Convert the wye connection Ri—Rj — Rh to its equivalent delta... b 480 mW 4.53 a Minimize the number of equations to write and solve by using the mesh current method... Thus, when the lo
Trang 12.34 a) i = 385 mA,so a warning sign should be
posted and precautions taken
b) Use the following resistors: 390 ft, 47 (1,
and 220 ft
2.35
2.36 a) Pa r m = 59.17 W;/> l e g = 29.59 W;
P t m n k = 7.40 W
b) ^ m = 1414.23 s; r leg = 7071.13 s;
'trunk = 70.677.37 S
c) All values are much greater than a few minutes
2.37 a) 40 V
b) No, 12 V/800 ft = 15 mA will cause a shock
2.38 3000 V
Chapter 3
3.1 a) 6 kfl and 12 kft, 9 kfl and 7 kft; simplified
circuit is
10 V
b) 3 kft, 5 kft, and 7 kft; simplified circuit is
3 mA
c) 300 ft, 400 ft and 500 ft; simplified circuit is
1200 Q
200 mV
3.2 a) 10 ft and 40 ft, 10011 and 25 ft; simplified
circuit is
60 V
b) 9 kfl and 18 kft, and 6 kfl; simplified circuit is
50 mA
c) 600 ft, 200 ft, and 300 ft; simplified circuit is
250 fl
0.2 A
3.3
3.4
3.15
3.16
3.18 3.23
3.24
a) b) c) a) b) c) a) b) c) a) b)
21.2 ft
10 kft
1600 ft
30 ft
5 kft
80 fl
66 V 1.88 W, 1.32 W 17,672 ft, 12,408 ft
1200 fl, 300 ft
1 W
1875 ft, 3750ft, 7.5 k f a)
b) c) d) e) a)
b) c) d)
36 V
2 A 0.96 A
24 V 6.4 V
25 mA
250 V
50 V
25 mA 4.167 mA
Trang 23.31 a) 49,98012
b) 498012
c) 23012
d) 5ft
3.35 a) R,„ = 50fl;
(25/12)
3.53
3.56
3.58
3.72
3.73
50 + (25/12) (k 25 b)
2500 mcas
c) Yes
3.51 a) 1500 (1
b) 28.8 mA
c) 750 a , 276.48 mW
d) 100012,92.16 mW
23.2 V, 21 V
a) A-connected R2—R3—R4 becomes Y-connected
512—2012—4ft; equivalent resistance is 3312
b) Y-connected R2—R4—R>, becomes A-connected
10012 —8012—20 ft; equivalent resistance
is 3312
c) Convert the delta connection R 4 —R s —Rf, to
its equivalent wye Convert the wye connection
Ri—Rj — Rh to its equivalent delta
9012
R { = 1.0372ft, R 2 = 1.1435 ft,/?3 = 1.212,
R 4 = 1.1435 ft, R 5 = 1.0372 ft, R a = 0.0259 ft,
R b = 0.006812, R c = 0.006812 R L{ = 0.025912
Pdiss = 624W = Pd d
3.74 a) R] = 0.426912, R2 = 0.4617 ft, R3 = 0.48 ft,
R4 = 0.4617ft, R5 = 0.4269 ft, Ra = 0.0085 ft,
Rh = 0.0022 ft, rtc = 0.002212, Rd = 0.008512
b) i, = 26.51 A, /?/?, = 300 W or 200 W/m;
i2 = 25.49 A, i\R2 = 300 W or 200 W/m;
ib = 52 A, ilRh = 6 W or 200 W/m;
Pd d= 1548 W =P{Sss
Chapter
4.1 a)
b)
c)
d)
e)
f)
