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8/4/2019 Cc tr trong mch in xoay chiu

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CC TR TRONG MCH IN XOAY CHIU

1. Mchin xoay chiu RLCc R thay i

Bi ton tngqut 1:

Cho mchin xoay chiu RLC trong R c th thay ic (R cn c gi l bin tr). Tm gi trca R :a. Cng hiu dng I ca mcht gi tr cci, (nu c)b. Cng hiu dng I ca mcht gi tr cc tiu, (nu c)c. in p hiu dng hai u R t cci, (nu c)d. in p hiu dng hai u R t cc tiu, (nu c)e. Cng sut ta nhit trn in trR t cci*Hngdn gii:Nguyn tc chung: tm cc tr ca mt biu thc no th chng ta xut pht t cng thc tngqut ca chng, thc hin cc php bini theo quy tc nu t s v mu su l ilng bin thinth ch mt biu thc thay i (chia c t v mu cho t s chng hn..)

B :

Btng thc Cauchy : Cho hai s khng m a, b khi Du bng xy ra khi a = b

Hm s bc hai , vi a > 0 t gi tr nh nht tiim

a. Cng hiu dng

vy R = 0 th Imax v gi tr

b.Vy khi R rt ln th cng dng in rt nh v gim dn v 0, (ng vi khi nimin tr: chobit khnng cn trs di chuyn ca cc in tch, tc l cn trdng in)c. in p hiu dng hai uin trl:

d. Ta c:


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e. Cng sut ta nhit trn R (cng l trn ton mch):

vip dng btng thc Cauchy ta c:

Du bng xy ra khi

Khi cng sut cci ca mch

Vy mch in xoay chiu RLC c R thay i t cng sut ta nhit trn R cc i:

KhiCh : Trong trng hp Pmax th h s cng sut ca mch khi l

Thng thng khi mchin c R thay i th bi thng yu cu tm R Pmax nn cc emch trng hp ny hn.

V d 1: Cho mchin RLC, R c th thay ic,in p hai u mch l:

. Tm R :a. Mch tiu th cng sut P = 90W v vit biu thc cacng hiu dng trong mch khi .b. Cng sut ta nhit trn mch cci Pmax v tnh gi tr Pmax*Hngdn gii:

Ta c:

a. Cng sut ca mch tiu th chnh l cng sut ta nhit trn in trR:

Vi


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lch pha ca u va i tha mn

Biu thccng dng in l

Vi

lch pha ca u va i tha mn

Biu thccng dng in l

b. vip dng btng thc Cauchy ta c:

Du bng xy ra khi


Vy khi th*Nhn xt : Trong mchin RLC m cun dy c thm in trhotng r th ta c th tm cng sutmch cci v cng sut ta nhit trn R cci Cng sut ta nhit P trn ton mch cci:


Du bng xy ra khi


Vy mch in xoay chiu RLC c R thay i v cun dy khng thun cm t cng sut ta

nhit trn ton mch t gi tr cc i khi


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Cng sut ta nhit trn in trR, (PR) cci:


Du bng xy ra khi


Vy mchin xoay chiu RLC c R thay i v cun dy khng thun cmt cng sut ta

nhit trn R cci khi:

V d 2: Cho mchin xoay chiu gm cun dy c r = 50, v tin c in

dung v in trthun R thay ic. Tt cc mc ni tip vi nhau, rit vo haiuon mch c hiuin th xoay chiu . Tm R :

a. H s cng sut ca mch lb. Cng sut ta nhit trn ton mcht cci. Tnh gi tr cci.c. Cng sut ta nhit trn in trR cci. Tnh gi tr cci ca cng sut.*Hngdn gii:

Ta c

a. H s cng sut ca mch l

Thay s ta cGiiphng trnh trn ta c cc nghim R cn tm

b. Cng sut tiu th trn on mcht gi tr cci khi


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Khi cng sut cci ca mchc. Ta c cng sut ta nhit trn R l:


