REVIEW QUESTIONS
6.1
R E VWhat
I E Wcharge
Q U E SisTonI OaN5-F
S capacitor when it is
6.5
The total capacitance of two 40-mF series-connected
capacitors in parallel with a 4-mF capacitor is:
6.5 (a) 3.8
ThemF
total capacitance
(b) 5 mFof two 40-mF
(c) 24series-connected
mF
capacitors
in(e)
parallel
with a 4-mF capacitor is:
(d) 44
mF
84 mF
(a) 3.8 mF
(b) 5 mF
(c) 24 mF
6.6
In Fig.
6.43,
if
i
=
cos
4t
and
v
=
sin
4t,
the
(d) 44 mF
(e) 84 mF
element is:
6.6 (a) aInresistor
Fig. 6.43,(b)
if i a=capacitor
cos 4t and v(c)= an
sininductor
4t, the
element is:
(a) a resistor (b) a capacitor (c) an inductor
|
e-Text Main Menu| Textbook Table of Contents |Problem Solving Workbook Contents
Answers: 6.1a, 6.2d, 6.3d, 6.4b, 6.5c, 6.6b, 6.7a, 6.8b, 6.9a, 6.10d.
▲
▲
▲
|
▲
connected across a 120-V source?
6.1 (a) 600
What
C charge is on a 5-F
(b)capacitor
300 C when it is
connected
across a 120-V
source?
(c) 24
C
(d) 12
C
(a) 600 C
(b) 300 C
(c) 24 Cis measured in: (d) 12 C
6.2
Capacitance
(a) coulombs
(b) joules
6.2 (c) henrys
Capacitance is measured
(d) in:
farads
(a) coulombs
(b) joules
6.3
When
total charge in a capacitor
is doubled, the
(c)thehenrys
(d) farads
i
energy stored:
6.3 (a) remains
When the
charge(b)
in aiscapacitor
thetotal
same
halved is doubled, the
v +
i
Element
!
stored:
(c) isenergy
doubled
(d) is quadrupled
(a) remains the same
(b) is halved
v +
Element
!
6.4
Can (c)
the voltage
waveform in Fig.
be associated
is doubled
(d) 6.42
is quadrupled
with a capacitor?
Figure 6.43 For Review Question 6.6.
6.4 (a) Yes
Can the voltage waveform
in Fig. 6.42 be associated
(b) No
CHAPTER 6
Capacitors and Inductors
227
with a capacitor?
v (t)
Figure
6.43 changes
For Review
Question
6.7
A 5-H
inductor
its current
by6.6.
3 A in 0.2 s.
(a) Yes
(b) No
The voltage produced at the terminals of the
6.9 10 Inductors
in parallel can be combined just like
L1
v (t)
inductor
is:
6.7
A
5-H
inductor
changes its current by 3 A in 0.2 s.
resistors in parallel.
+
!
The
at the
terminals
of the
(a) 75
V voltagev 1produced(b)
8.888
V
(a)10True
(b) False
+ (d) 1.2 V
is:
0
(c) 3inductor
V
+
v
v
1
2
t
L 2(b) 8.888 V
2
s (a)
6.10
For the circuit in Fig. 6.44, the voltage divider
! 75 V
!
6.8
If the(c)
current
inductor
formula
is:
0
3 V through a 10-mH (d)
1.2 Vincreases
1
2
t
L
+
L
L
+
L
from zero to 2 A, how much energy is stored in the
1
2
1
2
!10
(a) v1 =
vs
(b) v1 =
vs
6.8 inductor?
If the current through a 10-mH inductor increases
L1
L2
from
to 2Review
A, how
much
energy
is stored in the
(a)Figure
40
mJ
(b)
20 6.10.
mJ
!10
6.44zero For
Question
L2
L1
inductor?
v1 = For Review
vsQuestion
(d)6.4.
v1 =
vs
(c) 10
mJ
(d) 5 mJ
Figure(c)6.42
L1 + L 2
L1 + L 2
(a) 40 mJ
(b) 20 mJ
(c) 10 mJ
(d) 5 mJ
Figure 6.42 For Review Question 6.4.
(a) True (a) True
(b) False
v1
(b)CHAPTER
False 6
+++
Capacitors
and
Inductors
227
6.2
AInductors
40-µF capacitor
is can
charged
to 120 Vjust
andlike
is then
0
+
6.9
in parallel
be combined
L1
v22 LL 2
vss +! +
v
v
6.10
For
the
circuit
in
Fig.
6.44,
the
voltage
divider
v!s ! 2
4 6 8v 2 10 L2 2 12 t (ms)
6.10 allowed
For
the circuit
toin
discharge
to in
80Fig.
V. How
much
energy
is6
6.10
For
the circuit
6.44, the
voltage
divider
resistors
parallel.
CHAPTER
Capacitors
and
Inductors
227
!!!
+ v !
formula
formula is:
is:
formula
is:
lost?
1
True L1 +
(b) False L1 +
L
6.9 (a) Inductors
parallel
22 L1 + can
L1
L2 be combined
L22like
+
1 in L
1 just
1 + L2
!10
(a)
v
=
v
(b)
v
=
v
(a)
v
=
(a)
v
=
v
(b)
v
=
v
1
s
1
s
1
s
1
s
1
s
1
s
+
in
parallel.
v2
vs !