g)
4
11
10
9
s
6
4
6
4.2 a) 8 b) 3 c) 4 d) Avoid the topmost mesh and the leftmost mesh, which both contain current sources
4.3 a) 2 b) 5 c) 7 d) 1,4,7 4.4
4.8
4.9 4.13
4.17
4.19 4.24 4.26
4.27 4.33
4.34
4.38 4.39 4.42
4.44
4.48
a) 5 b) 3
c) -i s + ij + U = 0; —/1 + /4 + /3 = 0;
/5 — / 2 — /3 = 0 d) 2
e) /?,/! + tf3/3 - R 2 i 2 = 0;
/?3* 3 + R 5 i 5 - R4I4 = 0
120 V, 96 V
4 V a) - 6 8 A, 2.7 A, - 9 5 A, 2.5 A, - 1 2 A b) 3840W
a) 8800W b) 8800W
750 W 3.2 V a) -37.5 V, 75 W b) -37.5 V, 75 W c) Part (b), because there are fewer equations to write and solve
- 2 0 V a) 5.6 A, 3.2 A , - 2 4 A b) -8.8 A , - 1 6 A, 7.2 A a) 17,940 W
b) 17,940 W 259.2 W
2700 W a) 162.92 W b) 518.52 W c) Power delivered equals power absorbed
a) 2 raA b) 304 mW c) 0.9 mW
740 W
Trang 34.51 a) 5.7 A, 4.6 A, 0.97 A , - 1 1 A, 3.63 A
b) 5 > d e v = £ / ^ = 1319.685W
4.52 a) The constraint equations are easier to
formu-late in the node voltage method, making it the
preferred method
b) 480 mW
4.53 a) Minimize the number of equations to write and
solve by using the mesh current method
b) 4 m W
c) No, since the mesh current method still minimizes
the number of equations to write and solve
d) 200 mW
4.59 a) - 1 m A
b) - 1 mA
4.60 a) -0.85 A
b) -0.85 A
4.63 60 V source, positive at the top, in series with a
1011 resistor
4.64 1 mA current source, with current flowing from top
to bottom, in parallel with a 3.75 O resistor
4.71 a) 51.3 V
b) - 5 %
4.74 160 V source, positive at the bottom, in series with
a 56.4 kft resistor
4.77 8 ft (The voltage source is zero because there are
no independent sources in the circuit.)
4.83 2.5 H and 22.5 O
4.87 a) 6 f t
b) 24 W
4.91 a) 50 V
b) 250W
4.96 30 V
4.105 v { = 39.583 V,v 2 = 102.5 V
4.106 t»i = 37.5 V,v 2 = 105 V
4.107 V] = 52.0833 V,i>2 = 117.5 V
Chapter 5
input
non-inverting
input
positive power supply output
negative power supply
b) The input resistance; i n = 0
c) The open-loop voltage gain; (v p - v n ) = 0
d) ^ = 9 V
5.2 - 1 mA 5.3 a) - 1 5 V (saturates) b) - 1 0 V
c) - 4 V
d) 7 V
e) 15 V (saturates)
f) -1.08 V < v a < 4.92 V 5.8 a) Many possible designs; one uses a single 3.3 kft
input resistor and three series-connected 3.3 kft resistors in the feedback path
b) ±15 V
5.9 a) 0 < or < 0.40
b) 556.25 At A
