电工学答案（秦曾煌）：dg4

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?4.3??B?
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?4.3.25.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3
?4.4?èEaè?Dè?íq1 ó￥?
@è
^.,,,,,,,,,,,,4
?4.4.25.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4
?4.4.35.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4
?4.4.45.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,5
?4.4.55.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,5
?4.4.65.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6
?4.4.75.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6
?4.4.85.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7
?4.4.95.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,8
?4.4.115.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,8
?4.5?E F￥1 óDi ó.,,,,,,,,,,,,,,,,,,,,,,,,9
?4.5.15.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,9
?4.5.35.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,10
?4.5.45.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,11
?4.5.55.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,12
?4.5.65.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,13
?4.5.75.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,13
?4.5.115.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,14
?4.5.125.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,15
?4.7??
@è
^￥
q+?.,,,,,,,,,,,,,,,,,,,,,,16
?4.7.45.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,16
?4.7.55.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,17
?4.7.65.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,17
?4.8??
qy
￥4ú.,,,,,,,,,,,,,,,,,,,,,,,,,19
?4.8.25.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,19
?4.8.35.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20
1
List of Figures
154.3.2m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3
254.3.2m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3
354.4.6m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6
454.4.7m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7
554.4.8m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7
654.4.9m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,8
754.5.1m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,10
854.5.3m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,11
954.5.4m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,11
1054.5.5m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,12
1154.5.6m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,13
1254.5.7m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,14
1354.5.11m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,14
1454.5.12m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,15
1554.7.5m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,17
1654.7.6m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,18
1754.8.2m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,19
1854.8.3m.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20
2
4?????????
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4.3???BBB???
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4.3.2
è?164?F￥è?

FB??èau = 220p2sin314tV

!èa
è
@￥? IZ_?m1
U

k9
t = T6
t = T4t = T2
§W￥è
@èa
￥vlb
[333]
èaDè
@￥??wL?m2
Ub
m1:54.3.2m
m2:54.3.2m
Um = 220p2V U = 220V
I = U1
!C
= U!C = 220￡314￡64￡10?6A = 4:42A
3
(1) t = T6
H
u = 220p2sin(2… ￡ 1T ￡ T6)V = 220p2sin60–V = 110p6V
i = 4:42p2sin(60– +90–)A = 2:21p2A
(2) t = T4
H
u = 220p2sin(2… ￡ 1T ￡ T4)V = 220p2sin90–V = 220p2V
i = 4:42p2sin(90– +90–)A = 0
(3) t = T2
H
u = 220p2sin(2… ￡ 1T ￡ T2)V = 220p2sin180–V = 0
i = 4:42p2sin(180– +90–)A =?4:42p2A
4.4èèèEEEaaaèèè???DDDèèè???íííqqq111 ó ó ó￥￥￥???
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@
@èèè
^
^
^
4.4.2
μBCJ0? 10A?
@¤(
L?
1380Va30mAa50Hz
L?è
E1:6k?

kpL?è?b
[333]
?
^RL1 óè
^
E F
1
jZj =
p
R2 +(!L)2 = UI = 38030￡10?3? = 12700? = 12:7k?
L = 12…f
q
jZj2?R2 = 12… ￡50p12:72?1:62 ￡103H = 40H
4.4.3
B?L?¤U = 120V￥°
@è÷

I = 20A
?¤f = 50Hz
U =
220V￥?
@è÷

5I = 28:2Ab
kpL?￥èERè?Lb
[333]
¤°
@è÷
è?L?T¨
#èER = UI = 12020? = 6?b¤?
@è
÷

H

jZj =
p
R2 +(!L)2 = UI = 22028:2? = 7:8?
L = 12…f
q
jZj2?R2 = 12… ￡50p7:82?62H = 15:9mH
4
4.4.4
μBJZ7??W?è
L?
1380Va50Hz
L?èE2k?
L?è
?43:3H

kpL?è
@#?
qy
b
[333]
L?E F1
Z = R +j!L = (2￡103 +j2… ￡50￡43:3)? = 13:8￡103\81:6–?
I = UjZj = 38013:8￡103A = 27:6mA
cos’ = cos81:6– = 0:15
4.4.5
°;§5D?
@1 ó¤??
@èa

