Hệ số công suất điện Chuyên đề ôn thi ĐH CĐ Vật Lý Thầy Đoàn Văn Lượng

 Trang 1
BT: 
A .  không phân nhánh RLC.
I.m
+P = UIcos + UIcos(2t + ) (1)
+P = UIcos = RI
2
.
+
P UIcos
(2)
+
Z
R


cos
( Cos  (3)
+B:

2
2
R
R
U
P RI U I
R
  
(4)

2
. osP ZI c


,
2
2
UR
P
Z

(5)
cos =
R
U
U
(6)
II.  cos


+ = 1 ->  
(Z
L
= Z
C
) thì: P = Pmax = UI =
R
U
2
. (7)

+  = 
2

  
thì: P = P
min
= 0.
+: P
hp
= rI
2
=

22
2
cosU
rP
(8)
 r ( .
+ (8) => cos 
hp
 cos. Q cos 0,85.
+cos
ên dây.
+  thng  
sao   1.

III
1.
max

Khi L,C,

không 
L
và Z
C
không thay không gây
ra 
+ Tìm 
Ta có P=RI
2
= R
22
2
)(
cL
ZZR
U

=
R
ZZ
R
U
CL
2
2
)( 


,
Do U=Const nên 
max
thì (
R
ZZ
R
CL
2
)( 

) 
ng R và (Z
L
-Z
C
)
2
ta 

C
A
B
R
L
R
O
R
1
R

M
R
2
P

P
max
P< P
max

 Trang 2

R
ZZ
R
CL
2
)( 

R
ZZ
R
CL
2
)(
.2


=
CL

ZZ 2


R
ZZ
R
CL
2
)( 

)
min
là
CL
ZZ 2
lúc 
R=
LC
Z -Z
(9)

Z R 2
,
U
I
R2

;
R2
cos =

Z2

,
4

  
=> tan  = 1 (10)

2
max
U
P
2R

, (11)

2
max
LC
U
P
2 Z Z


(12)
và I = I
max
=
2
CL

ZZ
U

.
a.  :
 : : 

1
H, C =

4
10.2

F , u
AB
= 200cos100t(V).

A.50 ;200W B.100 ;200W C.50 ;100W D.100 ;100W
 Ta có :Z
L
= L = 100 ; Z
C
=
C

1
= 50 ; U = 100
2
V


2
R =
22
2
)(
CL
ZZR
RU

=
R
ZZ
R
U
CL
2
2
)( 


P
max
khi
R
ZZ
R
CL
2
)( 


hay R =Z
L
-Z
C
= 50  => P
max
=
R
U
2
2
= 200W. A.
2 : . 
RL
= 100
2
V, U
C
= 200V. 
 g
4
10
()
2

CF

.
A. 100W B. 100
2

W C. 200W D. 200
2
W

200
1
200
C
C
U
IA
Z
  
 =
2
2

= 100
2
.1.
2
2
=100W. 

b.
Câu 1: (ĐH-2008) 

L
, dung kháng
Z

C

C
 Z
L

0


m

A. R
0
= Z
L
+ Z
C
. B.
2
m
0
U
P.
R

C.
2
L
m
C

Z
P.
Z

D.
0 L C
R Z Z

 HD: Theo (9) : R
0
=|Z
L
 Z
C
| C
C
A
B
R
L

 Trang 3
Câu 2: 

1


4
10
3



2
cos100

A. R=120. B. R=60. C. R=400. D. R=60.
G HD: Z
L
= 100, Z
C
= 40, theo (9) R=|Z
L
 Z
C
| = 60 . 
Câu 3: 

1


4
10
3

120
2
cos100

A. P
max

=60W. B. P
max
=120W. C. P
max
=180W. D. P
max
=1200W.
 HD: Z
L
= 100, Z
C
= 40, theo (12)
2
max
LC
U
P
2 Z Z


= 60W . 
Câu 4: 

2
cos100

A. P
max
=55W. B. P
max

=110W. C. P
max
=220W. D. P
max
=110
2
W.
 HD: Theo (11)
2
max
U
P
2R

= 110W .
Câu 5: 


AB
=200cos100t (V). Khi R=100

A. 2A. B.
2
A. C. 2
2
A. D.
2
2
A
 HD: Theo (10)

U
I
R2

=
2
A. .
Câu 6: 


A.
2

. B.
4

. C. 0. D.
2
2

 HD: Theo (10)
4

  

Câu 7: 


A. 30
2

. B. 120. C. 60. D. 60
2
.
 HD: Theo (10)
Z R 2
=60
2
. .
Câu 8:  
                       u =
240cos(100t)V. Khi R = R
o

:
A. P = 115,2W B. P = 224W C. P = 230,4W D. P = 144W

 Trang 4
 HD:
L
= 200, Z
C
= 100 ) => R+r =|Z
L
 Z
C
| = 100.
2
max
LC
U

P
2 Z Z



2
max
(120 2)
P 144W
2 200 100


.

2. (P <P
max
):C
1
, R
2
P < P
max

2.1:
2
RIP 

2
22
.

