16 Electromagnetic induction

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1 Chatr : Elctromagntic Induction Elctromagntic induction Hint to Problm for Practic., 0 d φ or dφ Wb. A cm cm 7 0 m, A 0 cm 0 cm 00 0 m B 0.8 Wb/m, B. Wb/m,, dφ d BA (B.A) BA V. n 00, A 0. m, db 0. Wb/m, 0.0 n. d φ AdB n V. na m, B 0.08 Wb/m, B 0% of B 0. B, 0. dφ d(n AB) na(b B ) (B B ) (B 0.B ) V 0.. A m, 0. V, B 0% of B B. 0., A(B B ) (B B ) BorB 0.0 Wb/m. A 00 cm 00 0 m, n 000, B 0 T, θ 80, 0. d φ ( φ φ) nab( co θ) ( co80 ) (+) mv 7. dφ Wb, 0. d φ 0 0 mv A cm 0 cm 0 cm 0 0 m, B 0 Wb/m, φ 0, d φ φ φ (0 A B ) V.7 µv and dφ 0 Wb 9. A m, B 0.0 Wb/m, B 0% of B B, 0. A db A(B B ) ( ) V mv

2 0. r 7. cm 7. 0 m, n 00, db (7 ) 0 0 T,., na. db 00. (7. 0 ) V. l 0. m, v 0 m/, B 0 T, Blv V 0. mv. Blv 0. V. l. m, v 0 km/h 0.7 m/, 8 B H. 0 Wb/m, θ, tan.0 Blv B H lv tan θ V 9. µv. l π m, B 0 Wb/m, 0 mv 0 0 V. Bl ω Bl πf f Bl π Bl π π π r... 0 r..m.. Bl ω 0 (0.) V Std. XII Sci.: Phyic Numrical. r 0 cm 0 0 m, n 00 r..m. 00 0r... 0 B 00 G 00 0 T Bfπ π (0 0 ) 0 0 π π 0 V 8 π mv 7. d I 0 A, 0., V di 0. di 0. H 8. n 000, I A, B 0. 0 Wb nφ I mh V, 00 mh 00 0 H, di 00 ma 00 0 A. di di di A/ di di.[givn] ( r) 0. 0 mh 0 0 H, I A, t 0. di [ I i contant.]

3 . di A/, 0 V di M. M M 0 0. H di. M mh 0 H, di M. di 0 0. V. m 0 H, di 0 A, 0.0 M. di V 0 A/. mv 0 V, di 0 A/ M. di 0 0. mh 0. M. H, di 0 0 0A, 0.0, N 800 M. di V dφ M.dI. 0 0 Wb. n 000, n 00, 0. m, A. 0 m, di ( ) A, 0. µ onna For a olnoid, M 7 π di 0. 0 m V Chatr : Elctromagntic Induction 7. n 0, n 00, 0 V Tranformr action i only rtaining to A.C. uly. 0 n :, 0 V n n n V 9. N : N 0 :, I A N I N I I I N N 0 0. A N 0. N 0 :, I 0 A, 0 V N I N I I V and I A. 7% 0.7, P out W, Pout Pout Pin Vin Iin Pout I in V 0.8 A in. P 0 0 W, 7% 0.7 P0 Pin P0 0 P in 0.7 P in. 0 W. 00 in 00 πt Comaring with o in ωt ak 00 V and ω 00 π πf 00 π or f 0 Hz