Du bng xy ra khi

Khi cng sut cci ca mch:

Bi ton tngqut 2:Cho mchin RLC c R thay i.in p hiu dng hai u mchin l U. Khi R = R1 v R = R2 thmch tiu th cng mt cng sut (hay P1 = P2 ) Chng minh rng:

a.

b. Cng sut tiu th*Hngdn gii:a. Theo gi thit ta c P1 = P2

b. Ta c

Vy mch RLC c R thay i m R = R1 v R = R2 th P1 = P2 s tha mn

V d: (ihc 2009)


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tin p xoay chiu c gi tr hiu dng khng i vo hai uon mch gm bin trR mc nitip vi tin. Dung khng ca tin l 100. Khi iu chnh R th ti hai gi tr R1 v R2 cng suttiu th caon mchnh nhau. Bitin p hiu dng gia hai u tin khi R = R1 bng hai lnin p hiu dng gia hai u tin khi R = R2. Cc gi tr R1 v R2 l:A. R1 = 50, R2 = 100.B. R1 = 40, R2 = 250.C. R1 = 50, R2 = 200.

D. R1 = 25, R2 = 100.*Hngdn gii:Theo gi thit ta c P1 = P2

, (1)Mt khc, gi U1C l in p tin khi R = R1 v U2C l in p tin khi R = R2

Khi theo bi ta c

Li c , (2)Gii(1) v (2) ta c R1 = 50, R2 = 200.V d 2: Mt mchin gm mt tin C, mt cun cm L thun cm khng v mt bin trR c

mc ni tip.t vo hai u mchin mt hiuin th xoay chiu . Bit rngng vi hai gi tr ca bin tr: R1 = 18 v R2 = 32 th cng sut tiu th P trn on mch l nhnhau. Cng sut P caon mch c th nhn gi tr no trong cc gi tr sau?*Hngdn gii:

Theo chng minh cng thctrn ta c

2. Mchin xoay chiu RLC c L thay iBi ton tng qut:Cho mchin xoay chiu RLC trong L c th thay ic. Tm gi tr ca L :a. Cng hiu dng I ca mcht gi tr ccib. Cng sut ta nhit ca mcht cci. Tnh gi tr Pmaxc. in p hiu dng hai u L t cci*Hngdn gii:

a. Cng hiu dng

vy th Imax v gi tr

b. Cng sut ta nhit trn mch . Do R khng i nn

Gi tr


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c. in p hiu dng hai u cun cm l:

Vi , tDo h s hm s y t gi tr nh nht khi:

Khi gi tr nh nht ca hm s y l:

Vy

V din hnh:

V d 1: Cho mchinnh hnh v. Trong . Cun dy thun cm c tcm L thay ic.in p gia hai uon mch l u = 200cos(100t) (V). Xc nh t cm cacun dy trong cc trng hp sau:a. H s cng sut ca mchcos = 1.

b. H s cng sut ca mchcos = .c. in p hiu dng trn cun cm L l cci.*Hngdn gii:

Ta c

a. H s cng sut

b. Khi


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c. Theo chng minh trn ta c khi th in p hiudng hai u L t cci. Gi tr cci:

V d 2: Cho mchin RLC, L c th thay ic,in p hai u mch l .

Cc gi tr . Tm L :a. Mch c cng sut cci. Tnh Pmaxb. Mch c cng sut P = 80Wc. in p hiu dng gia hai u L t cci. Tnh gi tr cci.*Hngdn gii:

Ta ca. Cng sut ca mch P = I2.R. Do R khng i nn:

Khi

b.

T ta tm c hai gi tr ca L tha mn bi l

c. in p hiu dng hai u L t cci khi .

Gi tr cci

V d 3: Cho mchinRLC,in p hai u mchin l u = 200 cos(100t) (V). L thay ic.

