User Note:
Run View Show under the Slide
Show menu to enable slide selection.
Chapter 7 Capacitors and Inductors
Fig. 7.1 Electrical symbol and current-voltage … for a capacitor.
Fig. 7.3
(a) The current waveform applied to a 5µ F capacitor.
Fig. 7.5 (and 7.6) From Example 7.2.
Fig. 7.10 Electrical symbol and current-voltage …for an inductor.
Fig. 7.16 Circuit for Example 7.6.
Fig. 7.18 (and 7.19) Inductor combinations.
Figs. 7.20 (and 7.21) Capacitor combinations.
Fig. 7.27 An ideal op amp connected as an integrator.
Fig. 7.28
An ideal op amp connected as a differentiator.
Engineering Circuit Analysis Sixth Edition
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin
Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved.

Fig. 7.1 Electrical symbol and current-voltage conventions for a capacitor.
i c
Electrical symbol and current-voltage conventions for a capacitor.
+ v c
( ) i i c
( )
= C d dv dt dt
( )
!
v c
( )
= 1/ C % t
#$ i c
Stored Energy = E c
=
( )
Cv 2
( ) d "
An instantaneous change in capacitor voltage requires an infinite current. Therefore in practical circuits, a capacitor voltage cannot change instantaneously. Also, if the voltage across a capacitor is constant, the current through it is zero.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.3 (a) The current waveform applied to a 5µ F capacitor. (b) The resultant voltage waveform obtained by graphical integration.
Find the capacitor voltage that is associated with the current shown graphically below.
v c
( ) ( ) i c
( ) ( )
C = 5 µ F v c
( )
=
1
5 !
10 " 6 F
$ t
0
20 !
10 " 3 A d # = 4000 t V , 0 < t < 2 ms
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.5 and 7.6 From
Example 7.2.
Find the maximum energy stored in the capacitor of the circuit below, and the energy dissipated in the resistor over the interval
0 < t < 500 ms.
E c
=
( )
Cv 2 =
20 !
10 " 6 F
2
!
100 2 sin 2
( )
V 2 = 0.1sin
2
( )
J
Graph of capacitor energy as a function of time.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.10 Electrical symbol and current-voltage conventions for an inductor.
Electrical symbol and current-voltage conventions for an inductor.
i
L
+ v
L
( ) v
L
( )
= L d dt i
( )
!
i
L
( )
= 1/ L % t
#$ v
Stored Energy = E
L
=
( )
L i 2
L
( ) d "
An instantaneous change in inductor current requires an infinite voltage. Therefore in practical circuits inductor current cannot change instantaneously. Also if the current through an inductor is constant, the voltage across it is zero.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.16 Circuit for Example 7.6
Find the maximum energy stored in the inductor of the circuit below.
E
L
=
3H
2
!
12 2 sin 2
(
" t / 6
)
A 2 = 216sin 2
(
" t / 6
)
J
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Figs. 7.18 and 7.19 Inductor combinations.
L eq
= L
1
+ L
2
+ !
+ L
N
( c )
( d )
1/ L eq
= 1/ L
1
+ 1/ L
2
+ !
+ 1/ L
N
(a) N inductors connected in series; (b) equivalent circuit; (c) N inductors connected in parallel; (d) equivalent circuit for circuit in (c).
Inductors in series combine like resistors in series.
Inductors in parallel combine like resistors in parallel.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Figs. 7.20 and 7.21 Capacitor combinations.
(c)
(d)
1/ C eq
= 1/ C
1
+ 1/ C
2
+ !
+ 1/ C
N
C eq
= C
1
+ C
2
+ !
+ C
N
(a) N capacitors connected in series; (b) equivalent circuit;
(c) N capacitors connected in parallel; (d) equivalent circuit to (c).
Capacitors in series combine like resistors in parallel.
Capacitors in parallel combine like resistors in series.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.27 An ideal op amp connected as an integrator.
An ideal op amp connected as an integrator.
i
( )
= v s
( )
/ R
1 v
C f
( )
=
( )
$ t
"# i !
d !
v
C f
( )
=
(
1/ R
1
C f
)
$ t
"# v s
( ) d !
v out
( )
= "
(
1/ R
1
C f
)
$ t
"# v s
( ) d !
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.

Fig. 7.28 An ideal op amp connected as a differentiator.
An ideal op amp connected as a differentiator.
+ v
R f
( )
v i
( )
= C
1
R f
( )
= i d dt t
( )
R f v
R f v out
( )
= R f
C
1 d
( )
= !
R f
C
1 dt d dt s s
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.