 V ATRL1 óè
^b?X?
§
5￥?rèER1 = 280?
?
@￥èEè?sY1R2 = 20?L = 1:65H

è÷èaU = 220V

kpè
^?￥è
@§5

D?
@
￥èab?
?
èaF ?
^???220V
$è÷
q150Hzb
[333]
è
^9E F
Z = (R1 +R2)+j!L = [(280+20)+j2… ￡50￡1:65]?
= (300+j518)? = 599\59:9–?
è
^?è
@
I = UjZj = 220599A = 0:367A
§5

èa
UR = R1I = 280￡0:367V = 103V
?
@￥E F
Z2 = R2 +j!L = (2+j518)? = 518\87:8–?
?
@èa
U2 = jZ2jI = 518￡0:367V = 190V
UR +U2 = (103+190)V = 293V > 220V
y1_U = _UR + _U2
?
μr′MFb
5
4.4.6
í÷=
?


m3

{?
￥èaè
@1
u = 220p2sin(314t+20–)V
i = 4:4p2sin(314t?33–)A
kpN=
?
?
?íq1 ó￥?rè
^íq￥?
′
ip=
?
￥
?
qy
#
{?￥μ??
qí??
qb
[333]
=
?
E F1
m3:54.4.6m
Z =
_U
_I =
220\20–
4:4\?33–? = 50\53
–? = (30+j40)?
5?
1R = 30? XL = 40?
?N¤è?
L = XL! = 40314H = 0:127H
?
qy
1
cos’ = RjZj = 3050 = 0:6
{?￥μ??
q1
P = UI cos’ = 220￡4:4￡0:6W = 580W
í??
q1
Q = UI sin’ = XLI2 = 40￡4:42var = 774var
4.4.7
μBRC1 óè
^
?m4(a)
U
è÷èa1u
èEè?
￥èasY
1uRuc
X?è
^E F
12000?

q11000Hz
i
!uDuc-W￥Mêμ
130°

kpRC
i
a
üMê
uc1u?-
^ìab
[333]
?5iSèaè
@￥M
m[m4(b)]
?M
m Vn
6
m4:54.4.7m
R = jZjcos60– = (2000￡0:5)? = 1000?
XC = jZjsin60– = (2000￡0:866)? = 1732?
C = 1X
C!
= 11732￡2… ￡1000F = 0:1?F
ucìa?u30°.
4.4.8
m5(a)
^BMMè
^b?TC = 0:01?F

{?èau1 = p2sin6280tV
?
à
P
{èau2Mê
-M60–
ù?
￥v￥èER
$N
H
{èa￥μr
′U2??

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[333]
?5iSèaè
@￥M
m[m5(b)]
?M
m Vn

m5:54.4.8m
7
U2 = UR = U1 cos60– = 1￡0:5V = 0:5V
tan30– = URU
C
= RX
C
= R1
6280￡0:01￡10?6
= R￡6280￡0:01￡10?6
?

T VpR = 9:2k?
4.4.9
m6(a)
^BMMè
^bX?R = 100?

{??|
q1500Hzb?1p
{
èau2D
{?èau1W￥Mêμ145–

kpè?′b]
51?
u2Du1M
ê


ìa?-
μ?]
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[333]
Sèaè
@￥M
m[m6(b)]
?M
m Vn
m6:54.4.9m
tan45– = URU
C
= RX
C
= 1001
2… ￡500￡C
= C ￡2… ￡500￡100
?

T VpC = 3:18?F
5VèE

{
u2?-?u1
'5Vè?

{
u2ìa?u1b
4.4.11
μB220Va600W￥è
V
?¤?¨380V￥è÷
bà
Pè
V￥èa?
220V￥-?′
(1)?
1 óv￥èE
$(2)?
1 ó? F1v￥è
?L?

èE V-
{?9

$(3)Vr
q?
qy
1?