6.3
5 resistors
s,
voltage
across
a 40-mF
6.9
in parallel
cancapacitor
be combined
L2
LInductors
L6.44,
Ljust
L22 changes
11in Fig.
1
2 like
6.10 In
For
thethe
circuit
the voltage
divider
+ vL 1 !
1
resistors
in parallel.
!
from
160
V
to
220
V.
Calculate
the
average
current
(a)
True
(b)
False
! Review
formula is: L
Figure
Question 6.10.
6.10.
Figure
6.446.44 +For
For
Review
+Question
Figure
6.44
vFor
L1
L
1 Review Question 6.10.
22 TrueL2
(a)
(b)
False
1L
through
the
capacitor.
+
(c)
v
=
v
(d)
v
=
v
L
+
L
L
+
Figure
For Prob. 6.6.
v+2
vs !6.46
s
s
vv11 =
(d)
v voltage
= 11 divider
1 1 2 vs
2 s
(c) For
=
L2
6.10(c)
theLcircuit
inL
L1vv+
+ L6.44,
(a)
v1 =
vs1Fig.
v11 =
+
2 (b) the
s L2
+
L
v
v
L
+
L
1
2
L
2
s
1
2
1
2
2
!
6.10 is:
For
the circuit in Fig. 6.44, theLvoltage
divider
!
1 4t
2
formula
6.4
A current
of 6Lsin
A flows through a 2-F
!
formula
is:
L1the
+L
L
LL2 + L
2
1 +
capacitor.
voltage
the
capacitor
Figure6.1a,
6.446.2d,For
Review
Question
6.10. 6.8b, 6.9a, 6.10d.
+ v(t)
L2(b) across
1 vs
2
Answers:
6.3d,
6.4b, 6.5c,
6.6b, 6.7a,
L
(a) v1 Find
= L(a)
v
=
2 v =vL
1
s 1
1
v
(b)
v
=
v
6.7
At
t
=
0,
the
voltage
across
a
50-mF
capacitor
is
Answers:
6.1a,
6.2d,
6.3d,
6.4b,
6.5c,
6.6b,
6.7a,
6.8b,
6.9a,6.10d.
6.10d.
1
s
1
s
Answers:
6.1a,
6.2d,
6.3d,
6.4b,
6.5c,
6.6b,
6.7a,
6.8b,
6.9a,
given
(c) v1that
= v(0) =
v1 =
L11vV.
L 2 vs
s
L(d)
1
L1 + L 2
L1 + L 2 L2
10
V. Calculate
the
voltage
across
the capacitor for
Figure
6.44
For
Review
Question6.10.
6.10.
Figure
6.44
For
Review
Question
L
L
L
L
2
1
6.5
If the(c)current
in 2Fig.
6.45 is
applied
to1a v
t > 0 when current 4t mA flows through it.
(c) v1 =vs
vs v 1 =
(d) v1 = vs
v1 = waveform
(d)
s
L1 voltage
+ L2
20-µF capacitor,
v(t) across
the
L1 +find
L1 + LL
L2 the
21 + L2
Answers:
6.1a,current
6.2d, 6.3d,
6.4b, 6.5c,
6.6b,capacitor
6.7a, 6.8b,
6.8
The
through
a 0.5-F
is6.9a, 6.10d.
capacitor.
Assume
that
v(0)
=
0.
PROBLEMS
6(1 6.1a,
− e−t
) A.
Determine
the6.7a,
voltage
and 6.10d.
power at
Answers:
6.2d,
6.3d,
6.4b, 6.5c, 6.6b,
6.8b, 6.9a,
PPRROOBBLLEE M S
Answers:t 6.1a,
6.2d,
6.3d,
6.4b,
6.5c,
6.6b,
6.7a,
6.8b,
6.9a,
6.10d.
= v2(t)s.VAssume v(0) = 0.
Section 6.2
Capacitors
Section 6.2
6.2
Section
6.1
Capacitors
Capacitors
If the
voltage across a 5-F capacitor is 2te−3t V, find 6.9
the current
the capacitor
power. is 2te−3t V, find
P6.1R O B Li(t)
E MtheS voltage
If
acrossand
a 5-F
vv(t)
V
(t)
V voltage
If
the
across a 2-F capacitor is as shown in
10
Fig.10
6.47, find the current through the capacitor.
10
4L E M S
Section
CapacitorsCapacitors
P R O B6.2
Section 6.2
0
vv(t)
2 4 6 8 10 12 t (ms)
(t)vV(V)
(t) V
00
v (t)10V
10 2
44 66 88 10
10
10 12
12 t t(ms)
(ms)
!10 2
6.1
If the voltage across a 5-F capacitor is 2te V, find
P R Oand
B L E the
M S power.
the
current
the
6.2current
A 40-µF
capacitor is charged to 120 V and is then
allowed to discharge to 80 V. How much energy is
6.2
A 40-µF
40-µF capacitor
capacitor is charged to 120 V and
is then
6.2
A
lost?
