AC inductor circuits

Chapter 3.2 AC inductor circuits

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

  • 3.2.AC INDUCTOR CIRCUITS573.2AC inductor circuitsInductors do not behave the same as resistors. Whereas resistors simply oppose the flow of electronsthrough them (by dropping a voltage directly proportional to the current), inductors oppose changesin current through them, by dropping a voltage directly proportional to the rate of change of current.In accordance with Lenz’s Law, this induced voltage is always of such a polarity as to try to maintaincurrent at its present value. That is, if current is increasing in magnitude, the induced voltage will“push against” the electron flow; if current is decreasing, the polarity will reverse and “push with”the electron flow to oppose the decrease. This opposition to current change is called reactance,rather than resistance.Expressed mathematically, the relationship between the voltage dropped across the inductor andrate of current change through the inductor is as such:e = didtLThe expression di/dt is one from calculus, meaning the rate of change of instantaneous current(i) over time, in amps per second. The inductance (L) is in Henrys, and the instantaneous voltage(e), of course, is in volts. Sometimes you will find the rate of instantaneous voltage expressed as“v” instead of “e” (v = L di/dt), but it means the exact same thing. To show what happens withalternating current, let’s analyze a simple inductor circuit: (Figure 66,3.4)LELILETILELIET = ELI = IL90°Figure 3.4: Pure inductive circuit: Inductor current lags inductor voltage by 90o.If we were to plot the current and voltage for this very simple circuit, it would look somethinglike this: (Figure 66,3.5)Time +-e =i =Figure 3.5: Pure inductive circuit, waveforms.Remember, the voltage dropped across an inductor is a reaction against the change in currentthrough it. Therefore, the instantaneous voltage is zero whenever the instantaneous current is at