[Phan Nhật Hoàng_ Trần Văn Quân]Chuyên Đề Ku_ Bản Chính Thức

PHAN NHT HONG - TRN VN QUN

IN XOAY CHIU

CHUYN KU

2015

CHUYN KU 1 LI M U

1 Li m uien xoay chieu - mot chu e yeu thch cua cac ban am me Vt l ph thng!

Cai em me ay la ca mot qua trnh tm toi, hoc hoi, chng minh, xay dng nhng cong thc e hieuhe t nhng cai ep, cai sau sa c trong ien xoay chieu. Chnh v vay, chung toi nhng ngi am me Vat lpho thong vie t chuyen e nay e cac ban hieu them nhng van e sau sa c an cha trong bai toan tan sothay o i trong ien xoay chieu.

Cha c cac ban to mo v sao chuyen e lai mang ten chuyn KU, o la mot ieu that thu vi, cai ten naye bao quat oi dung cua chuyen e , khai thac ve bai toan thay o i tan so e cac ai lng ien ap hieudung cac phan t trong mach RLC bieu dien theo thong qua ien ap hieu dung hai au mach qua tham sok. Y tng chuyen e c thayNguyn nh Yn khi nguo n, sau o c anh Phan Nht Hong va mnhphat trien, va lam ro e cac ban hieu ban cha t. Cac cong thc trong chuyen e ra t de nh, c xay dngt ham tam thc bac hai nen oc qua cac ban co the hieu ngay. Mac du hnh thc no n gian nhng khikhai thac nhieu kha canh ve no th khong n gian mot chut nao. ac biet khi ke t hp nhng cong thcvi nhng cai cu th no se tr thanh nhng bai toan kho, neu i thi ban cha gap mot lan nao ma may motm li giai ma t ra t nhieu thi gian.

V vay, chuyen e nay se giup cac ban hieu ro them ve bai toan f bien thien, e cac ban khong s nona ma cam thay thch thu khi lam nhng bai toan ve f bien thien. Hi vong rang sau khi cac ban oc xongchuyen e , cac ban cam thay t tin hn vi mot dang mi trong bai toan f bien thien, t o co mot onglc u ln e vng tin trong chang ng ma cac ban a chon pha trc.

Noi dung chnh chuyen e c chia lam 3 phan:

k < 1 - Bai toan f thay o i e U = U = kU

k = 1 - Bai toan f thay o i e U = U, U = U

k > 1 - Bai toan f thay o i e U = U = kU(U = U = kU) hoac U = U = kU(U = U = kU)

mo i phan se co bai tap van dung e cac ban hieu ro hng ap dung nhng cong thc trong chuyen evao bai tap. Cuo i cung la bai tap luyen tap e cac ban ren luyen, cung co k nang lam bai cua mnh.

Cuo i cung, xin chan thanh cam n nhng ai Yu Vt l a oc, on nhan, quan tam chuyen e nay. Macdu ra t co gang trnh bay mot cach khoa hoc va mot cach chnh xac nha t nhng khong the tranh khoi saisot. Moi y kien tha c mac, ong gop cua ban oc xin lien he qua ia ch mail:[email protected].

Ngay 30/4/2015Tran Van Quan

LATEX by Tran Van Quan

PHAN NHT HONG - TRN VN QUN 1

CHUYN KU 2 NI DUNG CHUYN KU

2 Ni dung chuyn KU2.1 k < 1 - Bi ton f thay i UR = UR = kU(k < 1)2.1.1 Ni dung cng thc

Xet bai toan: at ien ap xoay chieu = 2() vao hai au oan mach RLC mac no i tiep, cuon daythuan cam, trong o thay o i c. Thay o i en gia tri va th ien ap hieu dung hai au ientr bang nhau va bang k lan ien ap hieu dung hai au mach( < 1). Khi o ta co ke t qua::Ke t qua 1: Ke t qua quen thuoc:

. = 1

:Ke t qua 2:

= | |1

Chng minh:Ta co

= = = + ( )

( 1) + 2. + = 0

( 1) + 2 +

= 0

+ ( 1) 2 +

= 0 (2.1.1.1)

S dung inh l Vi-et cho phng trnh (2.1.1.1) an ta co:

+ = =

2 ( 1)

= 2 +

1

. =

T hai ieu tren ta suy ra c ( ) = .

1 =

| |1 Cng thc trn thong nhn chng ta thy rt quen, chc hn chng ta lin tng ti cng thc ny: =| 2|

1.

