Download An inductor has the following important properties

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