−3t
6.1 Section
If the6.2
voltage
across
a 5-F capacitor is 2te−3t V, find
Capacitors
6.1
6.2
6.3
6.3
6.2
6.3
6.4
6.4
6.3
6.4
6.5
6.5
6.6 6.4
6.5
If the voltage across a 5-Fmuch
is 2teis V, find
allowed6.1
to discharge
energy
allowed
to
to 80 V. How capacitor
the
current
and
the
power.
the
current
and
the
power.
6.3If the voltage
In 5 s, the
voltage
across
a 40-mF
capacitor
changes
−3t
lost?
lost?
10
across
a 5-F
capacitor
is 2te
V, find
from
160
V
to
220
V.
Calculate
the
average
current
!10
6.2
A
40-µF
capacitor
is
charged
to
120
V
and
is
then
!10
the current
and the
power. to 120 V and is then
A
40-µF
capacitor
iscapacitor.
charged
0 50
10 12 t (ms)
In
5
s,
the
voltage
across
a
40-mF
capacitor
changes
through
the
allowed
to discharge
to 80
V. How much
energy is
In
5 s, the
voltage
across
a V.
40-mF
capacitor
changes
Figure 6.46
2 2 44For66Prob.886.6.
10 12 t (ms)
allowed
to
discharge
to
80
How
much
energy
is
0
from
160
V
to
220
V.
Calculate
the
average
current
lost?
A160
40-µF
capacitor
is 2charged
to 120
V andcurrent
is then
from
V to
V.6Calculate
the
average
0
1 220 of
lost?
6.4
A current
sin 4t At flows through a 2-F
!10
8 10 12 t (ms)
2 For
4 6 6.6.
through
the
capacitor.
allowed
to
discharge
to 80
V.
How
much
energy
ischanges
through
the
capacitor.
Figure
6.3
In 5 s,Find
the voltage
across
a 40-mF
capacitor
capacitor.
the
voltage
v(t)
across
the capacitor
!10 06.46
Figure
6.46
ForProb.
Prob. 6.6.
6.7
At t = 0,1 the2voltage
160
V=toa1220
V. Calculate
the changes
average current
In
5lost?
s,6.45
thegiven
voltage
across
40-mF
capacitor
Figure
For
Prob.
6.5.
that
v(0)
V.through
3 across
6 7 capacitor
4 5 a 50-mF
t (s) is
A current
current
of
6 from
sin
4t
A
flows
a
2-F
A
of
6
sin
4t
A
flows
through
a
2-F
!10
the
capacitor.the average current
10 V.6.46
Calculate
the 6.6.
voltage across the capacitor for
from
160 VFind
to through
220
V.
Calculate
Figure
For Prob.
capacitor.
the
voltage
v(t)
across
the
capacitor
In
5
s,
the
voltage
across
a
40-mF
capacitor
changes
capacitor.
Find
the
voltage
v(t)
across
the
capacitor
6.5
If the
current waveform in Fig. 6.45 is applied to a
t > 0 when current 4t mA flows through it.
through
the
capacitor.
6.7
At
tt =
0,
voltage
across
6.4
Ato
current
of Calculate
6find
sin 4t
Avoltage
flows
through
acurrent
2-F the
6.47
For
Prob.6.6.
6.9.
Figure
6.46
Prob.
given
that
v(0)
=
1
V.
from
160
V
220
V.
the
average
6.7
At
=
0, the
theFor
voltage
acrossaa50-mF
50-mFcapacitor
capacitorisis
20-µF
capacitor,
the
v(t)
across
given that v(0)capacitor.
= 1 V. Find the voltage v(t) across the capacitor
V.
Calculate
the
voltage
across
the
for
6.8 10
The
current
through
a 0.5-F
capacitor
is
through
the
capacitor.
10
V.
Calculate
the
across
thecapacitor
capacitor
for
capacitor.
Assume
that
v(0) =a0.2-F
Figure
6.46
For
Prob.voltage
6.6.
A
current
of
6
sin
4t
A
flows
through
6.7
At
t
=
0,
the
voltage
across
a
50-mF
capacitor
is
given
that
v(0)
=
1
V.
−t
If
the
current
waveform
in
Fig.
6.45
is
applied
to
a
t
>
0
when
current
4t
mA
flows
through
it.
6(1
−
e
)
A.
Determine
the
voltage
and
power
at
If
the
current
waveform
inFig.
Fig.
6.45
applied
to a
t >10current
0V.when
current
4t
flows
through
Calculate
the voltage
across
the
capacitorit.
for
capacitor.
Find
the
voltage
v(t)
across
the
capacitor
The
voltage
waveform
in
6.46
isisapplied
across
6.10
The
through
an mA
initially
uncharged
4-µF
A
current
of
6
sin
4t
A
flows
through
a
2-F
20-µF
capacitor,
find
the
voltage
v(t)
across
the
t
=
2
s.
Assume
v(0)
=
0.
6.5
If
the
current
waveform
in
Fig.
6.45
is
applied
to
a
t
>
0
when
current
4t
mA
flows
through
it.