N xut pht t bi tonmch RLC c thay i n gi tr vm c hai gi tr dng in bng nhauv b hn cng dng in hiu dng cc i k ln = =

( > 1) th =

| 2| 1

Thc ra hai cng thc c cng bn cht, tht vy:Ta c = = = = = =

1

( < 1). p dng cng thc trn vi s tng

1 la tan so goc khi mach xay ra cong hng



quan ca v 1 ta c: =| |

1 1

= | |1

. Thc ra hai bi ton l mt nhng s phn

chia ra nh vy s gip ta hiu r bn cht v c nhiu cch chng minh cho mt bi ton hay cng thcng nh no .

2.1.2 Bi tp vn dng

Vn dng 1: at ien ap xoay chieu = 2 cos() vao hai au oan mach RLC mac no i tiep chacuon day thuan cam, trong o thay o i c. Thay o i en gia tri hoac th ien ap hieu dung

hai au ien tr bang nhau va eu nho hn ien ap hieu dung cc ai hai au ien tr 32 lan. Bie t rang

= 100 (/) va =1 . ien tr R co gia tri la:

A. 100. B. 1003. C. 200. D. 160.

Li gii

Lu in p hiu dng cc i hai u in tr chnh l in p hiu dng hai u on mchBai toan ch mang tnh cha t ap dung cong thc co ngay:

= | |1

=1.100.

32

1 34

= 1003

ap an B.Vn dng 2: at ien ap xoay chieu = 2 cos(2) vao hai au oan mach gom oan AM chamot cuon day thuan cam co o t cam L no i tiep ien tr R, oan MB cha tu ien co ien dung C thayo i c, trong o thay o i c. Co inh ien dung cua tu gia tri , ngi ta thay o i en gia tri th ien ap hieu dung hai au ien tr la va ien ap hai au AM lech pha so vi dong ien goc .Thay o i en gia tri < th ien ap hieu dung hai au ien tr la va ien ap hai au AM lechpha so vi dong ien goc . Bie t rang = =

2 va =

3 . To ng + co gia tri bang:

A. 6 . B.4 . C.

2 . D.

3 .

Li gii

Khi thay o i f, t cong thc tren ta suy ra:

= 1

.( ) tan tan =1

=1 12

12

= 3

Bien o i ta co: sin( )cos. cos = 3 cos. cos =

12

=3 = 0



Vay + =3

ap an D.

2.2 k = 1 - Bi ton f thay i UL = U, UC = U2.2.1 Ni dung cng thc

Xet bai toan: at ien ap xoay chieu = 2() vao hai au oan mach RLC mac no i tiep, cuon daythuan cam, trong o thay o i c.Thay o i en gia tri th ien ap hieu dung hai au cuon cam thuan bang ien ap hieu dung hai auoan mach ( = ). Khi o ta co ke t qua::Ke t qua 1: = ma = th:

=2

Thay o i en gia tri th ien ap hieu dung hai au cuon cam thuan bang ien ap hieu dung hai auoan mach ( = ). Khi o ta co ke t qua::Ke t qua 2: = ma =

= 2

Chng minh.:Ke t qua 1: Ta co

= = = + ( )

= + 2 +

2 =

2 =

2

12=

2

2 =1

2

=2 =

2

:Ke t qua 2: Mot cach chng minh tng t ta cung co:

= = = + ( )

2 =

2

2 =

2

= 2 = 2



Ta i mot bai toan to ng quat: : Cho oan mach RLC no i tiep, vi tan so f thay o i c. Thay o i = + (Hz) th = . Thay o i = (Hz ) th = . Bie t rang he so cong sua t trong haytrng hp la x. Tm bieu thc tnh thong qua x va ?Khi = (Hz ) th : = = = ()

+ ( ) = + 2 + 2 + = 0Giai phng trnh tren ta thu c = (1 1 ).(1) . = (1 + 1 ).Ta co cong thc giai nhanh kha quen thuoc : = . =

2

.2( + ) = ( + )

= =

1

=

=

( + ) =

1 =

:Ke t qua 3:

> 0 > = (1 1 ) =(1 1 )

1

< 0 < = (1 + 1 ) =(1 )1 + 1

Ba ke t qua tren la nhng ke t qua quan trong, van dung giai nhanh c ra t nhieu bai toan kho!

2.2.2 Bi tp vn dng

Vn dng 1: at ien ap = 2 cos (2) () ( thay o i) vao hai au oan mach mac no i tiep gomien tr R, tu ien co ien dung C, cuon cam co o t cam L (vi 2 > ). Khi = th = va6 ( + ) ( + ) = 7 ( + ). Khi = + 75 () th = . Tnh .

A. 50 Hz. B. 60 Hz. C. 75 Hz. D. 100 Hz.

Li gii

e giai quye t bai toan at ra e ta phai tm ra x, ma x la he so cong sua t nhe!. + +

= 76.

+ + (1 1

) +

= 76.

