By W Shepherd; Li Zhang Crowther
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11 for a typical cycle. The polarity of the inductor voltage eL (t) is Copyright ᭧ 2004 by Marcel Dekker, Inc. All Rights Reserved. 36 Chapter 2 such as, by Lenz’s law, to oppose the change of inductor current. While the current is increasing, 0 Ͻ t Ͻ t1, the induced emf in the inductor has its positive point nearest the cathode. When the inductor current is decreasing, t1 Ͻ t Ͻ t3, the induced emf in the inductor tries to sustain the falling current by presenting its positive pole furthest from the cathode in Fig.
1 into Eq. 7 If a capacitor of reactance Xc is connected across the supply, as in Fig. 13, the capacitor instantaneous current is given by ic = = Em sin ( ωt + 90 ) Xc Em cos ωt Xc The resultant instantaneous supply current is therefore is = ic + iL = π, 3π,… E Em cos ωt + m sin ωt 0, 2π,… Xc R Copyright ᭧ 2004 by Marcel Dekker, Inc. All Rights Reserved. 7 A. The load current and load power are not affected by the terminal capacitance. 94 The introduction of the capacitor has caused a considerable reduction of the power factor.
48 Chapter 2 FIG. 17. 19 Derive the following transcendental equation for conduction angle c in a series R-L diode circuit with sinusoidal phase angle ⌽ and a supply e סEm sin t sin(c מ⌽) םsin ⌽εמcot⌽c ס0 If ⌽ ס45Њ, solve the equation by iteration to obtain c. 20 A circuit consists of a resistor R, inductor L, and diode D in series, supplied from an ideal sinusoidal of instantaneous value e סEm sin t. a. Derive an expression for the time variation i(t) of the instantaneous current in terms of Em, |Z| (͙ סR2 ם2L2), and ⌽ ( סtanמ1 L/R.