4 . n 00, A 00 cm 00 0 m, B 0 Wb/m, f 00/ min 00 0 / 0 o n AB(πf) o mv. 0 cm 0 0 m, b cm 0 m, n 000, f 0 r., o 0 V 0 n A B ω n A B πf o B πnaf Wb/m. f 0 Hz, o, θ 90 o in (ωt + θ) o o in (πft + 90) o co πft co π 0 co 0 (π)t co 0 co 0 πt 0 0 πt 0 or t 0π π 0 7. I o 0 A, f 0 Hz, t 0, I I o in ωt I o in πft I 0 in ( π 0 0 ) I 0 in (0) 0 8. A 8. n 00, A 0.0 m, f 0 r..., B 0.0 T, 0 Ω o nabω nab πf o V o I rm I rm π π A P max rm I rm π.7. P max W 8. W 9. rm 0 V o rm o rm. 0. V 0. I 0 in 00 πt Comaring with I I o in πft w gt, I o 0 A and f 00 Hz Io 0 I rm 0 A. I o 0 A Io 0 I rm 7.07 A. 00 Ω, 0 in (0 πt), t 0 Comaring with o in ωt o 0 V o I o I o A 0.0 A 0 A Io I rm I rm A. 0 A I I o in ωt I 0.0 in (0π 0 ) 0.0 in A Std. XII Sci.: Phyic Numrical

5 ,000 Ω 0 Ω, E o 00 V o I o I 00 o 0 I o 0 A A ammtr giv r.m.. valu of currnt, I rm Io A. 0 Ω, 0 V, I 0. A Z I Z Ω Z + X X Z ( 90) ( 0) X Ω X πf X πf H. o 0 V, f 0 Hz, mh 0 H, 9 Ω Z + X + (π f) + π f 9 + (.) (0) ( 0 ) Ω o I o Z I o A Io I rm I rm A Chatr : Elctromagntic Induction. mh 0 H, o 0. V, f 0 Hz rm f π rm I o / f o o I I o / π o o 0. π f A 7. 0 Ω, X 0 Ω, rm 0 V Z Z + X Z 0 Ω rm I rm Z 0 0 A 8. o 00 V, f 0 Hz, 0. mh 0. 0 H X πf Ω o I o X A 9. I D.C. A, V D.C. 0 V, V A.C. 00 V, F 0 Hz, I A.C. A Whn connctd to D.C., 0 VD.C. 0 0 Ω ID.C. r.m.. X I r.m.. X 00 0 Ω X πf X 0 π f H

6 0. 0. H, rm 0 V, f 0 Hz X πf X X 7 Ω rm I ak 0..07A X 7. C 00 µf 00 0 f, f 0 Hz. X c πfc Ω.8 Ω. C 0 µf 0 0 F, V, f khz 0 Hz X c π fc Ω I X c.8.7 A. mh 0 H, V, f khz 0 Hz f or C π C π f C ( ) F µf. I X A. I C Xc I C 8. 0 A 0.8 A. 0 Ω, H, f 0 Hz, C 0. µf 0. 0 F, rm V. X π f X. 0 X 70 Ω X c πfc Std. XII Sci.: Phyic Numrical X c X c Ω Z + C (X X ) 0 + (70 790) Z 90 Ω rm 0 I. 0 A Z 90 V l I. X V V c I.X C V V r I V. E 0 in t, 0. H, C µf 0 F, Ω Comaring with E o in ωt, o 0 V, ω rad/ ω πf πf or f π f 0 Hz o rm 0 9. V X πf X Ω X c πfc X c Ω Z + (X X ) Z + (. 7.) Ω C

7 co φ Z φ co Z co 98.9 co (0.) µh 0 H, C 0 µf 0 0 F 0 F, 0 Ω, V, f khz 0 Hz Z + (X X ) Z c 0 + (. 0 0 ) (8.8.9) Z 0. Ω I Z A. l I X l V c I X C c V r I r V 0.9 V 7. H, f 0 Hz, φ π X πf π 0 π 0 Ω tan φ X X tan φ 0 tan Ω, P 000 W P I rm 0 Ω I rm P A 0 I o Irm 0 0. A Chatr : Elctromagntic Induction o I o V r.m V I A 9. rm 0 V, Ω Io I rm I o I rm I o 0 A o I rm I 0 0 A P I 0 00 W rm 0. rm 00 V, f 0 Hz, 0 Ω 0 rn V I A. 0 rm P av (00) P av 0 00 W Enrgy nt J. P W, 0 00 V, P rm I rm P I rm 0. rm A. 0. mh 0. 0 H, Ω, C 0 µf 0 0 F, o 0 V f r π C f r khz 7