(1 1 ) + = 0, 8.

en ay thay x=0,8 vao cong thc khi > : t =(1 1 )

1 = 50()

ap an A.Vn dng 2:Cho oanmach RLC no i tiep, vi tan so f thay o i c. Thay o i = +75Hz th = .Thay o i = (Hz ) th = va

+ +

= 23 . Gia tri = gn gi tr no nht ?A. 55 Hz. B. 60 Hz. C. 75 Hz. D. 100 Hz.

Li gii

Goi x la he so cuong sua t cua mach ien trong hai trng hp + +

= 23 + (1 1 )

+ = 23 = 0, 8 =

(1 1 )1

= 50()



ap an A.Vn dng 3:at ien ap xoay chieu co gia tri hieu dung U khong o i, tan so thay o i c vao hai auoan mach gom ien tr thuan, cuon cam thuan va tu ien mac no i tiep. Khi = th ien ap hieu dunghai au tu ien = . Khi = +75 th ien ap hieu dung hai au cuon cam = va he so congsua t cua toan mach luc nay la 1

3. Hoi f gn vi gi tr no nht sau ay ?

A. 75 Hz. B. 16 Hz. C. 25 Hz. D. 180 Hz.

Li gii

Cac d kien a qua ro rang! Ch viec thay d kien vao la ra ke t qua thoi!

=(1 1 )

1 =

1 1 13

.75

1 13

= 16, 85().

ap an B.Cac v du tren, neu thc s cong thc qua co ng kenh hay kho nh th mot cach lam n gian khac makhong kem phan hieu qua la dung phng phap Chun ha s liu e giai quye t chung, d nhien xet vekha canh thi gian th cong thc se giup chung ta giai ra t nhanh, nhngmot nhc iem cua no la ch apdung cho mot so bai nha t inh. V vay trong khuon kho bai vie t, chung toi ch neu ra nhng cong thc denh va neu cach nh hieu qua cho ban oc!Ta quay lai vi bai tap van dung th nha t.Vn dng 1: at ien ap = 2 cos (2) () ( thay o i) vao hai au oan mach mac no i tiep gomien tr R, tu ien co ien dung C, cuon cam co o t cam L (vi 2 > ). Khi = th = va6 ( + ) ( + ) = 7 ( + ). Khi = + 75 () th = . Tnh .

A. 50 Hz. B. 60 Hz. C. 75 Hz. D. 100 Hz.

Li gii

Ro rang cong thc oc giup chung ta giai bai nay trong vai chuc giay. Nhng dung chuan hoa so lieu chobai toan nay cung khong phai la lo i i to i! Khi = . Ta chon = 1T giai thie t 6 ( + ) ( + ) = 7 ( + ), vi = 1 ta suy ra:

6 (1 + ) ( + ) = 7 (1 + )

6 + 6. + 6 7 = 0 (1)

Mat khac = ta suy ra

= = 1 + ( ) = + 12

(2)



T (1) va (2) ta suy ra c(mot cong cu tnh nghiem manh la may tnh CASIO fx 570 ES PLUS): =0, 5; =

54 Khi = + 75 = ta co = suy ra:

= = 1 + ( )

1 + 2 . = 0

Vi = =

54 va

= Ta suy ra:

1 + 54

2.54.12 = 0

T o ta suy ra = 2, 5 Nen: + 75 = 2, 5 = 50

ap an A.Quay lai vi van dung 3.Vn dng 3:at ien ap xoay chieu co gia tri hieu dung U khong o i, tan so thay o i c vao hai auoan mach gom ien tr thuan, cuon cam thuan va tu ien mac no i tiep. Khi = th ien ap hieu dunghai au tu ien = . Khi = +75 th ien ap hieu dung hai au cuon cam = va he so congsua t cua toan mach luc nay la 1

3. Hoi f gn vi gi tr no nht sau ay ?

A. 75 Hz. B. 16 Hz. C. 25 Hz. D. 180 Hz.

Li gii

Gia s = = + 7 = ( > 1). Khi o ta co to ng tr cam khang va dung khang cua mach lan ltla , , T gia thie t cos =

=

13

ta chon = 1, = 3.Mat khac = = = 3Lai co: = + ( ) = 3 2 = 3 + 2Khi = th to ng tr, cam khang, dung khang cua mach lan lt la: , =

,

= T gia thie t

= 1 + = 2.

+ 1 = 2. .

3 + 1 = 2

Vi 2 gia tri cua ke t hp vi > 1 ta suy ra = 3

5 26Nen ta suy ra:

+ 75 = 3

5 26 16, 86

ap an B.



