Points in the RL plane

Chapter Points in the RL plane

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • Problem 13-2What will be the inductive reactance of the above coil if the supply is a battery that sup-plies pure dc?Because dc has a frequency of zero, XL6.2800. 50 0. That is, there willbe no inductive reactance. Inductance doesn’t generally have any practical effect withpure dc.Problem 13-3If a coil has an inductive reactance of 100 at a frequency of 5.00 MHz, what is its in-ductance?In this case, you need to plug numbers into the formula and solve for the unknownL. Start out with the equation 100 6.285. 00 L31.4L. Then, recall that be-cause the frequency is in megahertz, or millions of hertz, the inductance will come outin microhenrys, or millionths of a henry. You can divide both sides of the equation by31.4, getting L100/31.43.18µH.Points in the RL planeInductive reactance can be plotted along a half line, just as can resistance. In a circuitcontaining both resistance and inductance, the characteristics become two-dimen-sional. You can orient the resistance and reactance half lines perpendicular to eachother to make a quarter-plane coordinate system, as shown in Fig. 13-5. Resistance isusually plotted horizontally, and inductive reactance is plotted vertically, going up-wards.In this scheme, RL combinations form impedances. You’ll learn all about this inchapter 15. Each point on the RL plane corresponds to one unique impedance value.Conversely, each RL impedance value corresponds to one unique point on the plane.For reasons made clear in chapter 15, impedances on the RL plane are written inthe form RjXL, where R is the resistance and XL is the inductive reactance.If you have a pure resistance, say R5Ω, then the complex impedance is 5 j0,and is at the point (5,0) on the RL plane. If you have a pure inductive reactance, such as 234 Inductive reactance13-4Inductive reactance isdirectly proportional toinductance and also tofrequency.