8 I At ronanc, Z 0 0 A. rm 0. V, 00 µh 00 0 H, C 00 F 00 0 F, Ω, f r π C f r f r khz At ronanc, Z rm I rm A X π f r X 707. Ω V I rm X V A, X at ronanc, V C. V. 0 Ω, 0. H, C 0 µf 0 0 F, o 0 V, f 0 Hz X πf Ω X c πfc X c Ω Std. XII Sci.: Phyic Numrical. 00 mh 00 0 H, C 0. µf 0. 0 F, 00 Ω At ronanc, Z 00 Ω f r π C f r Hz. 00 mh 00 0 H, f r 0 Hz f r π C C π f r F 7. rm 00 V, mh 0 H, f r 000 khz 0 Hz For ronanc, ωc C ω π f r ω (.) F C.7 F rm I X rm πf π A co φ Z I 8 ma 0 co φ φ co (0.70) 80.9 r.m.. I c x c I c 8 ma x r.m.. 8

9 8. 00 Ω, 0. H, C 00 µf F, 0 0 V, f 0 Hz Z Z + (X X ) C 00 + ( ) ( 7.87) 000+ (.).7 Z Ω 0 I max A For ronanc, f r π C f r.9. Hz At ronanc, Z o I rm I o.97.7 A 9. 0 mh 0 0 H, C µf 0 F f r π C f r f r 0 Hz 0 Chatr : Elctromagntic Induction Hint to Multil Choic Qution. N 00, A 0 m, B 0 T, φ NBA wbr. dφ 0 0% of 0 80% of d φ mv Ω, φ 0.7 Wb, φ 0. Wb, 0 φ ( ) d V I 0 0. A q It C. mc 0. 0 Ω, t dφ / i i t 0. B 0 T, A 00 cm 00 0 m n 00, 0. V φ nab t t nab t 00 (00 0 ) 0 t d ( t t +) A. 0 V, v 8 m/, B 0. 0 Wb/m Blv l Bv m 9

10 7. t 0., A π 0 m, A 00 0 m, B T, B. T φ φ BA BA t t. (00 0 ) (. 0 ) V mv 8. di A,. V, mh di 9. For tady currnt, di 0 M di 0 0. M 0 H, ω 0π rad/ I I 0 in ωt di I 0 ω co ωt S M di MIω co ωt Max. S 0 8 0π ( co ωt ) 0. π.78 V.8 V. φ. Wb, di A φ MdI P φ. M di P 0. H. Join thm in aralll for min. inductanc + + P min H. H. Th inductor ar joind in aralll + + X..7 H Std. XII Sci.: Phyic Numrical. C µf 0 F, dv/ V/ dφ0 Dilacmnt currnt I d ε 0 but φ EA VA d whr A ara of th lat d ditanc btwn th lat. d0 VA I D ε0 d ε0 A dv d ε0 but C A caacity of th caacitor d dv I D C 0 0 A µa. According to rorty of continuity, Charging currnt Dilacmnt currnt 0.8 A. 80 mh 80 0 H, I 0.7 A 7. E I 80 0 (0.7) 0.09 J 0.0 J N N N N Thr i no chang in frquncy. N N 0 :, 0 V N N 0 V 0 V V V 0 0 V 9. V 00 volt, V volt, I A V V I I V I P I V 0.A 0 ma 00 0