2.3 k > 1 -Bi ton f thayiUL = UL = kU(URL = URL = kU), k > 1hocUC = UC = kU(URC = URC = kU), k > 12.3.1 Bi ton f thay i m in p hiu dng hai u cun cm thun (hai u t in) bng

nhau v bng ( > 1) ln in p hiu dng hai u mch

Xet bai toan: at ien ap xoay chieu = 2() vao hai au oan mach RLC mac no i tiep, cuon daythuan cam, trong o thay o i c.Thay o i en gia tri hoac th ien ap hieu dung hai au cuon cam bang nhau va bang lan ienap hieu dung hai au oan mach. Khi o ta co ke t qua::Ke t qua 1: = hoac = ma = = ( > 1) th:

1 =

+ 2

2 . =

1

Thay o i en gia tri hoac th ien ap hieu dung hai au tu ien bang nhau va bang lan ien aphieu dung hai au oan mach. Khi o ta co ke t qua::Ke t qua 2: = hoac = ma = = ( > 1) th:

1 =

12.

1

+ 1 3 . =

1 .


= = = + ( )

= + 2 + ( 1) 2 + + = 0

( 1) 2 +

+ = 0

( 1) + 2 +

= 0 (2.1.1)

S dung inh l Vi-et cho phng trnh (2.3.1.1) an ta c:

+ = =

2

.

1 = 2 .

1

1 =

+ 2

. = =

1.

1 . =

1

.

2 la tan so goc khi ien ap hieu dung hai au tu at gia tri cc ai3 la tan so goc khi ien ap hieu dung hai au cuon cam thuan cc ai



:Ke t qua 2: Ta co

= = = + ( )

( 1). 1. 2 +

+ = 0

( 1). 1 + 2

. 1 + = 0(2.1.2)

S dung inh l Vi-et cho phng trnh (2.3.1.2) an 1 ta c:

1+ 1

= = 2

..

1

1 =12.

1

+ 1

1. 1

= =

1 . =

1

2.3.2 Bi ton f thay i m in p hiu dng hai u RL(RC) bng nhau v bng ( > 1) lnin p hiu dng hai u mch

Xet bai toan: at ien ap xoay chieu = 2() vao hai au oan mach L,R,C mac no i tiep theo tht o, cuon day thuan cam, trong o thay o i c.Thay o i en gia tri hoac th ien ap hieu dung hai au RL bang nhau va bang lan ien ap hieudung hai au oan mach. Khi o ta co ke t qua:

:Ke t qua 3: = hoac = ma = = ( > 1) th . =

1

Thay o i en gia tri hoac th ien ap hieu dung hai au RC bang nhau va bang lan ien ap hieudung hai au oan mach. Khi o ta co ke t qua:

:Ke t qua 4: = hoac = ma = = ( > 1) th . = 1


= +

+ ( )=

+ = ( + 2. + ) ( 1) + ( 1) 2. + = 0

+ ( 1) 2 + (

1) = 0

( 1) + ( 1) 2 +

= 0 (2.2.1)



S dung inh l Vi-et cho phng trnh (2.3.2.1) an ta c: . =

1

:Ke t qua 4: Bien o i tng t ta cung co:

= +

+ ( )=

1 +

( 1) 2 +

= 0(2.2.2)

S dung inh l Vi-et cho phng trnh (2.3.2.2) an 1 ta c: . = 1

T cc kt qu trn, d nh v vn dng gii nhanh bi tp trc nghim nn nh:

: = hoac = ma = = hoac = = ( > 1) th

. =

1

: = hoac = ma = = hoac = = ( > 1) th

. = 1

2.3.3 Bi tp vn dng

Vn dng 1: Cho mach RLC no i tiep, hieu ien the hieu dung hai au oan mach la U, tan so goc thay o ic =

1, 5

va = 2th hieu ien the hai au cuon cam co cung gia tri va bang kU. Gia tri cua k

gn gi tr no nht trong cach gia tri sau ay:A. 1,2. B. 2. C. 1,75. D. 2,42.

Li gii

A p dung cong thc oc ao sau =

1

1 =

=

263

= 64 = 1, 6

ap an A.Bi ton tng qut: Cho mach RLC no i tiep, hieu ien the hieu dung hai au oan mach la U, tan so gocthay o i c = hoac = vi

1 +

1 < 2 th hieu ien the hai au cuon cam co cung gia

tri va bang kU. Tm gia tri cua ien tr R?

ap so : = 2

Vn dng 2: at ien ap = 2. (2) () vao hai au oan mach RLC no i tiep. Lan lt thay



o i tan so = ; = + 30() th hieu ien the hai au cuon cam co gia tri bang hieu ien the ccai hai au oan mach. Khi = 20() th hieu ien the hieu dung hai au ien tr at cc ai. Giatri cua f gn gi tr no nht trong cac gia tri sau ay ?