Khi mch c L = L1 = (H) v L = L2 = (H). Th mch c cng cng dng in hiu dng

nhng gi tr tc thi lch pha nhau gc .a. Tnh R v Cb. Vit biu thc ca i*Hngdn gii:

Ta c

a. Do


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Theo bi th u1 v u2 lch pha nhau gc nn c mt biu thc l nhanh pha hn i v mt biu thcchm pha hn i.

Do nn u1 nhanh pha hn i cn u2 chm pha hn i.

Khi

Trong

Vy cc gi tr cn tm l

b. Vit biu thc ca i Vi

Tng trca mch

lch pha ca u v i:

Biu thc cacng dng in i l:

Vi

Tng trca mch:

lch pha ca u v i:

Biu thc cacng dng in i l:*Nhn xt: Cch gii trn l tng qut cho trng hp lch pha bt k. Tuy nhin trong bi ton trnchng ta c th nhn xt c rng do cng dng in trong hai trng hp bng nhau nn trong hai

trng hp lch pha ca u v i c cng ln. Khi u1 s nhanh pha hn i gc l gii ra Rlun ch khng cn phi khai trin cng thclng gic.

3. Mchin xoay chiu RLC c C thay iBi ton tng qut:Cho mchin xoay chiu RLC trong C c th thay ic. Tm gi tr ca C :a. Cng hiu dng I ca mcht gi tr cci


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b. Cng sut ta nhit ca mcht cci. Tnh gi tr Pmax.c. in p hiu dng hai u C t cci*Hngdn gii:

a. Cng hiu dng

vy th Imax v gi tr

b. Cng sut ta nhit trn mch P = I2.R. Do R khng i nn

Gi tr :

c. in p hiu dng hai u tin l:

Vi , t

Do h s hm s y t gi tr nh nht khi

Khi gi tr nh nht ca hm s y l

Vy:

V din hnh:

V d 1: Cho mchin RLC c , C thay i.in p hai uon

mch . Tm C :a. Mch tiu th cng sut P = 50Wb. Mch tiu th cng sut cci. Tnh Pmaxc. UC max*Hngdn gii:


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Ta c

a.

Nhn nghim ZC = 200 ta cb. Cng sut ca mch P = I2.R. Do R khng i nn:

Khi c. Theo cng thc chng minh cin p hiu dng gia hai bn t cci khi:

Khi

V d 2: Cho mchin RLC c C thay i, hiuin th hai uon mch:

Khi C = C1= F v C = C2 = F th mch c cng cng sut P = 200W.a. Tnh R v Lb. Tnh h s cng sut ca mchng vi C1, C2.*Hngdn gii:

a.Theo gii thit ta c:

Vi ZL = 300 ta cGiiphng trnh ta c nghim duy nht R = 100.

Vyb. Tnh h s cng sutng vi cc trng hp

Khi

Khi

4. Mchin xoay chiu RLC c tn s f hay thay iBi ton tng qut:Cho mchin xoay chiu RLC trong tn s gc thay ic. Tm :a. Cng hiu dng ca dng int cci. Tnh gi tr cci.


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b. Cng sut ta nhit trn mcht cci. Tnh gi tr cci.c. in p hiu dng hai u R, hai u L, hai u C t cci*Hngdn gii:a. Cng hiu dng:

Vy khi th cng hiu dng trong mcht gi tr cci v gi tr .b. Cng sut ta nhit trn mch P = I2.R.

Do R khng i nn

Gi trc. in p hiu dngt cci

URt cci

Khi

ULt cci

Vi , t

Do h s

Vy ULt cci khi

UCt cci


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Vi , t

Do h s

Vy UCt cci khi tn s gc

Nhn xt:- Do vai tr ca f v l nh nhau nn nu f thay i th bng php thay ta s gii quytc

lp bi ton m c f thay i.- Do vic tnh ton tm cc gi tr UL max hay UC max l tngi phc tp nn nhng bi ton dng

ny ch dng livic tm gi tr ( hay f ) cho in p hiu dngt cci.V din hnh:V d 1: Cho on mchin MN gm mtin trthun R = 100, cun dy thun cm c t