()
LC
RU
P
R Z Z



 
2
2
2
LC
U
R R Z Z 0
P
   
(13)

ph 
1
và R
2

- R
1
+ R
2
=

2
U
P
(14)
và R
1
.R
2
= (Z
L
 Z
C
)
2
(15)

a.Các Ví :
: (
có U và   
1
và R
2


1
, 
2

1
và P

2


1
= P
2
 R
1
.R
2
= (Z
L
 Z
C
)
2
 
1
 +
2
 = /2
  và I
 a. Ta có P = I
2
R =
R
ZZ
R
U
R

ZZR
U
Z
U
CLCL
2
2
22
2
2
2
)()(
cos






(*)
Khi P
1
= P
2
ta có
1
2
1
2
)(

R
ZZ
R
U
CL


=
2
2
2
2
)(
R
ZZ
R
U
CL




1
2
1
)(
R
ZZ
R
CL



=
2
2
2
)(
R
ZZ
R
CL


 R
1
 R
2
=
2
2
)(
R
ZZ
CL

-
1
2
)(
R

ZZ
CL


 R
1
 R
2
= (Z
L
 Z
C
)
2
(
1
1
2
1
RR

)  R
1
.R
2
= (Z
L
 Z
C
)

2



Z
L
 Z
C
/R
1
= R
2
/ Z
L
 Z
C
  tan
1
 = 1/tan
2
  
1
 +
2
 = /2 (2)
i
R
ZZ
R
CL

2
)( 

min
T
R
ZZ
R
CL
2
)( 

 2 Z
L
 Z
C

: R =
R
ZZ
CL
2
)( 
 R = Z
L
 Z
C
 P
max
=

2
2
U
R
=
2
2
LC
U
ZZ

Và Cos  =
AB
AB
R
Z
=
1
2
,
U
I
Z

=
2
U
R
=
2

LC
U
ZZ



 Trang 5
+4: : 

1
H, C =
3
10
6


F , u
AB
= 200cos100t(V).
0W?
Ta có:
2
2 2 2 2
LC
22
LC
RU
P' I R P'R U R P'(Z Z ) 0 (*)
R (Z Z )
      



 240R
2
(100
2
)
2
.R +240.1600 = 0. : R
1
= 30 hay R
2
=160/3 
+: 
)(
`1
HL


;
)(
4
10
3
FC






).100cos(.275 tU
AB


 
A.
)(45 R
B.
)(60 R
C.
)(80 R
D
:
)(100 
L
Z
;
)(40 
C
Z


)1(.
22
R
P
IRIP 

:
22

)()(
CLABAB
ZZRIZIU 

a có :
)2)()(.(
2222
CL
AB
ZZRIU 

Thay (1) vào (2) ta có :
))((
222
CL
AB
ZZR
R
P
U 
(3)

))40100((
45
75
222
 R
R
Hay: R
2

- 125R+ 3600 = 0

1
2
2
45
125 3600 0
80
R
RR
R


   




1
= 45 
2
= 80 n D
+: t L = 2/(H) C = 125.10
-6
/ (F)hai 

AB

= 150
2

cos(100t)(V).
a.Khi P = 90W Tính R
b..
 a.Ta có:
LZ
L
.


= 200 ,
C
Z
C
.
1


= 80

2
R =
R
ZZ
R
U
R
ZZR
U
Z
U

CLCL
2
2
22
2
2
2
)()(
cos








R
R
2
2
)80200(
150


= 90 
R
R
2
120


= 250  R = 160  
V  
b.P
max
khi
R
ZZ
R
CL
2
)( 

hay R = Z
L
-Z
C
= / 200-80/ = 120=> P
max
=
R
U
2
2
= 93,75W
+7: 

)(
10
4

FC



  giá

1
và R=R
2

21
.RR
?
A.
10.
21
RR
B.
1
21
10. RR
C.
2
21
10. RR
D.
4
21
10. RR

C
A
B
R
L
C
A
B
R
L

 Trang 6
Bài  Ta có:
)(100
10
.100
11
4





C
Z
C

Khi R=R
1
tiê :

)1(.
)(

1
2
1
2
2
1
2
2
1
2
1
R
ZR
U
R
Z
U
RIP
C



Khi R=R
2

)2(.
)(

2
2
2
2
2
2
2
2
2
2
2
R
ZR
U
R
Z
U
RIP
C



Theo bài:
21
PP 
Suy ra: (1)=(2) Hay:
2
2
2

2
2
1
2
1
2
2
.
)(
.
(
R
ZR
U
R
ZR
U
CC



Hay:
42
21
10. 
C
ZRR
n D
+8: 

1
L ( H )

ào h 

1
và R=R
2

21
.RR
?
A.
10.
21
RR
B.
1
21
10. RR
C.
2
21
10. RR
D.
4
21
10. RR

 Ta có:

1
100 100   
L
Z .L .



Khi R=R
1
tiê :
2
2
1
11
22
1


L
U .R
P I R
( R Z )
(1)
Khi R=R
2

2
2
2
22

22
2


L
U .R
P I R
( R Z )
(2)
Theo bài:
21
PP 
Suy ra: (1)=(2) Hay:
2
1
22
1


L
U .R
( R Z )
2
2
22
2

L
U .R
( R Z )

Hay:
2
12

L
R R Z
= 10
4
n D
+ 9: 
π
1

dung C=
2π
10
-4

 
AB
=200cos100
A. 50, 200. B. 100, 400. C. 50, 200. D. 50, 200.
HD:
L
= 100, Z
C
= 200, theo (13):
 
2
2

2
LC
U
R R Z Z 0
P
   
 R=50. C.

2.2
1
và R
2
.

1
và R
2

Theo (13
 
2
2
2
LC
U
R R Z Z 0
P
   

R

1
và R
2


2
12
U
RR
P

,

 
2
1 2 L C
R R Z Z





(14)

(15)
C
A
B
R
L

N
M

 Trang 7

1
và R
2


0

max
theo R
1
và R
2
.

0

max
, 
0
= |Z
L
 Z
C
|


1
và R
2
):

 
2
1 2 L C
R R Z Z
suy ra:
0 1 2
R R R


max
1 2 0
2
.
P
R R R
P






(16)

(17)

a.10. 
1
()LH


,
3
10
()
4
CF





120 2 os100 ( )u c t V


, 
a. Khi R = R
0
thì P
max
. Tính R
0
, P
max
?