?ZEb1
óè?
^?9 V[
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[333]
8
(1)è
V￥-?è
@
IN = 600220A = 2:73A
1 ó￥èE
R = 380?2202:73? = 58:7?
(2)è
V￥èE
RL = 2202:73? = 80:7?
1?è
V￥-?′?M
51 óè?L?aè
^￥E F
1
jZj = 3802:73? = 139:3?
L?? F1
XL =
q
jZj?R2L =
q
(139:3)2?(80:7)2? = 114?
L?è?1
L = XL! = 114314H = 0:36H
(3)1 óèE
H
cos’ = 1
r
q1
· = PNP
N +RI2N
= 600600+58:7￡(2:73)2 = 0:58
1 óL?
H
· = 1
?
qy
1
cos’ = RLjZj = 80:7139:3 = 0:58
V?
? A??¨aB?ZEb9 V1 óè?
? F1114?
è?
′1C = 1!X
C
= 1314￡114F = 28?F
i V4úè??
qy
b
4.5EEE F F F￥￥￥111 ó ó óDDDiii ó ó ó
4.5.1
m7?

kpè
@VA0èaVV0￥
b
[333]
[_U11? I??

5_Z1?_U1?-90–
?
^
9
m7:54.5.1m
_I0 = _I1 + _I2 = (j10+ 100\0–
5+j5 )A
= (j10+10p2\?45–)A = (j10+10?j10)A
= 10A
A0￥
110Ab
_U0 =?j10 _I0 + _U1 = (?j10￡10+100\0–)V
= (100?j100)V = 141\?45–V
V0￥
1141Vb
4.5.3
m8(a)?
I1 = 10A
I2 = 10p2A
U = 200V
R = 5?
R2 = XL

k
pI
XC
XL#R2b
[333]
3'5¨M
ms?1ZLbm8(b)
U￥è
^?
[i ó|
^
￥è
a_U11? IM

7aT_I1
_I11_U1?-90–
yR2 = XL
#_I21_U1ìa45–

?yI1 = 10A
I2 = 10p2A
#_ID_U1]M
7OI = 10A
_UR9D_U1]Mb
7_U = _UR + _U1
??]M
'U = UR +U1b
UR = RI = 5￡10V = 50V
U1 = U?UR = (200?50)V = 150V
?N¤XC = U1I
1
= 15010? = 15?
jZ2j =
q
R22 +X2L = U1I
2
= 15010p2? = 15p2?
10
m8:54.5.3m
y1_I2D_U1￥Mêμ145–

[
R2 = XL = jZ2jp2 = 1p2 ￡ 15p2? = 7:5?
4.5.4
m9(a)?
I1 = I2 = 10A
U = 100V
uDi]M

kpI
R
XC
#XLb
[333]
TM
m
[_UR1? IM

_I2D_UR]M
_I1?-?_UR 90–
_I = _I1 + _I2 =
m9:54.5.4m
11
10p2\45–A
_UL?-?_I 90–
_UD_I]M
_U = _UL + _URb?
^¤
I = 10p2A = 14:1A
R = URI
2
=
p2U
I2 =
p2￡100
10? = 14:1?
XC = URI
1
=
p2￡100
10? = 14:1?
XL = ULI = UI = 10010p2? = 7:07?
4.5.5
9
m10(a)?￥è
@_IòE Fíq
￥èa_U1D_U2
iTM
m
9
m10(b)?ò|
^è
@_I1D_I2èa_U
iTM
mb
[333]m10(a)
Uè
^
m10:54.5.5m
_I = _U
Z1 +Z2 =
10\0–
2+2+j3A = 2\?36:9
–A
_U1 = Z1 _I = 2￡2\?36:9–V = 4\?36:9–V
_U2 = Z2 _I = (2+j3)￡2\?36:9–V = p13\56:3– ￡2\?36:9–V
= 7:21\19:4–V
m10(b)
Uè
^
_I1 = Z2
Z1 +Z2
_I = 1?j
1+j +1?j ￡2\0
–A = (1?j)A = p2\?45–A
_I2 = Z1
Z1 +Z2
_I = 1+j
1+j +1?j ￡2\0
–A = (1+j)A = p2\45–A
_U = Z1 _I1 = p2\45–p2\?45–V = 2V
M
m
{b
12
4.5.6
m11?
X?U = 220V
R1 = 10?
X1 = 10p3?
R2 = 20?