5.11 0<i?f<60kft 5.12 a) Inverting summing amplifier b) - 6 V
c) - 0 5 V < v „ < 2 V
5.14 a) 14 V
b) 3.818 V < v a < 9.273 V
5.17 a) Non-inverting amplifier
b) 2v s
c) - 6 V < v s < 4 V
5.18 a) 10.54 V
5.25
5.26 5.28
5.33 5.34
5.43
5.45
b) -4.55 V < v g < 4.55 V c) 181.76 kft
a) - 1 5 1 V b) 34.3 kft c) 250 kft
20 kft a) 16 V
b) - 4 2 V < v b < 3 8 V
19.93 kft < R x < 20.07 kft a) 24.98
b) -0.04 c) 624.5 a) -19.9844 b) 736.1 jaV c) 5003.68 ft d) - 2 0 , 0 V, 5000 ft a) 13.49
b) 999.446 mV, 999.834 mV c) 387.78/AV
d) 692.47 pA e) 13.5,1V,0V,0A
Trang 45.49 a) 2 k f l
b) 12 mfl
Chapter 6
6.1 »f(mV)
e) v(V)
6.4
4
3
2
1
0
(
-1
- 2
- 3
- 4
—
l /*""~3
l
4
1.4
1.2
1 F
0.8
0.6
0.4
0.2
-0
0 1
a) / = 0
i = 50/ A
/ = 0.5 - 5 0 / A
/ = 0
b) v = 0
v = lV
v = -\V
v = 0
p = 0
p = 50/ W
/? = 50/ - 0.5 W
/7 = 0
w = 0
w = 25/2 J
/(s)
/(s)
4 / < 0
0 < / < 5 ms
5 < / < 10 ms
10 ms < / / < 0
0 < / < 5 ms
5 < / < 10 ms
10 ms < / / < 0
0 < / < 5 ms
5 < / < 10 ms
10 ms < / / < 0
0 < / < 5 ms u> = 25/2 - 0.5/ + 0.0025 J 5 < / < 10 ms
to = 0 10 ms < /
6.16 a) - 5 0 X 104/ + 15 V
b) 106/V
c) 1.6 X 106/ - 12 V
d) 52 V
6.17
/(jxs)
t (ms)
6.21 8 H
6.25 a) -5e~ Al A
b) -4e~4 ? - 6 A c) - e_ 4 i + 6 A d) 40 J
e) 400 J f) 360 J 9) 1(4)(-6)2 + j(16)(6)2 = 360 J (checks)
6.26 2 ^cF, initial voltage is 25 V 6.31 a) - 2 0 e "2 5' V
b) -16<T25' + 21 V c) -4<T25/ - 21 V d) 320/AJ e) 2525/AJ f) 2205/xJ
g) \(2 X 10"6)(21)2 + |(8 X 1()"6)(-21)2 =
2205 /xJ
6.39 a) 16 ^ + 32/2 = 2-±
at at
b) -16<Tf + 32e_2f + 32e-' - 32e~2' = 16e"
c) 34<T' - 4e~2tV
d) 30 V, which is consistent with the circuit's behavior
6.44 a) 2721.6 mJ
b) 2721.6 mJ c) 518.4 mJ d) 518.4 mJ
Trang 56.45 a) - 4 5 A
b) No
6.48 a) 50mH,2.4
b) 0.2 X 10~6Wb/A,0.2 X 1 0_ 6W b / A
6.49 0.8 nWb/A, 1.2 nWb/A
6.53 There is no difference in the output voltage for
these two circuits
Chapter
7.4
7.5
7.7
7.23
7.26
7.35
7.36
a)
b)
c)
d)
e)
a)
b)
c)
d)
e)
f)
9)
h)
i)
i)
k)
I)
a)
b)
c)
d)
a)
b)
c)
a)
b)
c)
a)
b)
a)
b)
c)
d)
7
5 mA, 15 mA
5 mA, - 5 mA
5,,-20.000/ m A
-5e-2 0-, ) 0 0'mA
The current in a resistor can change
instantaneously
0 A
160mA
65 mA
160 mA
225 mA
0 A
160e"2n"' mA
OV
-3.2 V
OV
-32e~ 2m V
225 - 160e"200' mA
2 A
20 ms
2e~ 5i)t A, -160e~5lM V, -144<T50' V
69.92%
1.6e~5()fmA,32<r5()' + 8V, -8<T50' + 8 V
800/d
160/xJ,640/J