1
và R
2

max


2
1 2 0
max
1 2 0
.
2
.
R R R
P
R R R
P








Gii:  Imax? Tính giá tr này?
Cm kháng:
. 100( )
L

ZL

  
. Dung kháng:
1
40( )
C
Z
C

  
.
2
2
2
0
0
2
22
22
0
0
0
0
.

()
()
()
LC

LC
LC
UR
U U U
I P I R
ZZ
Z R Z Z
R Z Z
R
R
     





Pmax khi
2
0
0
()
LC
ZZ
R
R



0
2

0
()
2
LC
LC
ZZ
R Z Z
R

  

Nên Pmax khi
0
100 40 60( )
LC
R Z Z     
. 
22
max
0
(120)
120(W)
2 2.60
U
P
R
  




2
1 2 0
max
1 2 0
.
2
.
R R R
P
R R R
P








-T công thc tính công sut ta có:
2
2
1
1 1 1
22
1
.
.
()
LC

UR
P I R
R Z Z


.
- Khi R = R
2

2
2
2
2 2 2
22
2
.
.
()
LC
UR
P I R
R Z Z
  

.

2
2
2 2 2
2

1 2 1 2 2 1 2 1
2 2 2 2
12
2 2 2
1 2 2 1 2 1 1 2 0
.
.
. . ( )( )
( ) ( )
. ( ) ( )( ) . ( ) (1).
LC
L C L C
L C L C
UR
U
P P R R R R R R Z Z
R Z Z R Z Z
R R R R R R Z Z R R Z Z R
       
   
        


 Trang 8

max
1 2 0
2
.
P

R R R
P

.
Ta có:
22
2
2
11
1 1 1
2 2 2
1 1 1 2 1 2

. (2).
( ) .
LC
U R U R
U
P P I R
R Z Z R R R R R
    
   
.

2
max
0
(3)
2
U

P
R

P =
2
max 0
0 0 1 2
2
12
2.
22
. . ( )
U
PR
R R R R VeTrai DPCM
U
P
RR
   


1. 
0


0

trên R là
A. P B. 2P C.
2

P D. 4P

2
R =
R
U
2
=
R
U
2
2
0
(1)

2
R =
R
U
2
0
(2)
Suy ra:
P
P'
= 2 => 
+2 :
0

 

0
,  thì

0

0
là
A. 7,5 B. 15 C. 10 D. 50
HD: 
0
thì
0Max L C
P R Z Z  

Khi R
1
=R
0
+10 hay R
2
=R
0
-t =>
2
12 LC
R R ( Z Z )


2
0 0 0

( 10)( 5)R R R   

0
5 50 0R  
=> R
0
=10  ..

b.
Câu 9: 


A. 4W. B. 100W. C. 400W. D. 200W.
HD: Theo (14)  P=U
2
/(R
1
+R
2
)=200W. 
Câu 10: 
Khi R = R
1
và R = R
2

1
+ R
2
=

100. Khi R = R
1

A. 400 W. B. 220 W. C. 440W. D. 880 W.
 P
1
= P
2
=>
22
1
1
)(
CL
ZZR
R

=
22
2
2
)(
CL
ZZR
R

> (Z
L
 Z
C

)
2
= R
1
R
2

 Trang 9
P
1
=
22
1
1
2
)(
CL
ZZR
RU

=
21
2
1
1
2
RRR
RU

=

21
2
RR
U

= 400W.  A
h 2: 
 
 
2
2
2 2 2
2
2
. . . 0
LC
LC
U
P RI R P R U R P Z Z
R Z Z
      



-et:
2
12
U
RR
P


(1)
và
 
2
12
.
LC
R R Z Z
(2)
S
2 2 2
12
12
200
400
100
UU
R R P W
P R R
     

.  A
Câu 11: 


A. 60V. B. 40V. C. 30V. D. 100V.
HD: Theo (14)  U
2
=P(R

1
+R
2
)=3600  U=60V. 
Câu 12: 


0

A. 60. B. 65. C. 130. D. 98,5.
HD: Theo (16)
0 1 2
R R R
R
0
=60 
Câu 13: 
2

R
1

2


 B.12;100W;  
Theo (16):
0 1 2
R R R
=12 Theo (13)  P

Max
=U
2
/2R
0
= 60
2
/ 24=150W. Chon A
Câu 14: 
L

C

00W. 

o

A. P = 200W B. P = 400W C. P = 100W D. P = 50W
Vì Z
L
= Z
C

Z
1
= R ,
2
1
200
U

P
R

W. (1) Z
2
= 2R ,
2
2
2
U
P
R

(2)

1
2
200
100
22
P
P   
W. C
Câu 15: 
0


max

0



A. 2P
max
. B. P
max
/2. C. 0,4P
max
. D. 0,8P
max
.
HD: Khi P
max

0
=Z
L
,
2
max
0
U
P
2R

, 
0

5
R

0

0
U
I
5.R

 
2
=
2
0
2U
5R


max
P4
0,8
P5

 P = 0,8P
max
.  D

 Trang 10
Câu 16: 
x

63,8CF




r = 70
1
LH



R
x
:
A.
0 ;378,4W
B.
20 ;378,4W
C.
10 ;78,4W
D.
30 ;100W

 P = I
2
R=
R
ZZ
R
U
ZZR
RU

CLCL
2
2
22
2
)()( 





x
+ r = R
x

Z
L
; Z
C
=

6
10.8,63.314
1
2
1
fC

50
P = P

max
 y = R +
R
3500


-
2
3500
R

Khi R < 50  
Khi R > 50  
 .

x
= R  r = 0
P

=
4,378
)(
22
2


CL
ZZr
rU
W R

x
= 0, P

= 378,4 W. 

3. i k RLC.
  