kpò?
è
@
ü (?
qb
[333]
!_U = U\0–1? IM

m11:54.5.6m
_I1 = _U
R1 +jX1 =
220\0–
10+j10p3A =
220\0–
20\60–A = 11\?60
–A
_I2 = _U
R2 =
220
20 A = 11A
_I = _I1 + _I2 = (11\?60– +11)A = 11p3\?30–A
P = R1I21 +R2I22 = (10￡112 +20￡112)W = 3630W
4.5.7
m12(a)?
X?u = 220p2sin314tV
i1 = 22sin(314t? 45–)A
i2 =
11p2sin(314t+90–)A

kpòNV
#è
^?
R
LCb
[333]
?m12(b)￥M
m V?
I2 = I1 sin45– = 22p2 ￡
p2
2 A = 11A
I1 = 22p2A = 15:6A
13
m12:54.5.7m
y_I_U]M
#
I =
q
I21?I22 =
s
22p
2
2
112A = 11A
XC = UI
2
= 22011? = 20?
C = 1!X
C
= 1314￡20F = 159?F
jZ1j = UI
1
= 22022
p2
= 10p2?
R = jZ1jcos45– = 10p2￡
p2
2? = 10?
XL = jZ1jsin45– = 10?
L = XL! = 10314H = 0:0318H = 31:8mH
4.5.11
m13
U￥è
^?
X?_UC = 1\0–V
p_Ub
[333]
m13:54.5.11m
14
_IC = 1\0–
j2 A = j0:5A
_IR = 1\0–
2 A = 0:5A
_I = _IR + _IC = (0:5+j0:5)A
_U1 = (2+j2)(0:5+j0:5)V = j2V
_U = _UC + _U1 = (1+j2)V = p12 +22\arctan2V = p5\63:4–V
4.5.12
m14
U￥è
^?
X?Uab = Ubc
R = 10?
XC = 1!C = 10?,Zab1è
??μb
kp_U_I]M
HZab??

$
[333]
7Zab = R1 +jXL
m14:54.5.12m
?p¤
Zbc =?jRXCR?jX
C
=?j10￡1010?j10? = (5?j5)?
[
_U = _Uab + _Ubc = (Zab +Zbc) _I
= [(R1 +jXL)+(5?j5)] _I = [(R1 +5)+j(XL?5)] _I
?_U_I]M
5

T￥′?A1
,
'
XL?5 = 0 XL = 5?
?yUab = Ubc
5jZabj = jZbcj
q
R21 +X2L = p52 +52
3-¤R1 = 5?
?
^Zab = (5+j5)?
15
4.7???
@
@
@èèè
^
^
^￥￥￥
q
q
q+++???
4.7.4
μBR
L
C1 óè
^
¤?
q V??￥è÷

è÷èaU?
10V
?
q9F
H
è
@V10mA(500Hz)9F?Kv′60mA(1000Hz)b
kp(1)èER
è?Lè?C￥′
(2)~?
Hè?

￥èaUC
(3)~
?
HH??è??
%￥Kv
b
[333]
(1)~?
Hf0 = 1000Hz
jZ0j = R = UI
0
= 1060￡10?3? = 166:67?
d~?
Hf = 500Hz
(XL?XC)2 = jZj2?R2 = (UI )2?R2 = ( 1010￡10?3)2?166:672
XL?XC = §985:4?
yf < f0
è
^?è??
#|
XL?XC =?985:4?
~?
Hd~?
H￥Z?
 ó ?-
2…f0L? 12…f
0C
= 0
2…fL? 12…fC =?985:4
6:28￡1000L? 16:28￡1000C = 0
6:28￡500L? 16:28￡500C =?985:4
3-¤
L = 0:105H C = 0:24?F
(2)
UC = XCI0 = 16:28￡1000￡0:24￡10?6 ￡60￡10?3V = 39:56V
(3)
W = WL +WC = 12LI20 + 12CU2C
= [12 ￡0:105￡0:062 + 12 ￡0:24￡10?6 ￡39:562]J
= (1:87￡10?4 +1:88￡10?4)J = 3:8￡10?4J
16
4.7.5
m15
U￥è
^?
R1 = 5?b???è?C′
Pè
@I1Kl
iN
H?
¤
I1 = 10A
I2 = 6A
Uz = 113V
p = 1140WbpE FZb
[333]
?C′
PIKl
?
Hi óè
^?
3~?
_ID_Uab]Mb?M
m V¤
m15:54.7.5m
I =
q
I21?I22 = p102?62A = 8A
y1
P = RI2 +R1I21
[
R = P?R1I
2
1
I2 =
1140?5￡102
82? = 10?
jZj = pR2 +X2 = UZI = 1138? = 14:1?
?N¤
X = §
q
jZj2?R2 = §10?
Z = R +jX = (10§j10)?
'
Z = (10+j10)?Z = (10?j10)?
4.7.6
è
^?m16
U
X?R = R1 = R2 = 10?,L = 31:8mH,C = 318?F