cm , tin c in dung , mc ni tip. Mc hai u M, N vo ngunin xoay

chiu c in p tc thi , tn s f ca ngunin c thiu chnh thay ic.a. Khi f = f1 = 50 Hz, tnh cng hiu dng ca dng in v tnh cng sut tiu th P1 trn onmchin MN. Vit biu thccng dng in tc thi chy trong on mch.b. iu chnh tn s ca nguninn gi tr f2 sao cho cng sut tiu th trn on mchin MN lc l P2 = 2P1. Hy xc nh tn s f2 ca ngunin khi . Tnh h s cng sut.*Hng dn gii:

a. Khi f = f1 = 50 Hz

Cng hiu dng ca dng in trong mch l:

Cng sut tiu thu trn on mchin l:

lch pha ca u v i trong mch:

Biu thc cacng dng in trong mch l:b. Khi thay i f P2 = 2P1 tc P2 = 144W

Ta cy l trng hp xy ra cnghngin, thay s ta tm c:


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H s cng sut khi V d 2: Mt mchin xoay chiu RLC c R = 100, L = 1/(H) v C = 10-4/2 (F) mc ni tip.

on mchc mc vo mt hiuin th xoay chiu c tn s f c th thay i. Khi hiuin thgia hai u tint gi tr cci th tn s f c gi tr l bao nhiu?*Hngdn gii:

Ta c:

Vi , t

Do h s

Vy UCt cci khi tn s dao ng

+ Cho C1, C2 m I1 = I2 (P1 = P2)

Hi C PMax ( CH) p1 2

2

C C

c L

Z ZZ Z

+ Cho L1, L2 m I1 = I2 (P1 = P2)

Hi L PMax ( CH) p 1 22

L L

L C

Z ZZ Z

BI TP LUYN TPDng 1: Mch c R thay i

Bi 1: Cho mch RLC c C thay i,

Khi C = C1 = F th dng in tr pha so viin p u

Khi C = C2 = th in p hiu dng 2 u tin cci

a. Tnh R v tn s gc , bitb. Bit UC max = 250V. Vit biu thcin p u hai u mchin


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Bi 2: Cho mchin RLC; u = 30 cos(100t) (V).R thay ic. Khi mch c R = R1 = 9 th

lch pha gia u v i l 1 . Khi mch c R = R2 = 16 th lch pha gia u v i l 2. bita. Tnh cng sutng vi R1 v R2b. Vit biu thc cacng dng inng vi R1, R2

c. Tnh L bit C = . .d. Tnh cng sut cci ca mch

Bi 3: Cho mchin RLC; u = U cost (V). R thay ic. Khi mch c R = R1 = 90 th lch

pha gia u v i l 1 . Khi mch c R = R2 = 160 th lch pha gia u v i l 2. bit

a. Tm L bit C = . ; = 100rad/s

b. Tm C bit L = (H); = 100rad/s

c. Tm . Bit L = (H); C = .

Bi 4: Cho mchin RLC; u = U cos100t (V).R thay ic ; Khi mch c R = R1 = 90 u v R= R2 = 160 th mch c cng cng sut P.

a. Tnh C bit L = (H)b. Tnh U khi P = 40W

Bi 5: Cho mchin RLC, R c th thay ic, Hiuin th hai u mch l u = 200

cos(100t) V; L = (H), C = . . Tm R :

a. H s cng sut ca mch l

b. Hiuin th hiu dng gia hai uin trl UR = 50 Vc. Mch tiu th cng sut P = 80W

Bi 6: Cho mchin RLC, R c th thay ic, Hiuin th hai u mch l u = 240

cos(100t) V; C = . .Khi mch c R = R1 = 90 u v R = R2 = 160 th mch c cng cng sut P.a. Tnh L, Pb. Gi scha bit L ch bit Pmax = 240W v vi 2 gi tr R3 v R4 th mch c cng cng sut l P =