20-µF
capacitor,
find
the
voltage
v(t)
across
the
6.7
At
t=
0, the
voltageinaacross
acapacitor
50-mF
is
that
v(0)
= 1Draw
V.voltage
agiven
30-µF
capacitor.
the current
waveform
capacitor
is shown
Fig.
6.48.
Findcapacitor
the
6.8
The
current
through
0.5-F
isis voltage
capacitor.
Find
capacitor
capacitor.
Assume
that
v(0)
=v(t)
0.theacross
20-µFthe
capacitor,
find
voltagethe
v(t)
across the
6.8
The
current
through
a
0.5-F
capacitor
capacitor.
Assume
that
v(0)
=
0.
Calculate
the
voltage
across
capacitor
−t
the
across
a 02-F
is
as power
shown
in
through
across
capacitor
<capacitor
tvoltage
< 3.the
6.7 6.9
AtV.
tIf
=
0,
voltage
across
acapacitor
50-mF
isfor
6.8 10
The
current
through
afor
0.5-F
is capacitor
6(1
−
ethe
)the
A.
Determine
the
and
atat
−tvoltage
givenit.that v(0)
= 1 V.
capacitor.
Assume that v(0) = 0.
6(1
−
e
)
A.
Determine
the
voltage
and
power
−t
If the current waveform in Fig. 6.45 is applied to a
tt10
>
0
when
current
4t
mA
flows
through
it.
Fig.
6.47,
find
the
current
through
the
capacitor.
− eAssume
) A. Determine
voltage the
and capacitor
power at for
V.
Calculate
the
voltage
=6(1
2 s.
v(0)
=the
0.across
i(t)
6.11 Find
A voltage
of 60across
cos 4πt
appears across
6.12
the voltage
theVcapacitors
in thethe
circuit
terminals
of
aa 3-mF
capacitor.
Calculate
the
current
terminals
of
3-mF
capacitor.
Calculate
the
current
228
ofthrough
Fig. 6.49
under
dc
conditions.
the
capacitor
and
the
energy
stored
in
through the capacitor and the energy stored in itit
from
s.
fromt t ==00to
to tt =
= 0.125
0.125 s.
eq for the circuit
PART 1 Find CDC
Circuits(c) in Fig. 6.51.
6.19
Obtain the equivalent capacitance of the circuit in
6F
Fig.
6.54.
6.16 CFind
Find
circuit
in Fig.
eq for
6.16
CeqCfor
thethe
circuit
in Fig.
6.51.6.51.
eq
40
3"
C1
20 "
10 "
0
3"
+
50"" v2
50
!
60 V1
+
!
20
20""
++
v
v11 !40
CC11
For Prob.
!! 6.12.
3"
Figure
6.49
++ 60 V
!! 60 V
Figure6.49
6.49
Figure
5 mF
15 mF
30 mF
20 20
mFmF 30 mF
C2
2
++
v2v2
!!
CC
eq eq
t (s)Figure 6.51
3
6.17
40 mF 4 F
CC
22
For Prob. 6.12.
For Prob. 6.12.
For
Prob.
15 mF
15
mF 6.16.5 mF5 mF
2F
vs
(b)
Prob.
6.16.6.16.
Figure
6.516.51 ForFor
2F
Prob.
Figure
5 mF
5
mF
6.17
thethe
equivalent
capacitance
for 20
the
6.17 Calculate
Calculate
equivalent
capacitance
forcircuit
the circuit
in in
Fig.
6.52.
AllAll
capacitances
are in
15mF.
mF
Fig.
6.52.
capacitances
are
in mF. 15 mF
Series and Parallel Capacitors
15
5
1
4F
3
3F
5
(c)
15
3
6
6
15
3
Figure 6.50 For Prob. 6.15.
Figure 6.54 For Prob. 6.19.
a2
b
through
the capacitor
and the energy stored in it
6.13
What
is
the
total
capacitance
of
four
30-mF
6.14
Two capacitors (20 µF and 30 µF) are connected to
t = 0 tooft four
= 0.125
s.
6.13
What
is theconnected
totalfrom
capacitance
30-mF
capacitors
in:
a 100-V
source. Find the
energy stored in each
capacitors
connected
in: (b) in:
(a) parallel
series
capacitor
if they are
connected
2 the circuit in Fig. 6.51.
C eq
6.12
Find
the voltage
across the capacitors in the circuit
1
6.16
Find Ceq for
(a)
parallel
(b)
series
2 6
6 4
C
8
eq
(a) parallel
(b)
series
1
of Fig. 6.49 under dc conditions.
6.20
For the circuit
6 determine:
6 in Fig. 6.55,
6.14
Two capacitors (20 µF and 30 µF) are connected to
20
mF
30
mF
6.14
Two
capacitors
(20
µF
and
30
µF)
are
connected
to
a 100-V source.
Find thecapacitance
energy stored
each
(a)6.17.
the voltage across each capacitor,
6.15
Determine
the equivalent
for in
each
of the
Figure 6.52 For Prob.
a
100-V
source.
Find
the
energy
stored
in
each
capacitor
if
they
are
connected
in:
circuits in Fig. 6.50.