C) sao cho
1
ωL =
ωC
(hay Z
L
=Z
C
) thì có 


Z
L
=Z
C
;
1
L
C


;
1


LC

(18)


: Z = Z
min
= R; U
R
= U
Rmax
= U (19)
:
max
U
II
R

(20)
:

2
max
U
PP
R

(21)


=0; 
u
= 
i
; cos=1 (22)
C
A
B
R
L
N
M

 Trang 11

U
LCmin
= 0. (23)
 
3.1
3.  

0
cos100

0

AB
cùng p
:

A 200W B 50W C 100W D 120W
 
0

2
max
U
P
R


LC
LC
ZZ
tan 3 Z Z R 3
R
Z 2R

     
 
=>
2 2 2
max
2
U R U U
P P 4P 200W
Z 4R R
     



tan( ) 3 2
3
LC
LC
ZZ
Z Z R Z R
R


       
(1)
Và
2
22
2
200
U
P I R R U R
Z
   
(2)
- Khi u và I cùng pha ta có:
2
axm
U
P
R

(3)
- 

ax
200
m
PW

4. 

u
AB
= 200cos(100

t)(V)L =

1
(H)R = 100



 


Ta có Z
L
=

L = 100

; R = 100

; U = 200/

2
= 100
2
V
P = I
2
R =
R
Z
U
2
2

U và R P 

Z =
22
)(
CL
ZZR 
 Z
C
= Z
L

= 100

=> C =

4

101


C
Z
(F) Z = R =>
R
U
P
2
max

= 200W.
U
v
= U
AM
= I.Z
AM
=
22
L
ZR
Z
U


U và
22
L

ZR 
= 100
2

U
AM
 Z  Z
C
= Z
L
= 100

=> C
=

4
101


C
Z
(F) Z = R
=> U
vmax
=
AM
Z
R
U
=

2100
100
2100
= 200V
L
R
B
C
A
V
M

 Trang 12

Câu 17: 0 

AB
=200cos100

A 100W B 50W C 200W D 150W
HD: Theo (21) P=U
2
/R = 100W. 
 
Câu 18: 
dung C, R = 50 
2
cos100

A 50W B 100W C 200W D 150W

HD: U
MBmin
=U
LCmin
= :
P=P
max
=U
2
/R=50W. 
3.2.
Câu 19: (ĐH2008) 

1
LC


 
 D. 
HD: P
max
 C
Câu 20: 

u
AB
=U
0
cos
A. 1. B.

4

. C. 0. D.
2
2
HD: P
max
khi) =0; cos=1. 

3.3
P
max
6) ta suy ra

2
1
C=
ωL


(24)
Câu 21: /


A. 0,5/ (H). B. 0,5. (H). C. 0,5 (H). D.0,5./2 (H).


C
A
B

R
L
C
A
B
R
L

 Trang 13
3.4
P
max
) ta suy ra

2
1
L=
ωC


(25)
Câu 22:  

3
/5

A. 0,5/ (H). B. 5/ (H). C. 0,5 (H). D. 5 (H). HD: Z
L
= Z
C

=50   L=0,5/ (H).  A
3.5.  ( f hay

) 
( hay f) 
+ o :
2
22
()
LC
RU
P
R Z Z
;
2
axm
U
P
R
khi
2
11
2
    
LC
Z Z f
LC
LC



 = 
0
P
max

0
1

LC


+  = 
1
 = 
2

R

khi
12
  

 
12
f f f
.
f

12

ff

12
f f a
và
12
?II

Ta có :
1 1 2 2
22
12
( ) ( )
L C L C
Z Z Z Z Z Z     

2
12
12
1
2
ch
LC
a
  
  











1
, 
2
, 
0
:
0 1 2 1 2
1
LC
   
   
 
12
f f f
(26)

+
axCM
U
khi:
2
22
2
1

(2 )
2
R
f
LC L

  
(27)
+
axLM
U
khi:
22
22
2
(2 )
2
f
LC R C



(28)
+  5:            L =
1
()
2.
H

     

4
10
()
2.

CF


100 2cos2
AB
u ft



 
: 
2
2
cos
U
P UI R
Z




max
khi Z
min

Ta có
 
2
2
LC
Z R Z Z  
, nên Z
min
khi Z
L
= Z
C


2
1LC



22
41f LC


 :
4
11
2
1 10
2.
2. 2.


f
LC



= 100 (Hz).
C
A
B
R
L
N
M
C
A
B
R
L

 Trang 14

2 2 2 2
max
22
min
100
200
50
U U U

P R R
Z R R
    
(W).


Câu 23: 
0
cost có U
0
 
. u = 200cos 2

f t (V). .
 f= f
1
=25Hz và f= f
2

 f
0
là:
A. 75Hz. B. 125Hz. C. 62,5Hz. D. 50Hz.
HD: ) 
12
f f f
=
25.100 50f Hz
C
Câu 24: (ĐH 2009) 

0
cost có U
0
 
  = 
1

 = 
2

A.
12
2
LC
   
. B.
12
1
.
LC
  
. C.
12
2
LC
   
. D.
12
1
.

LC
  
.
HD: )
0 1 2 1 2
1
LC
   
   
C
Câu 25. Cho L = 1H, C = 50F và R = 50
u = 220cos(2ft)(V), trong 
o


max
. 
A. P
max
= 480W B. P
max
= 484W C. P
max
= 968W D. P
max
= 117W
Câu 26. 
2




A. 72 (Hz) B. 34,72 (Hz) C. 60 (Hz) D. 41,67 (Hz)
 Khi f = f
1
= 50 (Hz) :Z
C1
= 1,44 Z
L1

1
2
1
fC


1

LC =
2
1
2
4.44,1
1
f

(1)

2

Khi f = f

2

Z
C2
= Z
L2

2
2
1
fC

= 
2

LC =
2
2
2
4
1
f

(2)
So sánh (1) và (2) , ta có:
2
2
2
4
1

f

=
2
1
2
4.44,1
1
f



f
2
= 1,2 f
1
= 1,2 . 50 = 60(Hz) 


1

2

max
.