2 4 « - « " raA
- Se -5om + 8 0 V
2880/d
- 2 - 3 e -5 0 0 , ,' A , 4 8 - 4 8 e -5 , K , ( ,' V
6 0 V , 0 V
- 5 mA
0.333 mA
5/AS
0.333 -5.333<r2 ( , a ( , 0 , )'mA
7.37
7.51
7.53 7.55
7.56
7.68
7.69
7.71 7.78 7.85 7.87
7.95
7.96 7.103
7.104
7.105
a) b) a) b) c) d)
e)
5 + 15e-1000'A
5 0 - 4 5 0 < T1 ( l o a ,V
3.4 mA
- 6 0 + 90e~20,)0' V
a)
b)
c)
d) e) f) a) b) c) d) a) b)
c)
d) e) a) b)
c)
d)
e)
50 V
- 2 4 V
0.1 fis
-18.5 A
- 2 4 + 74<Tlt,7'V -18.5e-1 ( ) 7'A
90 V
- 6 0 V
1000/AS 916.3/AS
4 - 4 < T2 0' A 80e"20fV 2.4 - 2.4e~20' A 1.6 - 1.6<T20'mA Yes
40 - 40e"500(" mA
1 0 e - 5 0 o o , v
24 - 24e"5000' mA Yes
-5.013 V
-5V, 0 < t < 5 s; -5£>-(U('" 5) V, 5 s < t <
83.09 ms a) b)
2.25
272.1 /AS
- 1 6 0 0 / + 8 V , - 1 5 + l l e -2 0 0' V ,
23
80 a) b) a) b) a) b) c)
- 1600* - l l e "2 0 0' V
ms 1.091 MO 0.29 s 8.55 flashes/min 559.3 kH 24.32 flashes/min 99.06 mA
$43.39 per year
CO
Trang 6Chapter 8
8.1 a) -10,000 rad/s,-40,000 rad/s
b) overdamped
c) 3125 ft
d) -16,000 +/12,000 rad/s,
-16,000 - /12,000 rad/s
e) 2500ft
8.7 a) 25 nF
b) 2500ft
c) 75 V
d) 30 mA
8.8
8.9
8.18
8.19
8.20
8.29
8.30
8.31
8.50
e) -8000, (30 cos 6000? + 71.25 sin 6000?) mA
a) 8 kft, 40 H, 625 rad/s, 500 rad/s
O.&T250* -0.8<T10()"fmA,
02e- 25{)[ - 32e- xmt mA
a) l k f t , l / x F , 6 0 0 0 V / s , 8 V
b) (-3000? + 2)^ 5 ( l l l , mA
8.11 a) 500 rad/s, 400 rad/s, 1.5625 H,4/xF,
- 1 5 mA, 60 mA
b) 18.75e"200' - 18.75<r8()0'V
c) 75<T200' - 7 5 ^8 0 0' mA
800/
d) - 6 0 e -2 0 0' + 15(TftUUf mA
5e~ 2im + \Qe-* m) <V
\5e~ 25m cos 3122.5? + 721e~ 2mi sin 3122.5? V
15e- 4m] 'V
60 - 105e"W)00' cos 6000? - 90e"800<)rsin 6000? mA
60 - 750,000?e"104' - 105eT104' mA
60-80ff-8 n 0 r + 2Off-32WfV
8.51 60 - 120,000?e -2000(
- 60e 2000( V
8.52 60 - 60e>-200(" cos 1500? - 80<r20(K)/ sin 1500? V
8.63 a) 0 < ? < 0.5" s:
v n (t) = l0t 2 V,v lA (t) = -1.6? V;
0.5 + < ? < ?sal:
v 0 (t) = -5?2 + 15? - 3.75 V,
v ol (t) = 0.8? - 1.2 V
b) 3.5 s
8.64 0 < ? < 0.5 ~ s:
v a {t) = 10 - 20e"' + Hfe~*V,
v oi (t) = -0.8 + 0.8e~aV,
0.5+ < ? < ?sal:
Vo {t) = - 5 + 19.42ff"(t-a5) - 12.87e_ 2 ( f-a 5 )V,
8.68 a) 55.23fis
b) 262.42 V c) ?max = 53.63 /xs, v(t max ) = 262.15 V
8.69 a) 40 mJ
b) -27,808.04 V c) 568.15 V
Chapter 9 9.1 a) 80 V
b) 500 Hz c) 3141.59 rad/s d) -0.5236 rad e) -30°