(b) thecapacitance
energy
stored
in each capacitor.
50 "
6.18
Determine the equivalent
at terminals
4
capacitor
if they are connected
in: 10 "
8
(a) parallel
(b) series
C eq
a-b of the circuit in 8Fig. 6.53.
4 mF
(a) parallel
(b) series
5 mF
15
40 mF
6.15
Determine
the
equivalent
capacitance
for
each
of
the
Figure
6.52
For
Prob.
6.17.
12 F
4F
circuits in Fig.
6.50.
+ for each of20
6.15
Determine
the equivalent
capacitance
the" 6.18+ Determine
Figure
For
Prob. 6.17. 4 mF
5 mF6.52
6 mF
the equivalent
capacitance at terminals
4 mF
v2
v
C2
C1
circuits in Fig. 6.50.
3"
1
a-b
of
the
circuit
in
Fig.
6.53.
a Determine the equivalent capacitance at terminals
6.18
!
!
+ 60 V
6F
3F
Figure
a-b of the circuit in
Fig.+6.51
6.53. For Prob. 6.16.
!
12 F
4F
6 mF
2 mF
12 mF
120
V
! 3 mF
5 mF
6 mF
4 mF
2
mF
12 F
4F
6.17
Calculate the equivalent capacitance for the circuit
3 mF
ba
5 mF
6 mF
4 mF
3F
3F
4F
6F
Figure 6.49
(a)
For Prob. 6.12.
6F
|
▲
Section (a)
6.3
6.23
6.24
in Fig. 6.52. All capacitances are in mF.
a
Figure
6.53
2 mF 6.18.
For Prob.
3 mF
2 mF
b
Figure 6.55
Series and Parallel Capacitors
4F
b
Figure
6.53
12 mF
5
3 mF
12 mF
For Prob. 6.20.
For Prob. 6.18.
15
3
Textbook
Table
of
Contents
Problem
Solving
Workbook
Contents
e-Text What
Main
Menu
|
|
6.13
is
the
total
capacitance
of
four
30-mF
6.21
Repeat
Prob.
6.20
for
the
circuit
in
Fig. 6.56.
(a)
capacitors connected in:
▲
▲
|
▲
4F
+
!
40 mF
40 mF
mFthe circuit
10 mF
Calculate the equivalent capacitance10for
in Fig. 6.52. All capacitances
35 mFare in mF.
3F
6F
What is the total capacitance of four 30-mF
capacitors
connected
in:
6.11
A voltage
of 60 cos 4π t V appears across the
(a) 6.3
parallel Series
(b)of series
Section
and Parallel
Capacitors
C eq
terminals
a 3-mF
capacitor. Calculate the current
Section 6.3
40 mF
5F
ForCapacitors
Prob. 6.10.
SeriesFigure
and6.48
Parallel
Section 6.3
6.13
+
v1
!
Capacitors and
206.50
mF6.50 For
30 For
mF
Figure
Prob.
Figure
Prob.
6.15.6.15.
Find
across
the capacitors
capacitors
thecircuit
circuit
50 " ininthe
10(mA)
" the
Findthe
thevoltage
voltagei(t)
across
ofofFig.
Fig.6.49
6.49 under
under dc
dc conditions.
conditions.
6.12
6.12
CHAPTER 6
(c)
6.16
Figure 6.53
For Prob. 6.18.
∗
6.25
F
C
C C2
C1C+ C2 C eq
C1C+
1
2
i1 =
is , C eq i(b)
is
2 =
C C1 + C 2
C1 + CC2
C
assuming that the initial conditions
are zero.C
Figure 6.62
C
C
6.30
For Prob. 6.29.
Find the voltage and the power at t = 3 s.
Inductors
Section
6.4
Inductors
Figure 6.62Inductors
For Prob. 6.29.
Section
6.4
The current6.31
through aThe
10-mH
inductor
6e−t/2
A.
current
in aiscoil
increases
uniformly from−t/2
0.4 to
Section 6.4
6.30 and the
Thepower
currentt =
through
a 10-mH inductor
is 6e
Find the voltage
3 s.the
1 A6.4
in 2 satso
that
voltage
acrossisthe
coilA.is
6.30
The
current
through
a 10-mH
inductor
6e−t/2
Section
Inductors
A.
(b)
Findthethe
voltage
and
the power
at3 s.t = 3 s.
Figure
For
Prob.
6.26.
Three
capacitors,
C1 =
5 µF,
C2 =
10 are
µF,zero.
and
assuming
that6.59
the
initial
conditions
C6.31
Find
voltage
andfrom
the inductance
power
at t =of
60
mV.
Calculate
the
the coil.
C
The
current
in
a
coil
increases
uniformly
0.4
to
6.30
The current through a 10-mH inductor is 6e−t/2 A.
C3 = 20 µF, are connected in(b)
parallel
(b) across a
1 A in 2 s so
that theThe
voltage
across
the
is increases
6.23 Figure
Three
capacitors,
C1 6.26.