1

2


P
1
=P
2
 Z
1
=Z
2
 |Z
L1
Z
C
| = | Z
L2
 Z
C
| 
L1 L2
C
ZZ
Z
2


=>:
12
2
2
LL
C





L
= Z
C
suy ra:

L1 L2
L
ZZ
Z
2


=>
12
LL
L
2




(29)


(30)

 Trang 15

1

2

max


1

2

P
1
=P
2
 Z
1
=Z
2
 |Z
L1
Z
C
| = | Z
L2
 Z
C
| 

C1 C2
L
ZZ
Z
2


=>
2
12
11
2L
CC




(31)

Theo (18) Z
L
= Z
C
:

C1 C2
C
ZZ
Z
2



,
12
2 1 1
C C C

,
12
12
2C .C
C
CC





(32)


L,C,


R,C,


R,L,




22
max
UU
P =
22
:
LC
LC
R Z Z
Khi R Z Z




 sau:








2
max
2
U
P =
1

:
LC
R
Khi Z Z L
C

  

 sau:





2
max
2
U
P =
1
:
LC
R
Khi Z Z C
L

  

 sau:

2
max
U
P =
1
:
2
LC
R
Khi Z Z f
LC
  

 sau:





6: 
2
cos 100

t (V). Khi C = C
1
=
4
10
4



(F) và C = C
2
=
4
10
2


(F)

1,
C
2
.
+Khi C = C1=
4
10
4


F ta có :
1
1
1
400( )
C
Z
C


  
. Tng tr:
2 2 2 2
11
( ) ( 400) .
L C L
Z R Z Z R Z     

- Công sut:
2
2
11
22
.
.
( 400)
L
UR
P I R
RZ


(1)
+Khi C = C2 =
4
10
2


F ta có:

2
2
1
200( )
C
Z
C

  
. Tng tr:
2 2 2 2
22
( ) ( 200) .
L C L
Z R Z Z R Z     

- Công sut:
2
2
22
22
.
.
( 200)
L
UR
P I R
RZ



(2)
 : P1 = P2 :
22
12
2 2 2 2

P P 300( ).
( 400) ( 200)
L
LL
U R U R
Z
R Z R Z
     
   


3
()
L
Z
LH

  
.
- Tìm R:
22
2
11
2 2 2 2

. (200) .
. 200 100( )
( 400) (300 400)
L
U R R
P I R R
R Z R
      
   

R
O
R
1
R
0
R
2
P

P
max
P<P
max
f
O
f
0
P

P
max
C
L
O
L
0
P

P
ma
x
O
C
0
P

P
max

 Trang 16
- H s công sut khi C = C1=
4
10
4


:
1
1

100 1
os .
100 2 2
R
c
Z

  

- H s công sut khi C = C2=
4
10
2


:
2
2
100 1
os .
100 2 2
R
c
Z

  

7: 

R=100Ω


y khi
1
L=L
và khi
1
2
L
L=L =
2


1

A.
-4
1
4 3.10
L = (H);C= (F)
π 2π
B.
-4
1
4 10
L = (H);C= (F)
π 3π
C.
-4
1
2 10

L = (H);C= (F)
π 3π
D.
-4
1
1 3.10
L = (H);C= (F)
4ππ


 Do công suát P
1
= P
2
=> I
1
= I
2
=> Z
1
= Z
2


L1
 Z
C
)
2
= (Z

L2
 Z
C
)
2
. Do Z
L1
 Z
L2
nên Z
L1
 Z
C
= Z
C
 Z
L2
= Z
C
-
2
1L
Z

=> 1,5Z
L1
= 2Z
C
(1)
tan

1
=
R
ZZ
CL

1
=
R
Z
L
4
1
và tan
2
=
R
Z
Z
R
ZZ
C
L
CL



2
1
2

=
R
Z
L
4
1



1
+ 
2
=
2

=> tan
1
. tan
2
= -1 => Z
L1
2
= 16R
2
=> Z
L1
= 4R = 400 => L
1
=


4
1

L
Z
(H)
Z
C
= 0,75Z
L1
= 300 => C =

3
10
.
1
4

C
Z
(F) B
18: Cho mn xoay chiu AB cha R, L,C ni tin tr thun và cun dây thun
cm 2R = Z
L
n MB có t n dung có th u mch vào hin th xoay chiu
u = U
0

0
ii C = C

0
công sut mt giá tr cc thêm
t C
1
vào mch MB công such gim mt na, tip tc mc thêm t C
2
vào m công sut
ca m C
2
là:
A. C
0

0
B. C
0

0
C. C
0
/3 hoc 2C
0
D. C
0

0

 Khi C= C
0
=> P

max
=
2
U
R

0
LC
Z Z 2R


1

0
:
bb
2 2 2
max L C C
1
P P R (Z Z ) (2R Z )
2
     

=>
0
b
0
b
C
C b 0

C
C b 0
Z
Z R C 2C
2
3Z
2
Z 3R C C
23

   



   





2

0

1

b


0



b
= 2C
0
> C
0

2

b
:
20
0 0 2
1 1 1
C 2C
C 2C C
   


b
=
2
3
C
0
<C
0

2

song song C
b
:
0 0 2 2 0
21
C C C C C
33
   


 Trang 17
19:   

L
= 2Z
C
  trong m

2
A C, L là:
A.
1
10
m

F và
2
H

B.