A. 200 Hz. B. 100 Hz. C. 150 Hz. D. 250 Hz.

Li gii

A p dung cong thc hay : ( + 30) = 2( 20)

(2) 1 ( + 30) = 2( 20)

2 1 (402 + 30) + 202 = 0 = 202, 2 () = 6, 75 ()De dang thay c e to n tai th f phai co gia tri = 202, 2 ()Chon ap an A.Vn dng 3: at ien ap xoay chieu = 2 cos(2) vao hai au oan mach RLC mac no i tiep cocuon day thuan cam, trong o thay o i c. Thay o i en gia tri hoac th he so cong sua t machtrong hai trng hp bang nhau, + 4 = 200. Thay o i en gia tri hoac = + th ienap hieu dung hai au cuon cam thuan co gia tri bang nhau va bang 5 (), la tan so khi mach xay racong hng. Bie t rang > > 30. co the nhan gia tri nao trong cac gia tri sau:

A. 39 Hz. B. 49 Hz. C. 43 Hz. D. 30 Hz.

Li gii

Ta co + 4 4 = 4 + 4

4 = 50

Mat khac lai co = = 5 . =52

( + ) =

52

Ma > 30 52

> 30 + 30 44, 8

Vay 44, 8 50ap an B.Vn dng 4: Cho oan mach AB nh hnh ve.

Trong hop X va hop Y cha khong qua 2 trong 3 phan t la ien tr thuan R, cuon cam thuan L va tu ienC. Bie t rang hop X va hop Y khong cha o ng thi L va C. at ien ap = 2 cos(2) () vao hai auoan mach AB, thay o i c. Khi = = 50 th dong ien hieu dung chay trong mach at gia tricc ai. Thay o i en gia tri = 25 hoac > 2 th ien ap hieu dung hai au oan AM co gia tribang nhau va bang ( > 1) . Thay o i en gia tri = 255 hoac = 40 th ien ap hieudung hai au oan MB co gia ri bang nhau va bang ( > 1). Gia tri cua la:

A. 305 Hz. B. 405 Hz. C. 505 Hz. D. 605 Hz.


CHUYN KU 3 BI TP LUYN TP

Li gii

Mnh xin trnh bay cach giai nhanh bai toan!

Nhan thay rang . < . Nen ta suy ra . = 1

= 5

Mat khac . > . Nen ta cung suy ra c . =

1 = 505

V sao lai co inh hng giai nhanh nh vay, mnh xin trnh bay cach t duy nh sau:Ta a bie t c cac ke t qua quan trong a neu tren. Khi o ta xac inh cac phan t trong hop knthong qua cac trng hp:

Vi > 1 th X va Y khong the cha ien tr thuan R

Xet thay . > . Ta cha c chan mot ieu rang hop X co the ch cha cuon cam thuan L hoac chahai phan t RL. Khi o mi to n tai hai gia tri tan so e . = ( > 1);

Xet thay . < . Ta cung cha c chan mot ieu rang hop Y co the ch cha tu ien co ien dung Choac cha ca hai phan t RC. Khi o mi to n tai hai gia tri tan so e . =

1

( > 1);

Lu y = 1

.

ap an C.

3 Bi tp luyn tp3.1 bi

Bi tp luyn tp s 1: at mot ien ap xoay chieu o n inh = 2 cos(2) vao hai au oanhmach RLC khong phan nhanh, trong o f thay o i c. Thay o i f en gia tri hoac th ien aphieu dung hai au cuon cam thuan co gia tri bang nhau va bang ()( > 1), + = 22500 ().Thay o i f en gia tri = 97 th ien ap hai hieu dung hai au tu ien at gia tri cc ai. Gia tri cua kgn nht vi:

A. 2,47. B. 3,47. C. 4,47. D. 5,47.Bi tp luyn tp s 2:Cho oan mach xoay chieu AB gom cac oan mach AM cha cuon day khongthuan cam co o t cam L, oan MN cha ien tr thuan R, oan NB cha tu ien co ien dung C. atien ap = cos(2) trong o () thay o i c vao hai au oanmach AB. Thay o i en giatri hoac = 3 th ien ap hieu dung hai au oan AN ln gap k lan ien ap hieu dung hai au oanmach AB ( > 1). Thay o i en gia tri =

12 hoac = 4 th ien ap hieu dung hai au oan MB

ln gap 2k lan ien ap hieu dung hai au oan mach AB ( > 1). Gia tri k gn gi tr no nht trong cacgia tri sau:

A. 2. B. 3. C. 10. D. 5.Bi tp luyn tp s 3: Cho oan mach gom cuon day khong thuan cam no i tiep vi tu ien. at vaohai au mach ien ap xoay chieu = 2 cos (2) , tan so thay o i c. Khi tan so co gia tri



th cong sua t tieu thu cua mach ln nha t. Khi tan so co gia tri = 0, 4 th he so cong sua t cua cuonday la 0, 84. Khi tan so co gia tri hoac ( + ) th ien ap hieu dung hai au tu nh nhau eu la = (). Gia tri cua la:

A. 1,23. B. 1,31. C. 1,46. D. 1,57.Bi tp luyn tp s 4: at ien ap xoay chieu = cos ( + ) () vao hai au oan machRLC mac no i tiep (2 > ), cuon day thuan cam va thay o i c. Thay o i en gia tri hoacgia tri ( < ) th cng o dong ien hieu dung chay trong mach eu nho hn cng o dongien hieu dung cc ai k lan ( > 1), khi o dung khang cua tu ien trong hai trng hp thoa man1

1= 1100 . Thay o i en gia tri hoac gia tri th ien ap hieu dung hai au tu ien eu co

gia tri bang 2

(), dung khang tu ien trong hai trng hp nay thoa man + = 43750 ().Thay o i en gia tri th ien ap hieu dung hai au tu ien at gia tri cc ai, dung khang tu ien luco la =

40014

(). Gia tri k gn gi tr no nht trong cac gia tri sau:A. 3,16. B. 2,27. C. 2,83. D. 4,12.

3.2 Li gii chi tit

Bi tp luyn tp s 1: at mot ien ap xoay chieu o n inh = 2 cos(2) vao hai au oanhmach RLC khong phan nhanh, trong o f thay o i c. Thay o i f en gia tri hoac th ien aphieu dung hai au cuon cam thuan co gia tri bang nhau va bang ()( > 1), + = 22500 ().Thay o i f en gia tri = 97 th ien ap hai hieu dung hai au tu ien at gia tri cc ai. Gia tri cua kgn nht vi:

A. 2,47. B. 3,47. C. 4,47. D. 5,47.

Li gii

Ta ap dung cong thc

1 = + 2

= + 2

2, 47ap an A.Bi tp luyn tp s 2:Cho oan mach xoay chieu AB gom cac oan mach AM cha cuon day khongthuan cam co o t cam L, oan MN cha ien tr thuan R, oan NB cha tu ien co ien dung C. atien ap = cos(2) trong o () thay o i c vao hai au oanmach AB. Thay o i en giatri hoac = 3 th ien ap hieu dung hai au oan AN ln gap k lan ien ap hieu dung hai au oanmach AB ( > 1). Thay o i en gia tri =

12 hoac = 4 th ien ap hieu dung hai au oan MB

ln gap 2k lan ien ap hieu dung hai au oan mach AB ( > 1). Gia tri k gn gi tr no nht trong cacgia tri sau:

A. 2. B. 3. C. 10. D. 5.

Li gii



T cac cong thc tren ta co ngay:

. =

1 3 =

1

. =4 1

2 2 =

4 12

Chia ve theo ve hai ang thc tren ta c 32 =2

1.4 1 2.

ap an A.Bi tp luyn tp s 3: Trch e thi th so 1 - Bui nh Hieu - nam 2015Cho oan mach gom cuon day khong thuan cam no i tiep vi tu ien. at vao hai au mach ien ap xoaychieu = 2 cos (2) , tan so thay o i c. Khi tan so co gia tri th cong sua t tieu thu cuamach ln nha t. Khi tan so co gia tri = 0, 4 th he so cong sua t cua cuon day la 0, 84. Khi tan so cogia tri hoac ( + ) th ien ap hieu dung hai au tu nh nhau eu la = (). Gia tri cua la:

A. 1,23. B. 1,31. C. 1,46. D. 1,57.

Li gii

Ta co ke t qua quen thuoc: + ( + ) =

2

( + ) = 1

=

1 .

1

( ) = =2 1

1

= 2 1 1

+ = 12, 5 1

1

1 = 12, 5 sin 1 1

= 12, 5 (1 0, 84) 1

1

= 1, 46ap an C.Bi tp luyn tp s 4: at ien ap xoay chieu = cos ( + ) () vao hai au oan machRLC mac no i tiep (2 > ), cuon day thuan cam va thay o i c. Thay o i en gia tri hoacgia tri ( < ) th cng o dong ien hieu dung chay trong mach eu nho hn cng o dongien hieu dung cc ai k lan ( > 1), khi o dung khang cua tu ien trong hai trng hp thoa man1

1= 1100 . Thay o i en gia tri hoac gia tri th ien ap hieu dung hai au tu ien eu co

gia tri bang 2

(), dung khang tu ien trong hai trng hp nay thoa man + = 43750 ().Thay o i en gia tri th ien ap hieu dung hai au tu ien at gia tri cc ai, dung khang tu ien luco la =

40014

(). Gia tri k gn gi tr no nht trong cac gia tri sau:A. 3,16. B. 2,27. C. 2,83. D. 4,12.