f) 2 ms g) 166.67 ^ s h) -80sinl0007r?V i) 333.33/AS
j) 166.67jiis
9.4 a) 600 Hz
b) 1.67 ms c) 10V d) 6 V e) -53.13°,-0.9273 rad f) 662.64/AS
g) 245.97^s
2
a) -195.72<rl066-67f + 200cos(800? - 11.87°) mA b) -195.72^- 1066-67/mA,
200 cos(800? - 11.87°) mA c) 28.39 mA
d) 200 mA, 800 rad/s, -11.87°
e) 36.87°
9.11 a) 111.8 cos(500? - 3.43°)
b) 102.99 cos(377? + 40.29°) c) 161.59 cos(100? - 29.96°) d) 0
9.13 a) 502,654.82 rad/s
b) 90°
c) -39.79 ft
d) 0.05/AF
e) -/39.79 ft
9.14 a) 400 Hz
b) -90°
9.8
9.9
Trang 79.85
9.15
9.24
9.28
9.29
9.32
9.37
9.45
9.46
9.49
9.55
9.59
9.60
9.64
9.76
9.77
9.83
9.84
c) 5fi
d) 1.99 mH
e) /5 ft
AAA /~W~lT\
j V V v
600/20° v f J
7-b) 8.32 /76.31° A
^ -/100 ft
c) 8.32cos(8000f + 76.31°) A
a) 200 /36.87° mS
b) 160 mS
c) 120 mS
d) 10 A
500 rad/s
42.43 cos(50,000f + 45°) V
42.43 cos(2000? + 45°) V
2/3 ft
227.68 / -18.43° V, (3.6 + /10.8)(1
2 / - 3 6 8 7 ° A, (100 - /50) ft
1 0 / - 4 5 ° A, (1.6 + /3.2) ft
188.43/-42.88° V
/80 = 80 / 9 0 ° V
36 cos 2000 fV
56.57 cos(10,000f - 4 5 ° ) V
a) 0.3536
b) 2 A
a) 5 cos(5000f - 36.87°) A, 1 cos(5000f - 180°) A
b) 0.5
c) 9 m J , 1 2 m J
512,000/60° ft
I
V = ( V / 2 ) - 1 R
o v in / m v a) 247.11/1.68° V
b) - 3 2 ft, 241.13/1.90° V
c) -26.90 ft
9.88 a) l { = 24 / 0 ° A, 12 = 2.04 / 0 ° A,
I3 = 2 1 9 6 / 0 ° A, I4 = 19.40/0° A,
I5 = 4 6 / 0 ° A, I6 = 2 5 5 / 0 ° A b) 0.42 / 0 ° A
9.89 a) 0 A
b) 0.436/0° A c) Yes; when the loads are equal, no power is lost
to the neutral line, so the cost of power is lower
Chapter 10 10.1 a) 409.58 W (abs), 286.79 VAR (abs)
b) 103.53 W (abs), -386.37 VAR (del) c) - 1 0 0 0 W (del),-1732.05 VAR (del) d) - 2 5 0 W (del), 433.01 VAR (abs)
10.2 a) Yes b) Yes 10.15 a) 15.81 V(rms) b) 62.5 W 10.18 a) 6.4 W, 4.8 VAR, 8 VA b) 6.4 W
c) 4.8 VAR 10.26 a) 0.96 lagging, 0.28; 0.8 leading,-0.6;
0.6 leading, - 0 8 b) 0.74 leading,-0.67
10.27 a) 1.875 + /0.625 ft
b) 0.9487 lagging
10.44 a) 20 + /20 ft b) 20 W c) With 22 ft and 1 mH, the load impedance is
22 + /5 ft and the load power is 17.7 W
10.47 a) 360 mW b) 4000ft,0.1/AF
c) 443.1 mW; yes d) 450 mW e) 4000 ft, 66.67 nF
f) Yes 10.48 a) 4123.1 ft, 0.1/xF, 443.18 mW b) Yes
c) Yes 10.64 90 W 10.65 a) 10 b) 250W 10.66 a) 28.8 ft b) 28.8 ft c) Yes
Trang 810.67 a) P L =
PH =
V 1 R\ + R 2
v\Ri + R2)
R1R2
PM = Yl
Ri