11 0. W 80 W, V 0 V Uing, I W V 80 0 A VI 0 Efficincy η VI %. N 00, B 0 T, A 0.0 m, t 0. NAB t V. NA 000 cm m 0. m, B π T, n 00 r..m 00 r... 0 E 0 NABω πnnab π π.7 V. max 0 mv 0 0 V, n 0, A 0 m, B 0. tla max nabω ω ω ω rad/. t 0. m co(πft) 8 co π π 8 co 8 volt. B 0 T, r 0 cm 0. m, 0 Ω, θ ωt 90, f 0 0 r... Altrnating currnt inducd in th coil i givn by, I I o in ωt π fnba in90 π 0 π( 0. ) π 0 A ma Chatr : Elctromagntic Induction. r 8 cm 8 0, B 0.0 T, ω 0 rad/ Bl ω 0 (8 0 ) 0 0 µv 7. rm 0 V, f 0 Hz, 0 Ω o I rm 0 0 A I max I rm A 8. Comaring with V V 0 in (ωt + θ) V 0 in (80 πt + 0.) V 0 0 V 9. V 0 V, V 0 V 0 ( ) 0 + V or V V V 0. E o 00 V, C µf 0 F E rm E0ωC I rm... Xc X ωc C ma. X 7 0. H π f. 00. X f X f X f X 0 0 Ω. C 0 µf 0 0 F, f 0 Hz Imdnc of circuit Z X c Z 00 πfc π π Ω

12 . Th ractanc of a caacitor, X c ωc πfc If th frquncy (f) i incrad, th ractanc dcra and hnc th currnt (I) incra. A dilacmnt currnt (I d ) conduction currnt, I d will b trild if th frquncy i trild.. X c or X C πfc f Xc f 0 X f 0 c X c X C 8 Ω. H, C 00 µf 0 F Th imdanc of combination Z πf πfc π 0 π Ω 7. 0 Ω, X 0 Ω, ω 00 rad/, I Z Z 0 I 0 Ω Z + (X c X ) (X c X ) (X c X ) X c X 0. Ω X c X Ω Ω π π 8. Pha diffrnc π π + π Ω, X 00 Ω, X c 0 Ω X Xc 00 0 tan φ 0 tan φ φ Std. XII Sci.: Phyic Numrical Ω, f 800 Hz Figur blow how th grah for th givn ca, tan θ X X V V ω ω...[ tan θ tan ] ω πf H 0 mh.. H, 0 Ω πf π 0. θ tan 0 tan (.). in(ωt + 90) or i inωt Thr i ha diffrnc of π btwn E and I P 0 V. V o 0 V, I o 0 0 A V I co P avg 0 0 θ co( π/ ) 0. W. o 0 V, I o 00 ma 00 0 A Powr rm I rm co θ Powr co 0 V θ V W

13 . N 0, A m, ω 0 rad/, B 0 T, 00 Ω Maximum owr diiatd in th circuit, E0 I0 EI 0 0 P max E rm I rm E But I 0 0 E0 E0 E P max 0 but E 0 NABω P max (NAB ω) (0 0 0) P max P max W 00 π. V co(ωt) in ω t + Pha diffrnc btwn V and I i π π Powr factor co 0 Powr diiatd 0 7. OQ I rm co θ. Thi contribut for owr. PQ I rm in θ. Thi do not contribut for owr. Hnc it i wattl. I wattl I rm in θ in θ P in θ θ 0 Powr factor co θ co 0 8. Ω, X Ω For an circuit Powr factor (co θ) O θ I rm E rm + X Q Chatr : Elctromagntic Induction H, C µf 0 0 F f r π C f r Hz V 0 V, 800 Ω, ω 0 rad/, C µf 0 F At ronanc, ω ωc and Z Currnt through th circuit, V I A Voltag acro i givn by V IX I ω But ω ωc I V ω C / V. V T 0 V For ronanc, V V C V T V 0 V 0 0. V V, I A, f 0 Hz, 0 V V I and Z I Ω and Z 0 0 Ω Powr factor co θ Z H, C µf 0 F At ronanc, ω C rad/

14 . In ri ronanc, Z 80 Ω Std. XII Sci.: Phyic Numrical. In ri ronanc, P.D. acro P.D. acro C 80 V. C µf 0 F, λ 00 m Th ocillating frquncy, f f π C π C π f C but f f vlocityof light(c) wavlngth( λ) 8 8 c λ () From q. (), H 0. 0

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