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22/12/2014 2 Circuit Analysis-1 Fall-2014 EE -1111 Instructor: Hafiz Zaheer Hussain Email: [email protected] www.hafizzaheer.pbworks.com Department of Electrical Engineering The University of Lahore Lecture # 25 & 26 22/12/2014 2 22/12/2014 3 Content Introduction Capacitor Energy storage in capacitor Series and parallel Capacitors Inductor Energy storage in Inductor Series and parallel Inductors Inductor An inductor is a passive element that stores energy in its magnetic field. Generally. An inductor consists of a coil of conducting wire wound around a core. 22/12/2014 5 Inductance An inductor is a passive element that stores energy in its magnetic field. Generally. An inductor consists of a coil of conducting wire wound around a core. For the inductor + di (t ) v(t ) L dt v L where L is the inductance in henrys (H), and 1 H = 1 volt second/ampere. Inductance is the property whereby an inductor exhibits opposition to the change of current flowing through it 22/12/2014 6 Symbols of Inductors Relationship Between Current and Voltage di (t ) v(t ) L dt Integrating gives Or where i(t0) = the total current evaluated at t0 and i() 0 (which is reasonable since at some time there was no current in the inductor). 22/12/2014 8 Relationship Between Current and Voltage Content Introduction Capacitor Energy storage in capacitor Series and parallel Capacitors Inductor Energy storage in Inductor Series and parallel Inductors Energy Storage in an Inductor The instantaneous power delivered to an inductor is di p (t ) vi Li dt The energy stored in the magnetic field is thus t di wL (t ) p(t )dt L i dt L idi dt 1 2 wL (t ) Li (t ) joules 2 t 22/12/2014 11 An Inductor Properties An inductor has the following important properties: 1. An inductor acts like a short circuit to dc, since from di (t ) v(t ) L dt v = 0 when i = a constant. 2. The current through an inductor cannot change instantaneously, since an instantaneous change in current would require an infinite voltage, which is not physically possible. 22/12/2014 12 An Inductor Properties An inductor has the following important properties: 3. Like the ideal capacitor, the ideal inductor does not dissipate energy. 4. A real inductor has a significant resistance due to the resistance of the coil, as well as a “winding capacitance”. Thus, the model for a real inductor is shown below. RW L CW In this course, however, we will use ideal inductors and assume that an ideal inductor is a good model. 22/12/2014 13 22/12/2014 14 22/12/2014 15 22/12/2014 16 22/12/2014 17 22/12/2014 18 22/12/2014 19 Content Introduction Capacitor Energy storage in capacitor Series and parallel Capacitors Inductor Energy storage in Inductor Series and parallel Inductors Series Inductor L1 L2 LN + + DC v 1- + v2 - + vN - v DC v i Leq - i di v1 L1 dt di v2 L2 dt di vN LN dt di di v v1 v2 vN L1 L2 LN Leq dt dt The equivalent inductance of series connected inductors is the sum of the individual inductances. Note: inductances in series combine in the same way as resistors in series. 22/12/2014 21 Parallel Inductor + v i i2 i1 L1 + iN L2 LN i 1 i2 vdt L2 Leq - - 1 i1 vdt L1 v i iN 1 vdt LN 1 1 1 1 i i1 i2 iN vdt vdt LN Leq L1 L2 The equivalent inductance of parallel connected inductors is the reciprocal of the sum of the reciprocals of the individual inductances. 22/12/2014 22 22/12/2014 23 22/12/2014 24 22/12/2014 25 22/12/2014 26 22/12/2014 27 22/12/2014 28