V 2 V 2
Pi
(Yl _ vL\(¥l\
(p L p ¥ )yp,)
PM - PL
b) 1125W
10.68 36ft, 24 ft
Chapter 11
11.2 a) acb
b) abc
11.3 a) Balanced, negative phase sequence
b) Balanced, positive phase sequence
c) Balanced, negative phase sequence
d) Balanced, positive phase sequence
e) Unbalanced, due to unequal amplitudes
f) Unbalanced, due to unequal phase angle
separation
11.7 v AB = 13,198.23 cos a>t V,
vBC = 13,198.23 cos(wr + 120°) V,
vCA = 13,198.23 cos(w/ - 120°) V
11.9 a) 15.24 A(rms)
b) 6583.94 V(rms)
11.11 a) I aA = 5 / - 3 6 8 7 ° A, IbB = 5/83.13° A,
IcC - 5 / - 1 5 6 8 7 ° A
b) Va b = 216.51 / - 3 0 ° V , Vb c = 216.51 / 9 0 ° V,
Vca = 2 1 6 5 1 / - 1 5 0 ° V
c) VA N = 122.23/-1.36° V,
VB N = 122.23/118.64° V,
VCN = 122.23/-121.36° V
d) VA B = 211.72/-31.36° V,
VB C = 211.72/88.64° V,
VC A = 211.72/-151.36° V
11.12 a)
1 + / 3 H
20/If
V(
150° / + \
rms) \-J
aA
39 - /33 n
b) 0.4 / - 1 7 3 1 3 ° A(rms)
c) 35.39/176.63° V(rms)
11.13 21.64/121.34° V(rms)
11.16 159.5 /29.34° V(rms)
11.22 6120/36.61° VA
11.24 a) 1833.46 / 2 2 ° VA
b) 519.62 V(rms)
11.43 a) W 2 ~ Wx = VL/L[cos (d - 30°) - cos (6 +
30°)] = 2V L I L $in0sm30 o = V L I L sm6
Thus, V 3 ( W2 - Wx) = VwLILsm 0 = QT
b) 2592 VAR, -2592 VAR, 3741.23 VAR, -4172.80 VAR
11.44 197.26 W, 476.64 W 11.52 a)
1.70 MVA
1.2MVAR
1.2 MW
b)
1.2 MW 11.53 a) 16.71 AIF
b) 50.14/aF 11.56 |Vab| = 12,548.8 V, so the voltage is below the acceptable level of 13 kV Thus, when the load at the substation drops to zero, the capacitor bank must be switched off
11.57 PL(before) = 81.66 kW, PL ( a f t e r ) = 40.83 kW
Chapter 12 12.2
12.3
12.7
12.9
12.10
12.14
a) (t + \0)u(t + 10) - 2tu(t) + (t - 10)«(f - 10)
b) -8(t + 3)u(t + 3) + 8(7 + 2)u(t + 2) + 8(r + l)«(f + 1) 8(f l)u(t 1 ) -8(/ - 2)u{t -2) + -8(/ - 3}M(/ - 3)
a) 5t[u{t) u{t 2)] + 10[«(f 2 ) -u(t - 6)] + (-5? + A0)[-u(t - 6) - -u(t - 8)] b) 10 sin irt[u{t) - u(t - 2)]
c) 4t[u(t) - u{t - 5)]
a) 1.0 b) 0 c) oo a) 26 b) 2.25
2/9
at SC °
3 ) f + c,2
b) * + J
c) 2 d) check
Trang 912.17 a)
b)
c)
d)
e)
12.22 a)
b)
12.40 a)
(.v + a)2
CO
2 i ~>
co cos 0 +
s 2 +
1
->
sr
sinh 0 +
(r
-1
v(.v + a)
1
.v sin 6 ->
of
y[cosh 0]
- 1)
13.9 a)
12.41
12.42
12.50
12.55
12.56
s(s + a)
[«?"' + 5e'2' + 2e-4']u(t)
b) [6 + 4e~2t + 2e~4t + e~("]u(t)
c) [4e'1 + 20cT'cos(2f + 36.87°)]M(?)