= 5 µF, C2 = 10 µF, and
6.31
The
current
acoil
coil
uniformly
6.31
current
in through
ain
coil
increases
uniformly
to 0.4 to
Find
the
voltage
and
the
power
atinductor
t = from
3 s. is0.4from
150-V
source.
Determine:
6.59
For Prob.
6.32
The
current
a
0.25-mH
60
mV.
Calculate
the
inductance
of
the
coil.
C3 = 20 µF, are connected in parallel(b)
across a
1AAcos
sA.so
that
the voltage
across
the
is the
112
inin
22t
s2so
that
the voltage
the coil
is coil
6.27theFigure
Assuming
theFor
capacitors
(a)
total
capacitance,
Determine
theacross
terminal
voltage
and
Figure that
6.59 Prob.
Prob. 6.26.are initially uncharged,
6.59
For
6.26.
6.31
The
current
in
a
coil
increases
uniformly
from
0.4
150-V source.
Determine:
mV.
Calculate
theisinductance
of the of
coil.
6.32
The current through 60
a60
0.25-mH
inductor
mV.
Calculate
the inductance
the coil. to
find
v
(t)
in
the
circuit
in
Fig.
6.60.
(b)
the
charge
on
each
capacitor,
o
power.
1
A
in
2
s
so
that
the
voltage
across
the
coil is
6.27
Assuming
thatcapacitance,
the capacitors
are For
initially
(a) the total
12 cos 2t A. Determine the terminal voltage and the
Figure
6.59
Prob.uncharged,
6.26.
6.32
The
current
through
a
0.25-mH
inductor
is
(c) vthe
total
energy
stored
the parallel
60 mV.
Calculate
the inductance
ofinductor
the coil. is
find
in the
circuit
Fig.in6.60.
6.32
The
current
through
a12-mH
0.25-mH
o (t)
power.
(b) the
charge
eachincapacitor,
6.33
The
current
through
a
inductor
is
6.27 onAssuming
that the capacitors are initially uncharged,
12
cos
2t
A.
Determine
the
terminal
voltage
and the
combination.
6.27
Assuming that the capacitors are initially uncharged,
is (mA)
12
cos
2t
A.
Determine
the
terminal
voltage
and the
6.32
The
current
through
a
0.25-mH
inductor
findstored
vo (t) in the circuit
(c)
the total energy
parallelin Fig. 6.60. 6.33
The current through power.
a412-mH
inductor
is the voltage, and also isthe energy
sin 100t
A. Find
find
v
(t)
in
the
circuit
in
Fig.
6.60.
i6.24
Assuming
that the capacitors
are
o
6 mFinitially uncharged,
power.
s (mA) Thecombination.
12 cosin2tand
A.also
Determine
the0terminal
voltages.and the
three6.27
capacitors
in the previous
problem are
4 sin 100t A. Find thestored
voltage,
the energy
the
inductor
for
< t < π/200
60
6
mF
find
v
(t)
in
the
circuit
in
Fig.
6.60.
6.33
The
current
through
a
12-mH
inductor
is
o
power.
placed in
series with a 200-V
source. Compute:
stored in the inductor for
0 < t < π/200 s.
is (mA)
6.33
The
current
through
12-mH
inductor
4
sin
100t
A. Find
the voltage,
andinductor
also
the energy
i
6.2460 The
three
capacitors
in
the
previous
problem
are
s
The
current
through
a a12-mH
40-mH
is is
+ The current6.34
(a) the total capacitance,
is (mA)
is
6
mF
6.33
The
current
through
a
inductor
is
6.34
through
a
40-mH
inductor
is
+
stored
the A.
inductor
< t < π/200
placed in iseries
with a 200-V source. Compute:
4 sin in
100t
Find for
the0voltage,
and s.
also the energy
60 on
3mF
mF
vo (t)
s (mA)
! 4 sin 100t A. Find !
(b) the charge
each capacitor,3 mF
6
the
voltage,
and
also
v
(t)
0, for inductor
t is<π/200
0the energy
in the
0<t <
s.
(a) the total capacitance,
0,stored
ti(t)
<inductor
0 =a 40-mH
is o
6 mF
6.34
The
current
through
+
0 (c)60the0total energy
!
stored
in
the
inductor
for
0
<
t
<
π/200
s.
i(t)
=
−2t
stored
in
the
series
combination.
!
−2t
60
A,
t >0
te A,
t > 0 ! te
t (s)
1 each2capacitor,
1 charge
2 t (s)
(b) the
on
3 mF
vo (t)
is
6.34
The
current
through
a
40-mH
inductor
0,
t
<
0
+
is
∗
6.34
The current
through
a 40-mH inductor is is
+ the voltage
6.25 (c)
Obtain
the equivalent
capacitance
of the
network
0
i(t)
=
the total
energy
stored
in the series
combination.
!Find
v(t).Find
−2t
the voltage v(t).
te!! A,
t >0
1
2 t (s)
3 mF 3 mF vo (t)vo (t)
Figure
6.60in Figure
For6.58.
Prob.
6.27.
shown
Fig.
0,
6.60
For Prob. 6.27.
0,
t <t 0< 0
−2t
∗
6.35 ! The
across aFind
2-H the
inductor
is
20(1
−
e
)
V.