3
10

mF và
4
H

C.
1
10

F và
2
mH

D.
1
10

mF và
4
H


:
P UI
hay
22
22
()

LC
UU
P
Z
R Z Z




LC
R Z Z
hay
( 2 )
C L C
R Z doZ Z

 
100 2( )
U
Z
I
  

Hay
22
( ) 100 2
LC
R Z Z  

11

100
10
C
C
Z C mF
Z

    


2
2 200
L
LC
Z
Z Z L H

     


 A
+20: ,
4
10
C






200cos100
AB
ut




A.
1
L


H B.
1
2
L


H C.
2
L


H D.
4
L


H


4
11
100
10
100 .
C
Z
C




   
;
2
100
1
100
P
I
R
  
A.
2
2
2
200 100
. 100 2
100
2

UR
P I R R Z U
ZP
      
.
Mà
 
 
2
2
22
100 2 100 100
L C L
Z R Z Z Z      

0( ai)
200 2
200 ( )
100
L
L
L
Z lo
Z
Z L H
  






     


C C.
+21: 
1
= U
2



= P
1

2
= Ucos(
3



= P
2 .

1
và P
2

là :
A.

P
1
= P
2
B.

P
1
= P
2
/
2

C.

P
1
= 2 P
2
D.

P
1
=
2
P
2

:  R nt C:

-
1
= U
2
 
1
= 0,5 ; 
1
=
1
Z
R


Z
1
= 2R

1
:

2
1
Z
R
2
+
2
1C
Z

Hay (2R)
2
= R
2
+
2
1C
Z


R =
3
1C
Z
mà Z
C1
=

CC
11
1



R =

C3
1
(1)

 Trang 18
P
1
= R
2
1
I
= R









2
1
1
Z
U
R
R
U
R
U
42
2
2








(2)
-
2
= Ucos(
3
) : Z
C2
=


3
11
2
C
C

(3)
So sánh (1) và (3) ta có: Z
C2
= R
p dùng u
2
:

2
2
22
2 C
ZRZ 
= R
2
+ R
2
= 2R
2


Z
2
= R
2

 P
2
=
R
U
R
U
R
Z
U
RRI
4

2
2/
2
2
2
2
2
2
2



















(4)
So sánh (2) và (4) ta có: P

1

= P
2

 A



IV. 
Câu 27: 
u 100 2cos100 t (V)


2
LH



A. 50W B. 100W C. 200W D. 350W
Câu 28: 
2
cos(100t+


2
10
3



A.720W B.360W C.240W D. 360W
Câu 29:. 
3
L = H
10π

-4
2.10
C = F
π

.u =120 2 cos 100πt (V)

1


max

1
, P
max

A.
1 max
R 20 , P 360W  
B.
1 max
R 80 , P 90W  

C.

1 max
R 20 , P 720W  
D.
1 max
R 80 , P 180W  

Câu 30: 


220 2 os(100 )
2
u c t



(V).  
A. 115W. B. 220W. C. 880W. D. 440W.
Câu 31:  ).

 
A.

LC
ZZ
B.

LC
ZZ
C.


CL
ZZ
D.
2
LC R


Câu 32:            ).
= 15,9

u 120 2cos100 t(V)


A. 240W B. 96W C. 48W D. 192W
Câu 33:.  ).
R=100


2
L = H
π


R
L
C
A
B
Hình 32
R

L
C
A
M
N
B
Hình 3.3
R
L
C
A
B
Hình 31

 Trang 19
AN
u = 200cos100πt (V)

A. 100W B. 50W C. 40W D. 79W

Câu 34: 

1
và R
2
sao cho R
1
+ R
2
= 100 


A. 50W. B. 100W. C. 400W. D. 200W.
Câu 35.  h 34). R=100


2
L = H
π

A và N là:
AN
u = 200cos100πt (V)

h là:
A. 100W B. 50W C. 40W D. 79W
Câu 36: 

120 2 cos(120 )ut


 R
1
=18

,R
2
= 32

thì 
  

A.144W B.288W C.576W D.282W
Câu 37: 

1
và R
2
sao cho R
1
+R
2
=90

A. 240w B. 160W C. 80W D. 190W
Câu 38: 
50 2 cos100ut


(V),
30
L
UV
,
60
C
UV


A.
3
0,8 10

60 , ;
12
R L H C F


   
B.
3
0,6 10
80 , ;
12
R L H C F


   

C.
3
0,6 10
120 , ;
8
R L H C F


   
D.
3
1,2 10
60 , ;
8

R L H C F


   

Câu 39: 
C


2

3



2



A. 72 W. B. 240W. C. 120W. D. 144W.
Câu 40: 
0
cos100

C1
= 300 
C2
= 100 

A. 400. B. 100

10
. C. 75. D. 200.
HD: Theo (31)
C1 C2
L
ZZ
Z
2


= 200. .
Câu 41: 
1
=2.10
-4

2
=10
-4


A10
-4
 B.10
-4
 C. 2.10
-4
 D. 3.10
-4


HD
12
12
2C .C
C
CC


= 10
-4
 
Câu 42: 
40r 

1
5
LH



3
10
5
CF





R

L
C
A
M
N
B
Hình 3.5

 Trang 20
A.
40
B.
60
C.
50
D.
30

Câu 43:  
 

A. 50W. B. 100W. C. 400W. D. 200W.
Câu 44: 

A B C D(rad/s).
Câu 45: 
10 2cos100 ( )u t V




1

=
9
và R
2
=
16

A. 8W B.
0,4 2
W C. 0,8 W D. 4 W
Câu 46: 
u = 200cos(100πt)
(V). Thay

10( )R 

40( )R 
 

A. 400 W. B. 200 W. C. 500 W. D. 600 W.
Câu 47:  có

120 2 cos(120 )ut



1
38( )R 

,
2
22( )R 
thì 
  
A. 120W. B. 484W. C. 240W. D. 282W.
Câu 48: 

200 2 os(100 )u c t


(V) khi
5
1
2,5.10 ( )C C F


và
5
2
5.10 ( )C C F



cùng cô
A B
C D
Câu 49:  

