222/12/2014

Circuit Analysis-1 Fall-2014EE -1111

Instructor: Hafiz Zaheer HussainEmail: zaheer.hussain@ee.uol.edu.pk

www.hafizzaheer.pbworks.com

Department of Electrical EngineeringThe University of Lahore

Lecture # 25 & 26

222/12/2014

3

22/12/2014

Content

Introduction

Capacitor

Energy storage in capacitor

Series and parallel Capacitors

Inductor

Energy storage in Inductor

Series and parallel Inductors

522/12/2014

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.

Inductor

622/12/2014

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

Inductance

( )( )

di tv t L

dt

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

+

-

Lv

Symbols of Inductors

822/12/2014

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).

( )( )

di tv t L

dt

Relationship Between Current and Voltage

Integrating gives

Or

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

1122/12/2014

Energy Storage in an Inductor

The instantaneous power delivered to an inductor is

( ) ( )t t

L

diw t p t dt L i dt L idi

dt

( )di

p t vi Lidt

The energy stored in the magnetic field is thus

21( ) ( ) joules

2Lw t Li t

1222/12/2014

An Inductor Properties

An inductor has the following important properties:

1. An inductor acts like a short circuit to dc, since from

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.

( )( )

di tv t L

dt

1322/12/2014

An Inductor PropertiesAn 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.

In this course, however, we will use ideal inductors and assume that an ideal inductor is a good model.

C

RW

W

L

1422/12/2014

1522/12/2014

1622/12/2014

1722/12/2014

1822/12/2014

1922/12/2014

Content

Introduction

Capacitor

Energy storage in capacitor

Series and parallel Capacitors

Inductor

Energy storage in Inductor

Series and parallel Inductors

2122/12/2014

Series Inductor

1 1

div L

dt 2 2

div L

dt N N

div L

dt

1 2 1 2N N eq

di div v v v L L L L

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.

DC

1L 2L NL

1v 2v Nv+ + + -- -

v

i

i

eqLv+

-

DC

2222/12/2014

Parallel Inductor

11

1i vdt

L

1 21 2

1 1 1 1N

N eq

i i i i vdt vdtL L L L

The equivalent inductance of parallel connected inductors is the reciprocal of the sum of the reciprocals of the individual inductances.

22

1i vdt

L

1N

N

i vdtL

1i 2i Ni

1L 2L NLv+

-

i

i

v+

-

eqLi

2322/12/2014

2422/12/2014

2522/12/2014

2622/12/2014

2722/12/2014

2822/12/2014