inductor, voltage drop always leads current by 90o, and so an inductor’s impedance phaseangle is said to be +90o. For a perfect capacitor, voltage drop always lags current by 90o, and so acapacitor’s impedance phase angle is said to be -90o.Impedances in AC behave analogously to resistances in DC circuits: they add in series, and theydiminish in parallel. A revised version of Ohm’s Law, based on impedance rather than resistance,looks like this:Ohm’s Law for AC circuits:E = IZI =Z =EZEIAll quantities expressed incomplex, not scalar, formKirchhoff’s Laws and all network analysis methods and theorems are true for AC circuits aswell, so long as quantities are represented in complex rather than scalar form. While this qualifiedequivalence may be arithmetically challenging, it is conceptually simple and elegant. The only realdifference between DC and AC circuit calculations is in regard to power. Because reactance doesn’tdissipate power as resistance does, the concept of power in AC circuits is radically different fromthat of DC circuits. More on this subject in a later chapter!5.2Series R, L, and CLet’s take the following example circuit and analyze it: (Figure 108,5.2)