0 the equivalent
6.25
Obtain
capacitance of the network
i(t)
=
0
i(t)
=
! voltage6.35
−2t
−2t
voltage
v(t). ate2-H
The voltage
across
inductor
ist 020(1
− e−2t ) V.
te
A,
>
0
A,
t
>
t
(s)
1
2
t
(s)
1
2
If
the
initial
current
through
the
inductor
is
0.3
A,
shown in Fig. 6.58.
Figure 6.60 For Prob. 6.27.
If the
initial
current
through
theis inductor
is )0.3
6.28
If v(0) = 0, find v(t), i1 (t), and i2 (t) in the circuit in
find the current
the
energy
stored
in athe
inductor
6.35and The
voltage
across
2-H
inductor
20(1 − e−2t
V. A,
Find
thecurrent
voltage
v(t).
6.28
in
Find
the
voltage
v(t).
Fig.
6.61. If v(0) = 0, find v(t), i1 (t), and i2 (t) in the circuit
find
the
and
the
energy
stored
in
the
inductor
at t = 1 s.
If the initial current through the inductor is 0.3 A,
Figure =
6.600,
For Prob. 6.27.
Figure
Prob.
Fig.6.60
6.61.
6.28
If v(0)For
find6.27.
v(t), i1 (t), and i2 (t) in the circuit in
at
tin
=voltage
1current
s.6.63across
6.35
The
voltage
2-H
inductor
− e−2t
−2t
find
the
and
theaaenergy
stored is
in 20(1
the
inductor
6.35
The
across
2-H
inductor
is
20(1
−)eV.
) V.
6.36
If
the
voltage
waveform
Fig.
is
applied
Fig. 6.61.
is (mA)
If
the
initial
current
through
the
inductor
is
0.3
A,
at
t
=
1
s.
across
the
terminals
of
a
5-H
inductor,
calculate
the
mF v(t), i1 (t), and i2 (t) in the circuit in 6.36
40 mF 6.28
Iffind
thethe
initial
current
through
inductor
is 0.3 A,
If
the
voltage
waveform
in Fig.the
6.63
is the
applied
v(0) = 0,50find
30IfmF
current
and=the
energy
stored
in
inductor
is (mA)
current
through
the
inductor.
Assume
i(0)
−1
A.
6.28 20 If v(0)
=
0,
find
v(t),
i
(t),
and
i
(t)
in
the
circuit
in
1
2
6.36
If
the
voltage
waveform
in
Fig.
6.63
is
applied
find
andofthea 5-H
energy
storedcalculate
in the inductor
across
inductor,
the
is Fig.
(mA)6.61. 50 mF
at t the
=the
1current
s.terminals
40 mF
Fig. 6.61.
across
the
terminals
of
a
5-H
inductor,
calculate
the
30 mF
at t = 1through
s.
20
current
the inductor. Assume i(0) = −1 A.
20
current
through
the
inductor.inAssume
= −1 A.
v (t) (V)
6.36
If
the
voltage
waveform
Fig. 6.63i(0)
is applied
100 mF 1
20
mF
3
5 t
2is (mA)
4
the terminals
of a 5-H
inductor,
the
6.36
Ifacross
the voltage
waveform
in Fig.
6.63calculate
is applied
is (mA) 0
10
20
v
(t)
(V)
current
through
the
inductor.
Assume
i(0)
=
−1
A. the
10
mF
20
mF
!20
0
vacross
(t) (V) the terminals of a 5-H inductor, calculate
1 12 2 3 3 4 4 5 5 t t
20
current through the inductor. Assume i(0) = −1 A.
Figure 6.58 !20
For Prob. 6.25.
1010
0
v (t)
(V)
0
!20
6.23
Figure 6.58
is
3
i2 2
+3
4
v
i1
for each circuit in Fig.
!i1 6.59.
1
i1
For
0 Prob. 6.25.
!20
1
2
4 mF
6 mF
5
6.26
Determine Ceq
!20
6.26
Determine Ceq for each
is circuit6in
i1 4 mF
mFFig. 6.59.
is
4 mF
6 mF
Figure 6.61
6.29
For Prob. 6.28.
is
6 mF
i1
5
4
t
i
i2 2
+
+ v 6.37
i
v ! 2
+
!
4 mFi2
For the circuit in Fig.
10e−3t
V and
Figure6.62,
6.61let vFor=Prob.
6.28.
i
v1 (0) = 2 V.s Find:
4 mF
6 mF
t
+
of Contents |Problem Solving Workbook Contents v
v
6.38
!
1
Figure 6.63
2
3
v (t) (V)
10
For Prob. 6.36. 0 0
10
0
5
4
1
1
t
2
2
3
3 4
4
5
t
5
t
The current in an 80-mH
increases
from
03
Prob.
6.36.
Figureinductor
6.63 For
5
t
1
2
4
For
Prob.
6.36.
Figure
6.63
to 60 mA. How much energy is stored in the
0
inductor?
Prob. 6.36.
Figure
6.63in anFor180-mH
50 t
2inductor3 increases
4 from
6.37
The
current
A voltage of6.37
(4 + 10toThe
cos
2t)
V
is
applied
to
a
5-H
60 mA.
