Intro Electric CircuitsElectr
Intro Electric CircuitsElectr ENGR 211
Christopher Newport University
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Date Created: 10/05/15
6 Inductance and Capacitance and Mutual Inductance Two new circuit elements Inductor An inductor is an electrical component that opposes any change in electrical current It is composed ofa coil ofwire wound around a supporting core An inductor can store energy Capacitor A capacitor is an electrical component that consists of two conductors separated by an insulator or dielectric material A capacitor can store electrical charge Inductors and capacitors are classi ed as passive elements and they cannot generate energy 61 Inductor The symbol for impedance is L and measured in henrys H The relationship between the Voltage and current at the terminals of an inductor v L dt r 1 r 11 jvdr itn L tn 0 If current is constant the Voltage across the ideal inductor is zero 0 Current cannot change instantaneously in the inductor 61 Example 6 I a my m For KO 0 For 0ltt 1 1 2 11 2d110 3 For 1ltt 2 11 gendr il 7 62 Power and Energy in the Inductor If the current reference is in the direction of the voltage drop the power di vi Li p dz In term of voltage 1 t p WEIR vdz39 1Z0 Power is the rate of energy change dw dz39 Li p dz dz Thus dw Lidz39 Integration on both sides 1 w Li2 2 63 Example 61b L a W it 0tlt 0 it 10te 5 t gt 0 Find the Voltage power of the inductor When the current reaches is maximum The maximum Value of current is 10751e 5 e 5 0 gt t 025 dt Voltage on the inductor vt Lg 0110751e 5 e e s a 7 5tVt gt 0 pa vi10te391m 75012e39m W r d w pr 64 tsl 100 l I t S 0 02 04 06 08 10 Figure 68 The variables 1 v p and w versus for Example 61 From NilssonRiedel Electric Circuits 6e July 2000 Prentice Hall Inc Example 6 3 L v mumH vt 0 lt 0 vt zotequot Vtgt 0 Find i 1 W 7le 7e 1011 2 1710te391m 7 e39m 100 u p vi 20te m 21710te m 7 e39m W 1 r it 201e39lnrdr0200 0 01 r d w pr 66 62 Capacitor It is represented by C and is measured in farads F The relationship between the voltage and current at the terminals of a capacitor izC dz vl jidz vl0 The power is dv vi Cv p dt The energy is 2 wz cv 2 o A capacitor does not permit an instantaneous change in its terminal voltage 0 If voltage is constant a capacitor behaves as an open circuit 0 Only a timevarying voltage can produce a displacement current 6 7 Example 6 4 169 c O l lt 0 i0 SOOOZA 0 g I lt 20w 02 5000lA 20 Zlt40us 0 I 2 40us Voltage For th v0 For Oltt 20us I vl 5 106 I 50001611 0 125109sz 0 For 20ltt 40us l vl 5106 IO2 50007d75 1061 125109 2 10VF 20 ort 2 40 us vtv40us10V 68 Power For tSO 19 For Oltt 20us pl 2 iv 2 500010231092 2 6251012z3W For 20ltt 40us p For t240 us Pl Energy For th wt0 For Oltt 20us pZ cv2 156251012 Z4J For 20ltt 40m wl 69 ilmA 50 l 1 l l t 5 0 10 20 30 40 50 60 rats Dlle 500 7 400 300 200 A 100 I l L 4 5 60 WuJ Namoa l l l l l l l 20 30 40 50 60 tlus o c Figure 612 The variables i v p and w versus 1 for Example 65 From NilssonFliedel Electric Circuits 6e July 2000 Prentice Hall Inc Example 5 5 0 lt0 22 2 0gtlt2 22 Fortlt0 1 vt EEer o ForOSKZ v0 V0Jxrdr mam For 22 v0 VZjlrdr 63 Serialparallel combination of inductance and capacitance Serialparallel combination of inductors or capacitors can be reduced to a single inductor and capacitor Inductor is serial u L2 n W V1 V2 a di vvvvLLL 2 31 2 0d LLL2L3 vL dt Inductors in parallel Total inductance Value iii i i LLLJ vdrit i z i z xzzL LZLMn IUZEIZEI 1 i vdritn Ltn 1 1 1 1 IZZZ 1tn1tn12tn13tn Capacitors in serial 1 2 ca 1 m a T0121 capacitor Value 1 1 1 1 c q q q vt ji1dr vtn Capacitors in parallel T0121 capacitor Value Cqqq dvt It C dt 64 Mutual Inductance lnductanceself inductance is the parameter that relates a Voltage to a timeVarying current in the same circuit Mutual inductance Two circuiw are linked by a magnetic eld If current is time Varying in the rst circuit it Will be resulting magnetic eld This magnetic eld induces Voltage in the second circuit that related to current in the rst circuit by parameter mutual inductance which is labeledM Two coils are labeled Liand L m M W O 2 Let s Write the mesh currents equation 1139 d39 7v i1R1LliiMi0 g dt dt d39 d39 i2R2iniMi0 dt dt Dot convention used to keep track the polarity of induced Voltage When the reference direction for a current enters the dotted terminal of a coil the reference polarity of the Voltage that it induces in the other coil is positive at its dotted terminal