"
"
"
c
c
c
???4ccc?????????
@
@
@èèè
^
^
^3
?4.3??B?
¥?
@è
^.,,,,,,,,,,,,,,,,,,,,,,3
?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?????????
@
@
@èèè
^
^
^
4.3???BBB???
¥¥¥???
@
@
@èèè
^
^
^
4.3.2
è ?164?F¥è ? 

FB??èau = 220p2sin314tV
!èa

@¥? IZ_ ?m1
U
k9
t = T6t = 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¥¥¥???
@
@
@èèè
^
^
^
4.4.2
μBCJ0? 10A?
@¤(  L ?
1380Va30mAa50HzL ?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 = 50HzU =
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 ?
1380Va50HzL ?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]

^9E F
Z = (R1 +R2)+j!L = [(280+20)+j2… £50£1:65]?
= (300+j518)? = 599\59:9–?

^?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)
Uè÷èa1uèEè ?
¥èasY
1uRucX?è
^E F
12000?
q11000Hzi
!uDuc-W¥Mêμ
130°
k pRCi
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?

P
{èau2Mê
 -M60–ù?
¥v¥èER$N
H
{èa¥μr
′U2??
$
[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


ìa? -μ?]$
[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[$
[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¥-?′?M51 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
Hcos’ = 1r
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?Fi 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 = 10AI2 = 10p2AU = 200VR = 5?R2 = XL
k
pIXCXL#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 = 10AI2 = 10p2A#_ID_U1]M7 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 = 10AU = 100VuDi]M
k pIRXC
#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_U2iTM
m 9
m10(b)?ò|
^è
@_I1D_I2èa_UiTM
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 = 220VR1 = 10?X1 = 10p3?R2 = 20?
k pò?

@
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 = 220p2sin314tVi1 = 22sin(314t? 45–)Ai2 =
11p2sin(314t+90–)A
k pòNV
#è
^?
RLCb
[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 = UbcR = 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]M5

T¥′?A1
,'
XL?5 = 0 XL = 5?
?yUab = Ubc5jZabj = jZbcj
q
R21 +X2L = p52 +52
3-¤R1 = 5?
?
^Zab = (5+j5)?
15
4.7???
@
@
@èèè
^
^
^¥¥¥
q
q
q+++???
4.7.4
μBRLC1 óè
^¤?
q V??¥è÷
è÷èaU ?
10V?
q9F
Hè
@V10mA(500Hz)9F?Kv′60mA(1000Hz)b
k p(1)èERè?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 < f0è
^?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
@I1KliN
H?
¤I1 = 10AI2 = 6AUz = 113Vp = 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

^ ?m16
UX?R = R1 = R2 = 10?,L = 31:8mH,C = 318?F
f = 50HzU = 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?
Vni 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

^¥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 ?Caè
@Ihl7 
e

?M.
k ????
¥?é?r?
#?
qy
bf = 50Hz.
[333]
y1DNi óCaIhl
[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?0:86653i 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

@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

@V¥
119:1Ahl
b
21
22