f = 50Hz
U = 10V

kpi ó|
^
èaUab#è
^￥PaQaS#cos’.
17
m16:54.7.6m
[333]
? F
XL = !L = 314￡31:8￡10?3? = 10?
? F
XC = 1!C = 1314￡318￡10?6? = 10?
i ó|
^￥?rE F
Zab = Z1Z2Z
1 +Z2
= (10+j10)(10?j10)10+j10+10?j10? = 10?
Vn
i ó|
^?èE?
OE′DRM?
#
Uab = U2 = 102 V = 5V
i ó|
^è
@
I1 = I2 = UabjZ
1j
= UabjZ
2j
= 510p2A = 12p2A
9è
@
I = UabjZ
abj
= 510A = 0:5A
è
^￥PaQaSacos’
P = RI2 +R1I21 +R2I22
=
"
10￡
1
2
2
+10￡
1
2p2
2
+10￡
1
2p2
2#
W = 5W
Q = XLI21?XCI22 =
"
10￡
1
2p2
2
10￡
1
2p2
2#
var = 0
S =
p
P2 +Q2 = p52 +0V ￠A = 5V ￠A
cos’ = PS = 55 = 1
Vn
'è
^)?~?
b
18
4.8???
q
q
qyyy
￥￥￥444úúú
4.8.2
¨m17
U￥è
^?¤í÷L?=
?
N￥
?/
U = 220V,I =
5A,P = 500Wb???DNi óB?
a?
′￥è?Ca
è
@Ihl
7
e

?M.
k????
￥?é
?r?
#?
qy
bf = 50Hz.
[333]
y1DNi óCa
Ihl

[N
^Bè???
b
m17:54.8.2m
?
P = UI cos’
¤
cos’ = PUI = 500220￡5 = 0:45
’ = 63–
?y1
jZj = UI = 2205? = 44?
#
Z = jZj\’ = 44\63–? = (20+j39:2)?
?
R = 20? XL = 39:2?
?N¤
L = XL! = 39:2314 H = 125￡10?3H = 125mH
19
4.8.3
m18?,U = 220V,f = 50Hz,R1 = 10?,X1 = 10p3?,R2 = 5?,X2 =
5p3?.(1)pè
@V￥
Iè
^?
qy
cos’1;(2)à
Pè
^￥?
qy
4
ú?0:866
53i óvè?
$(3)i óè?aè
@V￥
1

$
[333]
m18:54.8.3m
(1)
!_U = 220\0–V
X?
Z1 = R1 +jX1 = (10+j10p3)? = 20\60–?
Z2 = R2 +jX2 = (5+j5p3)? = 10\60–?
?
^¤
_I1 = _U
Z1 =
220\0–
20\60–A = 11\?60
–A
_I2 = _U
Z2 =
220\0–
10\60–A = 22\?60
–A
_I = _I1 + _I2 = (11\?60– +22\?60–)A = 33\?60–A
è
@V￥
133A,è
^?
qy
cos’1 = cos60– = 0:5
(2)
P = UI cos’1 = 220￡33￡0:5W = 3630W
cos’ = 0:866 ’ = 30–
C = P!U2(tan’1?tan’)F
= 3630314￡2202(tan60–?tan30–)F
= 275:7?F
20
(3)i óCa
XC = 1!C = 10
6
314￡275:7? = 11:6?
_IC = _U
jXC =
220\0–
j11:6A = 18:96\90
–A
_I = _I1 + _I2 + _IC = (33\?60– +18:96\90–)A
= (16:5?j28:58+j18:96)A = (16:5?j9:62)A
= 19:1\?30:2–A
è
@V￥
119:1A
hl
b
21
22