230,4W Tnh gi tr R3 v R4Bi 7: Cho mchinnh hnh v : UAB = 100 V; UAN = 100 V; UNB = 200V

Cng sut ca mch l P = 100 W.

a. Chng minh rng P = 100 W chnh l gi tr cng sut cci ca mchb. Vi hai gi tr R1 v R2 th mch c cng cng sut P. Tnh P v R2 bit R1 = 200Dng2: Mch c L thay i


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Bi 1: Cho mchin RLC, L c th thay ic, hiuin th hai u mch l u = 200 cos(100t)

V; C = . . R = 120a. Tnh L ULmax. Tnh UL max

b. Tnh L UL bng 175 V

Bi 2: Cho mchinnh hnh v, u = U cos100t (V), C = , R = 120

a. Tnh L vung gc vib. Tnh L UANt gi tr ccic. Tnh L cos = 0,6

Bi 3: Cho mchin RLC, L c th thay ic, Hiuin th hai u mch l u = 100

cos(100t) V; Khi mch c L = L1 = (H) v L = L2 = (H) th mch c cng cng sut P = 40Wa. Tnh R v Cb. Vit biu thc ca i ng vi L1 v L2

Bi 4: Cho mchin RLC, L c th thay ic, Hiuin th hai u mch l u = 170

cos(100t) V; R = 80, C = . , Tm L :a. Mch c cng sut cci. Tnh Pmaxb. Mch c cng sut P = 80W

Bi 5: Cho mchin RLC; u = 200 cos100t (V) R = 200 ; C = . . L c th thay ic

a. Khi L = H vit biu thc ca i tnh P

b. Tm L ULmax. Tnh ULmaxc. Tnh L Pmax , Tm Pmax

Bi 6: Cho mchin RLC, L thay ic, Hiuin th hai u mch l u = U cos(t) V; Khi

mch c v th gi tr tc thi ca cc dng inu lch pha mt gc sovi u

a. Tnh R v bit .b. Tnh v C bit R = 100c. Tnh C v R bit = 100rad/s

Bi 7: Cho mchin RLC mc ni tipnh hnh v , L c th thay ic u = 200 cos(100t)

V, , , R = 200 a. Vit biu thc ca i, tnh Pb. Vit biu thc ca UANc. Vit biu thc ca UMBd. Tnh gc hp bi UAM v UMBe. Tnh gc lch gia UAM v UMBDng 3: Mch c C thay i


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Bi 1: Cho mchin RLC, C thay i, hiuin th hai uon mch: u = 120 cos(100t) (V), R

= 240, . Tm C :a. I = Imax, P = Pmax. Tnh Imax, Pmax. Tnh UL khi .b. UC = UC max. Tnh UC max

Bi 2: Cho mchin RLC, u = U cost(V), C thay i, R = 120, U = 150V

a. Uc = UL = nU th phi chn L v C bng bao nhiu? p dng n = 4/3b. Uc tr pha hn u gc c tan = 4/3. Tnh Uc khi Bi 3: Cho mchin RLC, C thay i , hiuin th hai uon mch: u = 200cos(100t)V. Khi C =

C1 = v C = C2 = th i1 v i2u lch pha vi u mt gc rad.a. Tnh R, Lb. Vit biu thc i1 v i2Bi 4: Cho mchin RLC, C thay i , hiuin th hai uon mch: u = U0cos(100t)V. Khi C =

C1 = F v C = C2 = th mch c cng cng sut,nhng i1 v i2 ( ng vi 2 gi tr ca C) u

lch pha vi nhau mt gc rad.

a. Tnh R v bit L= H

b. Tnh L v , bitc. Tnh R v L, bit = 100(rad/s)

Bi 5: Cho mchin RLC, C thay i, u = 120 cos(100t)V. Khi C = C0 th UCmax = 200V. Khi P= 38,4W. Tnh R, L, C0

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