CHUYN KU 4 TN MN THM V MT VN KU

Li gii

Thay o i en cac gia tri va ma = = nen ta co:

= ( ) 1

(1)

Mat khac t cong thc ``oc'' ta lai co:

. = 1

=

1 .

1 (2)

T (1) va (2) ta suy ra: =

.

T o suy ra: = 1

1

1 . .

Lai co:1

+ 1= 2

. = 500010

Vay ta tnh c = 10 3, 16Bai toan la s "giao thoa" gia nhieu cong thc vi nhau, o la s ke t hp tao nen cai hay cho bai toan.Khi i thi viec oc k gia thie t e inh hng dang bai la mot viec lam ra t quan trong cho chung ta, vieco se giup cho ta tie t kiem thi gian ra t nhieu!

4 Tnmn thm vmt vn KUNh chung ta a bie t noi dung chnh cua chuyen e nay la KU- bai toan f bien thien, nhng van e KU vancon xua t hien trong ca bai toan L, C bien thien. Viec xay dng cong thc hoan toan da tren nghiem tamthc bac hai, o la ieu tu vi ma chung to i muon em lai cho cac ban.

4.1 Mt vn mi trong nhng ci c...

Ta i xet bai toan: at ien ap xoay chieu = 2 cos() vao mach RLC khong phan nhanh, trongo L thay o i c. Ban au = th mach xay ra cong hng. ieu chnh L en cac gia tri hoac th ien ap hieu dung hai au cuon cam thuan bang ( > 1) ien ap hieu dung hai au oan mach.ieu chnh en gia tri th ien ap hieu dung hai au cuon cam at cc ai, khi o ta co cac ke t qua::Ke t qua 1: Ke t qua quen thuoc

1

+ 1= 2:Ke t qua 2: Ke t qua mi

+ =2

1



Chng minh. Cong thc tren chng minh mot cac de dan bang nghiem tam thc bac hai, ta co:

= = + ( )

( 1) 2. + ( + ) = 0 ()

Coi phng trnh tren la phng trnh bac 2 o i vi , theo inh l Vi-et ta co:

+ = =

2 1 (1)

. = =

1(

+ ) (2)

Neu ta chia ve theo ve (1) cho (2) ta c: 1+ 1

= 2 + Lu y rang: =

+

1+ 1

= 2Vay suy ra 1

+ 1= 1

. Ke t qua 1 c chng minh xong.

Lu y them (1): Khimach xay ra cong hng th = + =2

1 + =2

1Ke t qua 2 c chng minh xong.V va co vai tro nh nhau nen trong bai toan C bien thien, cac ke t qua thu c cua hoan toantng t:

+ =2

1

. =

1( + )

Vay ta cung thu c them hai ke t qua tng t::Ke t qua 3:

+ = 2

:Ke t qua 4:1

+ 1= 2

1.1e cho de nh cac cong thc, ta ch can nh cac ke t qua ve cam khang va sung khang v chuungs co vaitro tng t nhau, sau o suy ra cac ke t qua L va C.

4.2 Bi tp vn dng

Vn dng 1: Cho mach ien xoay chieu AB nh hnh ve, cuon cam thuan co o t cam thay o i c.atien ap xoay chieu o n inh = 2 cos() vao hai au oan mach. Ban au = th mach xay racong hng. Thay o i L en hai gia tri = =

2 hoac = 3 th = = . Gia tri cua k la:



A. 2. B. 3. C. 4. D. 5.

Li gii

Ta s dung ngay cong thc: + =2

1 vi =

2 = 2

Ta de suy ra 2

1 =52 = 5

ap an D.Vn dng 2: at ien ap ien ap xoay chieu = 2 cos() () vao oan mach RLC khong phannhanh, trong o tu ien co ien dung thay o i c. Ban au = th mach ien xay ra cong hngien. Thay o i ien dung tu en gia tri hoac th = = ( > 1). Thay o i ien dungcua tu en gia tri hoac th dong ien chay trong mach co gia tri hieu dung bang nhau. Bie t rang1

+ 1= 3 1

+ 1. Gia tri cua k la:

A.1, 5. B.2, 5. C.3, 5. D.4, 5.