0

cos100 ( )u U t V



1
45R 
và
2
80R 


A. 100 W. B.
250
W
3
. C.
80 2
W. D. 250 W.
Câu 50:  = 
0

 = 
1
 = 
2

 là
A. 
0
= 

1
+ 
2
. B.
12
0
12


  
. C. 
0
= 
1
- 
2.
D.
2
0 1. 2
  


Câu 51: 
t


0.75
H




A.25

B.50

C.75

D.100


Câu 52: áp U=120V,
f 0 thì óc 60
0
, cô 
A. 288W B. 72W C. 36W D. 144W
Câu 53: 

1

2
=
2.100

A.
.
2
3
B. 0. C.
2
2

. D. 0,5.
Câu 54: 
2



/
A. 100W B.
100 3
W C. 50W D.
50 3
W

 Trang 21
Câu 55: 

tUu

cos2
(V) . Khi C = C
1


)3/cos(2

 tIi
(A). Khi C = C
2
 


2
là
A. 400 W . B. 200 W . C. 800 W . D. 600 W .
Câu 56: 

1
và R
2
ng

A.
21
2
2 RR
U
B.
21
2
RR
U

C.
21
2
2
RR
U

D.
21

21
2
4
)(
RR
RRU 

Câu 57: 
100R 




0
60


A.
3
LH


, P = 36W B.
1
3
LH


, P = 75W C.
1

LH


, P = 72W D.
1
2
LH


, P = 115,2W
Câu 58: 
200 2cos100ut


(V);
1,4
LH


;
4
10
2
CF




A.
25R 

hoặc
80R 
B.
20R 
hoặc
45R 

C.
25R 
hoặc
45R 
D.
45R 
hoặc
80R 

Câu 59: 


1

2


A.    
Câu 60: 
2


25

(H)
36.

4
10




A  rad/s.  
Câu 61: 
0
cos

1

2


A. 14mH. B. 7mH. C. 2mH. D. 10mH.
HD: Theo (30) C
Câu 62: 
0
cos

1
= 3
2
= 4


max
.
A. C=7F. B. 1F. C. 5 F. D. 3,43F.
HD
12
12
2C .C
C
CC


= 3,43F. 
Câu 63: -2009): 

1
và R
2


 Trang 22
C
A
B
R
2

L
M
R
1


1


2

1
và R
2
là:
A. R
1
= 50, R
2
= 100 . B. R
1
= 40, R
2
= 250 .
C. R
1
= 50, R
2
= 200 . D. R
1
= 25, R
2
= 100 .
HD:

22
12
1 2 1 1 2 2 1 2 1 2
2 2 2 2
12
(1) (2)& 2 2 (3)
CC
CC
RR
P P R I R I U U I I
R Z R Z
       



21
4 (4)RR

2
12
50 200
4
C
Z
RR     

Câu 64 -2010): 




4
10
4


2
10
4


A.

3
1
H B.

2
1
H C.

3
D.

2
H
HD: 
1

2
thì P

1
= P
2
nên ta có:
2 2 2 2 2 2 2 2
12
1 2 1 2 1 2
3
( ) ( )
2
CC
L C L C L
ZZ
I R I R Z Z R Z Z R Z Z Z L H


            

Câu 65 (-2011): 
ft2cos2Uu 
h

1



và 8


2



1
và f
2
là
A.
.f
3
4
f
12

B.
.f
2
3
f
12

C.
.f
3
2
f
12

D.
.f
4

3
f
12


 
1
:
 
4
3
.28
2
1
;62
2
1
1
1
1
1
11
 LCf
Z
Z
Cf
ZLfZ
C
L
CL




(1)

2

1)2(
2
2
LCf

(2)

12
1
2
3
2
3
2
ff
f
f

 
Câu 66: 
1



2


0
cos

t (U
0
và



LC
1
2



AM
và u
MB
là 90
0


A. 85 W B. 135 W. C. 110 W. D. 170 W.
Khi
LC
1
2




Z
L
= Z
C

P =
21
2
RR
U

(1)
Ta có: tan
1
=
1
R
Z
C

; tan
2
=
1
R
Z
L


2
- 
1
= 90
0
=> tan
1.
tan
2
= -1

1
R
Z
C

1
R
Z
L
= -1 => Z
L
= Z
C
=
21
RR
(2)


 Trang 23
P
2
= I
2
2
R
2
=
22
2
2
2
L
ZR
RU

=


21
2
2
2
2
RRR
RU
21
2

RR
U

= P = 85W.  A
Câu 67: 
3


2



A. L =
2
2

(H);P= 160W. B.L =
3

(H); P = 173,2W C. L =

2
3
(H);P = 200W D.L =
3
2

(H); P = 100W

22

C
ZR 
= 1. 100 = 100V
 
L
= Z
C
=50
3

3
=> L =

2
3
(H).