d) [490 + 250e"7'cos(r - 163.74°)]«(r)
a) [20/ - 4 + 4e-*]u(t)
b) [250 - lOOte'1 - 250e~f]u(t)
c) [30r - 8 + K)e 3lcos(t + 36.87°) ]u(t)
d) [20 - 2 5 f V - I5te~' - 20e"']«(0
e) [16 + S9A4te~ 2t cos (t + 26.57°) +
I13.14e_2rcos0 + 98.13°) ]u(t)
c) 5'(t) - 105(f) + [3(k'_5/ + 20e~10f]«(f)
a) / ( ( ) ' ) = 8,.f(oo) = 0
b) /(0^) = 13,/(00) = 6
c) / ( 0+) = 20, / ( o o ) = 0
d) / ( 0+) = 250, / ( o o ) = 490
0.947
588
Chapter 13
13.4 a) — 8 X 107s
13.6 a)
.v2 + 40,000* + 256 X 106
b) Zero at 0; poles at -8000 rad/s and
-32,000 rad/s
s 2 + 8000* + 25 x 106
b) Zeros at -4000 + /3000 rad/s and
-4000 - /30()() rad/s; pole at 0
16 x Uf
-^vw—
5000 (2
SI
150 V-s
b)
'©
-150s
+
V„ 2.5 s a
(s + 400)(.v + 1600)
c) (SO*-*** - 200e-l60()f)«(r)V
A/W-+ 10012
b)
c) 13.12 a)
5 x 10s n
s '
V
o.ob' n
75.v2 + 812,500.v + 6875 X
sis1 + 104v + 5 X 107)
/ + \ 137.5 /
1.25 mV
-Hv ^_7
106
[137.5 + 8().04^ 50()()'cos(5000/ + 141340) ] K ( 0
ii,
V-s
R
b)
c)
•48(s + 8000) .v2 + 8000* + 25 X 106
2.4(.v + 4875) .v2 + 8000s + 25 X 106
d) [80e"-")00fcos(3000f + 126.87°) ]u(t)V e) [2.5e- 4mt cos(3(mt - 1 6 2 6 ° ) ] H ( 0 A
13.21 a) [35 + 5.73e~' cos(7r + 167.91 ° ) ] H ( I ) V
b) Compare solution at t = 0 and t = oo to circuit at t = 0 and t = oo
13.22 a) [10 - Kk>""a5'cos0.5/]u(f)A b) 7.07e_OA cos(0.5r - 45°)w(r) V
c) Compare solutions at t = 0 and t = oo to circuit at t = 0 and t = oo
Trang 1013.29 a) 652 + 6s - 18 - 9 r - 30.v 18
s(s + 2)(5 + 3)' s(s + 2)(5 + 3)
b) Initial values: 6 A, - 9 A;
final values: - 3 A, - 3 A
c) [ - 3 + 3e~2' + 6e-3,]u(t)A,
[ - 3 - 3e~ 2 ' - 3e" 3 ']u(t)A
13.34 63.25*"ia*cos(50> + 71.57°)w(0 mA
240(5 + 40)
13.39 a) —
' s(s + 20)(5 + 80)
b) Initial value is 0 final value is 6 A
c) (6 - 4e~m - 2e~m)u(t) A
13.40 a) (-2e~ m + 2 e ^)' ) « ( 0 m A
b) (2< -2()(
2e- h l>(0 mA
13.42 a) 480(5 + 2.5)
5(5 + 4)(5 + 6)
b) [50 + 90e~4' - \4Qe~ ( "]u(t)V
13.50 a)
b)
c)
d)
e)
250
5 + 250
5
5 + 250
V
5 + 8000
8000
5 + 8000
, no zeros, pole at -250 racl/s
, zero at 0, pole at -250 rad/s
, zero at 0, pole at -8000 rad/s
, no zeros, pole at -8000 rad/s
100
, no zeros, pole at -500 rad/s
5 + 500
13.62 (e - l)e"?V
13.63 (1 - e)e-'V
13.77 16.97 cos (3/ + 8.13°) V
5(5 + 30,000)
13.79 a)
1 (5 + 5000)(5 + 8000)
b) (5e-5l)m - 4Ae-*m')u(t)V
13.80 a) = 1 * 2
; (5 + 400)(5 + 1000)
b) 13.13 cos(400f - 156.8°) V
13.87 a) 0.8 A
b) 0.6 A
c) 0.2 A
d) -0.6 A
e) Q.6e~ zxm '\t(t)A
f) - 0 6 e -2 x l% ( f ) A
g) -1.6 x 1(T38(0 - 72QOe'2xliftu(t)V
13.88 a) 80 V
b) 20 V
c) 0 V
d) 325(f)juA
e) 16 V f) 4V g) 20 V
13.92 a) i 2(0~) = *2<0+) = 0 A ;
1440TT( 122.92 V 2 5 - 3 0 0 0 T T \ / 2
300 V 2
5 + 1475 w
va = 252.89<Tl475jr/ + 172.62 cos(1207it + 6.85°) V y„(0+) = 424.26 V
c) V„ = 122.06/6.85° V(rms)
d) »„ (V)
t (ms)
13.93 a) - 2 0 5 8 ^- 1 4 7 5^ + 172.62 cos( 12()77-/ - 83.15°) V b)
v„ (V)
t (ms)
c) Voltage spikes in Problem 13.92 but not here