Li gii

Vi cong thc a chng minh tren, co ngay: 1+ 1

= 2

1.1

Van dung mot ke t qua quen thuoc ve bai toan L(C) bien thien ma hai gia tri L(C) cho cung mot gia tri hieudung dong ien: 1

+ 1= 2

Ke t hp vi d kien bai toan : 1+ 1

= 3 1+ 1

1 = 3 = 1, 5.ap an A.Vn dng 3:Trch e thi th THPT Quo c gia ngay 30/4/2015 Cau Lac Bo Yeu Vat Lat ien ap = 1202 cos (100) () vao oan mach RLC no i tiep. ien tr thuan R, tu ien iendung C, cuon day thuan cam, co the thay o i c o t cam. Thay o i = hoac = th eucho ien ap hieu dung hai au cuon cam ln hn gap k (k>1) lan ien ap hieu dung . Bie t rang8 = . Tm ien ap hieu dung nho nha t cua cuon cam khi = .

A. 606 . B. 802 . C. 603 . D. 803 .

Phn tch

Mot ieu hien nhien = , vi U khong o i th nho nha t khi k nho nha t. Vay ta can tm gia tri nhonha t cua k o. T o ta co inh hng giai!

Li gii



Ta co 8 = ..

= 18

Mat khac s dung ke t qua a chng minh tren: . =

1( + )

1. 1

=1 1 +

1 1 = + .

2.. 1 1 2.

18

34

1

23

Vay =23

= 803()

ap an D.Vn dng 4: Trch e thi th ai hoc lan 2 nam 2014 Dien an Vat l pho thongat ien ap xoay chieu co ga tri hieu dung = 905 () vao hai au oan mach gom ien tr ,cuon cam thuan ( thay o i c) va tu ien mac no i tiep. Khi = hoac = th ien ap haiau cuon cam co cung gia tri va bang 270 (). Bie t rang 3 = 150 () va to ng tr cua oan mach trong hai trng hp la 1002 () . e ien ap hai au cuon cam cc ai th cam khang cua mach khi o gan gia tri nao nha t?

A. 250 . B. 100 . C. 180. D. 300.

Phn tch

e bai co nhng d kien = 270, = 905 . Vay ta lien tng ngay en tham so k, = =

35

Th 2, vi lp d kien ve ien tr, cam khang va dung khang an trong hai bieu thc 3 = 150 va

+ = 1002, ta nh ngay nhng cong thc a chng minh tren: + =

2 1

. =

1.( + )

T o ta co li giai bai toan nh sau:

Li gii

T cong thc . =

1( + ). Vi =

35

va + = (1002) = 20000Ta suy ra: . = 45000 ().Ke t hp vi 3 = 150() c he:

. = 450003 = 150 .Giai he tren c = 150, = 300

Mat khac + =2

1 = 100 = 100. Vay = +

= 200 ap an C.Bai toan c inh hng lo i i nhanh chong neu ta bie t c nhng cong thc giai nhanh. ieu ora t co ch trong viec thi tra c nghiem.Bi tp tng t: at ien ap xoay chieu = 2 cos () vao oanmach gom cuon day khong thuancam mac no i tiep vi tu ien, trong o tu ien co ien dung thay o i c. Khi = hoac = th

ien ap hieu dung hai au tu ien co gia tri bang nhau va bang 2. Bie t rang +

.= 647 va to ng



tr cua cuon day bang 507 . Khi thay o i ien dung cua tu e ien ap hai au tu at cc ai th dungkhang cua tu co gia tri la:

A. 100 . B. 200 . C. 175 . D. 125 .ap an A.


CHUYN KU REFERENCES

References[1] Dien an Vat l pho ng thong http://vatliphothong.vn

[2] Cau lac bo Yeu Vat L https://www.facebook.com/club.yeu.vl

[3] Dien an Vat l pho thong, Tuyn tp in xoay chiu Din n vt l ph thng, 2015.

[4] Nguyen nh Yen, Phng php Chun Ha S liu .

[5] Bui nh Hieu va Nguyen nh Yen, CHINH PHC BI TP VT L IN XOAY CHIU, Lovebook.vn,8/3/2015.


Li m uNi dung chuyn KUk1 hoc UC1=UC2=kU(URC1=URC2=kU),k>1 Bi ton f thay i m in p hiu dng hai u cun cm thun (hai u t in) bng nhau v bng k(k>1) ln in p hiu dng hai u mch Bi ton f thay i m in p hiu dng hai u RL(RC) bng nhau v bng k(k>1) ln in p hiu dng hai u mchBi tp vn dng

Bi tp luyn tp biLi gii chi tit

Tn mn thm v mt vn KUMt vn mi trong nhng ci c...Bi tp vn dng

[Phan Nhật Hoàng_ Trần Văn Quân]Chuyên Đề Ku_ Bản Chính Thức

Documents

Transcript of [Phan Nhật Hoàng_ Trần Văn Quân]Chuyên Đề Ku_ Bản Chính Thức