Howinmuch
energyinductor
is stored in
the
current
an 80-mH
increases
from 0
inductor. Find the current
i(t) through the inductor
inductor?
60 mA.
How
much
energy
is stored
in the
6.37 toThe
current
inFor
an
80-mH
inductor
increases
from 0
Prob.
6.36.
if i(0) = −1 A.
Figure 6.63
Figure 6.67
5
05
Figure
6.63
6.37
6.38
6.40
1For Prob. 6.36.
2
0
t
1
0
2
t
For Prob. 6.42. 6 "
Figure 6.67
Section
6.5
Figure 6.67
For Prob. 6.42.
Series
For Prob.
6.42. and Parallel Inductors
for
each and
circuit
in
–5 current in
The
increases from 06.43 Find the equivalent
Sectioninductance
6.5
Series
Parallel
Inductors
1 an 80-mH
2 inductor
t
Fig.
6.68.
Section
6.5
Series
and
Parallel
Inductors
to 60 mA. How much–5energy is stored in the
6.43
Find the equivalent inductance for each circuit in
6.43
Find the equivalent inductanceFig.
for 6.68.
each circuit in
inductor?
–5
Figure 6.64
For Prob. 6.39.
A voltage of (4 + 10 cos 2t) V is applied to a 5-H
Figure 6.64
For Prob. 6.39.
inductor.
the 6.39.
current
i(t) through
the inductor
Figure 6.64 Find
For Prob.
if i(0) = −1 A.
Fig. 6.68. 5 H
5H
able of Contents |Problem Solving Workbook Contents
3A
3A
Figure
Figure6.65
6.65
4"
!
4"
3A
+
v
0.5 H C
!
0.5 H
4"
2F
5"
5"
(a)
For
Prob.6.40.
6.40.
For Prob.
1H
6H
R
160 mF
5A
5A
Figure 6.66
Figure 6.66
2 "160 mF
4 mH
2"
4 mH
5A
6.44
Figure 6.66
4H
6H
3H
6H
(c)
For Prob. 6.43.
10
4 mH
4
4
10
5
For Prob. 6.41.
2H
6.44in mH.
Obtain Leq for the inductive circuit of Fig. 6.69. All
inductances are
4
inductances are in mH.
For Prob. 6.41.
For Prob. 6.41.
4H
Figure 6.68 For Prob. 6.43.
Obtain Leq for the inductive circuit of Fig. 6.69. All
inductances
areLin
6.44
Obtain
for the inductive circuit of Fig. 6.69. All
eq mH.
160 mF
2"
4H
2H
4H
Figure 6.68
6H
(b)
3H
6H
3H
6.41 For
Forthe
thecircuit
circuit in
thethe
value
of Rof R
6.41
in Fig.
Fig.6.66,
6.66,calculate
calculate
value
thatwill
willmake
make 6.41
the
stored
in in
thethe
capacitor
the the
that
the energy
energy
stored
For
the circuit
incapacitor
Fig. 6.66,
calculate the value of R
same
as
that
stored
in
the
inductor
under
dc
same as that stored in the
under
dc
thatinductor
will make
the energy
stored in the capacitor the (c)
conditions.
(c)
conditions.
same as that stored in the inductor under dc
conditions.
Figure 6.68 For Prob. 6.43.
R
12 H
(b)
For Prob. 6.40.
R
2H
4H
4H
2H
Figure 6.65
4H
(a)
2H
(b)
5"
4H
2H
6H
0.5 H
6H
(a)
iL 12 H
2F
4H
4H
12 H
iL
1H
4H
4H
1H
2"
iL
2F
6H
1H
2"
+
+vC
vC!
5H
1H
Find vC , iL , and the energy stored in the capacitor
and inductor in the circuit of Fig. 6.65 under dc
6.40
Findstored
vC , iin
andcapacitor
the energy stored in the capacitor6 H
L , the
6.40 conditions.
Find vC , iL , and
the energy
andofinductor
the circuit
of Fig. 6.65 under dc
and inductor in the circuit
Fig. 6.65in
under
dc
conditions.
conditions.
2"
1H
10
12
3
5
6
12
3
6 12
232
6.45
PART 1
DC Circuits
Determine Leq at terminals a-b of the circuit in Fig.
6.70.
L
L
L
L eq
10 mH
L
L
L
60 mH
25 mH
20 mH
a
Figure 6.73
b
For Prob. 6.48.
30 mH
6.49
Figure 6.70
Find Leq in the circuit in Fig. 6.74.
For Prob. 6.45.
L
6.46
Find Leq at the terminals of the circuit in Fig. 6.71.
L
6 mH
L
8 mH
L
a
5 mH
L eq
6 mH
Figure 6.71
Figure 6.74
4 mH
b
10 mH
L
12 mH
8 mH
8 mH
∗
6.50
For Prob. 6.49.
Determine Leq that may be used to represent the
inductive network of Fig. 6.75 at the terminals.
For Prob. 6.46.
i
6.47
L
L
L
Find the equivalent inductance looking into the
a
2
4H
di
dt
+!