R
U

Câu 68: 


0
và 60
0

  
-4


-4

:
C1
+ Z
C2
= 2Z
L


C

 là: Z
Ci
=
180
c
i
Z



1
là Z
C1
=
1
180
c
Z


=
6
c
Z


2
là Z
C2
=
2
180
c
Z

=
3
c
Z


6
c
Z
+
3
c
Z
= 2Z

L
= 600 ;
C
= 1200
Suy ra: Z
C1
= 200 = 10
-4
; Suy ra Z
C2
= 400 = 10
-4


Câu 69: Cho mach R,L,C mc ni tip, vi C có th i. n mch
n áp
100 2 cos(100 )( )u t V


.
R=100
3
n ti,
 /3. Công suât tiêu th c
 
1

2
 :P
1

=P
2
 Z
1
=Z
2
 |Z
L1
Z
C
| = | Z
L2
 Z
C
|

C1 C2
L
ZZ
Z
2



C1
= 2Z
C2
=>
C1 C2
L

ZZ
Z
2


=>
C2
L
3.Z
Z
2


-1+ 2 = /3 1 = -/6 ; 2 = /6 => -tan1= tan2
Ta có:
1
2
2
33
3
33
LL
LC
ZZ
ZZ
RR


    
<=>

1
3
3
3
L
Z
R


<=>
3 100 3 3 300
L
ZR   
;
2
22
300 200
33
CL
ZZ   
;
12
2 2.200 400
CC
ZZ   

2 2 2 2
( ) (100 3) (300 400)
LC
Z R Z Z     

=200 .Ta có
100
0,5
200
U
IA
Z
  

P= I
2
.R= (0,5)2
2
(0,5) 100 3 25 3( )W


 Trang 24
Hay:
22
22
22
. 100 .100 3
25 3( )
()
(100 3) (300 400)
LC
UR
PW
R Z Z
  




Câu 70: 

A. 60Hz B. 50Hz C. 70Hz D. 
Câu 71: 
1
=2.10
-4

2
=10
-4


A10
-4
 B.10
-4
 C. 2.10
-4
 D. 3.10
-4

Câu 72: 

1



1

1


2

2

2

cos
2

1
+ cos
2

2
=
4
3

1
2
P
P

A. 1 B. 2 C. 3 D. 4
 P

1
= UI
1
cos
1
= I
1
2
R
1
=> I
1
R
1
= Ucos
1
=> I
1
= 2cos
1
(1)
P
1
= UI
1
cos
1
= 2Ucos
2


1
=> cos
2

1
=
U
P
2
1
=
10
3
(2)
P
2
= UI
2
cos
2
= I
2
2
R
2
=> I
2
R
2
= Ucos

2
=> I
2
= 4cos
2
(3)
cos
2

1
+ cos
2

2
=
4
3
=> cos
2

2
=
4
3
- cos
2

1
=
4

3
-
10
3
=
20
9
(4)

1
2
P
P
=
1
2
I
I

1
2
cos
cos


=
1
2
cos2
cos4



1
2
cos
cos


= 2
1
2
2
2
cos
cos


= 2.
10
3
20
9
= 3. 
Câu 73: 
0
cosu U t



0

,U



1
LL
hay
2
LL
v
12
LL


12
,PP

12
3;PP


12
,


12
/2.
  



1

và
2

là:
A.
/3 ; /6.

B.
/6 ; /3.

C.
5 /12 ; /12.

D.
/12 ; 5 /12.



Có P
1
= I
1
2
.R = U
2
.R/ { R
2
+ (Z

L1
- Z
C
)
2
}
P
2
= I
2
2
.R = U
2
.R/ { R
2
+ (Z
L2
- Z
C
)
2
}
Do P
1
= 3. P
2
ta có 3. { R
2
+ (Z
L1

- Z
C
)
2
} = { R
2
+ (Z
L2
- Z
C
)
2
} (1)
Do
12
/2.
  


1

2
hay {(Z
L1
- Z
C
)/R}= {(Z
L2
- Z
C

)/R}
Suy ra R
2
= (Z
L1
- Z
C
).(Z
L2
- Z
C
) (2)
Thay vào ( 1) ta có: 3.(Z
L1
- Z
C
). (Z
L1
- Z
C
+ Z
L2
- Z
C
) = (Z
L2
- Z
C
). (Z
L1

- Z
C
+ Z
L2
- Z
C
)
hay : 3.(Z
L1
- Z
C
) = (Z
L2
- Z
C
) (3) thay vào ( 2)
R
2
= 3.(Z
L1
- Z
C
)
2
hay (Z
L1
- Z
C
)
2

= R
2
/3
Và theo (3) suy ra (Z
L2
- Z
C
)
2
= 3. R
2

Mà Cos 
1
= R/Z
1
= R/
3
2
2
R
R 
=
2
3
suy ra
1

= /6


2
= R/Z
2
= R/
22
3RR 
=
2
1
suy ra
2

= /3


 Trang 25
h không phân nhánh RLrC ( có r).
I.mrLC không phân nhánh (:
P = UIcos hay P = I
2
(R+r)=
2
2
U ( R r )
Z

.
cos =
Rr
Z


.
+ P
R
= I
2
.R=
2
2
U .R
Z

22
LC
(R+r) (Z - Z )

+ Pr = I
2
.r =
2
2
U .r
Z

cos
d
=
d
r
Z

=
22
L
r
rZ


- 
max
: theo (9)
R+r=|Z
L
 Z
C
|, R=|Z
L
 Z
C
|  r

2
max
U
P
2(R r)


,
2
max

LC
U
P
2 Z Z



- 
Rmax

R
2
= r
2
+(Z
L
 Z
C
)
2



()

(12)

(17)
1: r =20 
0,8



C=
2π
10
-4
F  

A. 100 . B. 120 . C. 60 . D. 80 .
HD:
L
= 80, Z
C
= 200, theo (17) => R=|Z
L
 Z
C
|  r = 100. 
2: r =30 
0,8


C=
3
10
4


F v 


A. 100 . B. 120 . C. 50 . D. 80 .
HD: Z
L
= 80, Z
C
= 40, theo (17): R
2
= r
2
+(Z
L
 Z
C
)
2
=2500  R=50  . 

II.  : (L,r,C,

không )

max
: Khi L,C,

không 
L
và Z
C
không thay 
không gây ra 

Ta có P=(R+r)I
2
= (R+r)
2
22
Lc
U
( R r ) ( Z Z )  

C
A
B
R
L,r
C
A
B
R
L,r
N
M