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1 unts Unts- Englsh Swesh Sybol nae Mehans Mekanks Value Apltue apltu A aea aea A aeage aeleaton eelaeleaton a / s aeage eloty eelhastghet / s onstute nteeene östäknng oeent o ktonstal ton - ensty 3 enstet kg / Destute nteeene utsläknng Dsplaeent stäka x Double slt Dubbelspalt Eeny eknngsga Enegy eneg E J N Joule Esape eloty Flykthastghet P g P P R P / s Foe kat F N kg/ s Fequeny ekens s Hz Fton s ktonstal oeent Gatng gtte gatatonal g aeleaton tt all / s aeleaton pulse Ipuls I kg / s nutane sel-nutane ntal eloty begynnelsehastghet L / s nstantaneous / s eloty oenthastghet lnea oentu öelseäng P kg / s ass Massa kg Newton Hetz 9.8 / s Heny behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

2 unts Unts- Englsh Swesh Sybol nae Magnet Fel Magnetska löestäthet B esla Magnet lux Magnetskt löe Wb Webe peetly elast ollson ullkolgt elastsk stöt peetly nelast ollson ullkolgt oelastsk stöt peo Peo (Sängnngst) s Phase angle Fasnkel powe eekt P W J / s Watt pessue tyk P Pa spng onstant jäekonstant k N Sngle slt enkelspalt e t s N / Pasal oque oent N Note: not Joule! Volue Voly V Wok abete W J N Joule 3 Sybo unts Unts- Englsh Swesh l nae Eletostats an Det Cuent, DC Elektsk, lkstö hages lanng, el-äng Q C Coulob (elet) uent (elektsk) stö I A C / s Apee (elet) potental (elektsk) spännng V V W / A Volt (elet) el (elektsk) ältstyka E N / C esstane Resstans R V / A Ohs esstty Ressttet apaty Kapatans C F C / V Faa Eletooto oe Elektootosk spännng V Volt behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

3 Englsh Swesh Opts Optk nent angle Inallsnkeln eaton angle Bytnngsnkeln Sybo l Unts Untsnae nex o eaton Bytnngsnex n spee o lght n auu ljusts hastghet akuu / s oal length Bänn o powe objet stane age stane Dopte öeålets astån tll spegel elle lns Blens astån tll spegel elle lns agnaton Latealöstong objet heght öeålets stolek h O age heght blens stolek h P Englsh Swesh Sybol Heat an Väeläa oh O D o o o o unts 3. Untsnae heoynas eoynak heat Väeeneg Q J Joule kal klo aloe tepeatue epeatu K Keln C Centgae tepeatue hange tepeatuänng K Keln spe heat spek äekapatet J /( kg K) 8 / s Latent heat o uson heat o apozaton spekt sältäe (spek sältentalpttet) spekt ångblnngsäe (spek L L V J / kg kal / kg J / kg kal / kg ångblnngsentalpttet) behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 3

4 able 4- Spe Heats, & 4-3 Latent Heat, L Substane Spe Heat Meltng ep. Heat o Fuson Bolng pont Heat o Vapozaton Kal/[Kg. C] kj/[kg. C] C Kal/Kg kj/kg C Kal/Kg kj/kg Ethyl alohl Ie Wate Stea Ion (Fe) Alunu (Al) Lea (Pb) Coppe (Cu) Mable..88 Glass..84 Huan boy behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 4

5 Mehans D-oton; Lnea oton Mekank Lnjebunen öelse splaeent x : stäka; nstantaneous eloty : oenthastghet; aeage eloty : eelhastghet; ntal eloty : begynnelsehastghet; aeage aeleaton a ; ass : assa; oe F : kat ; pessue P : yk; aea A Constant aeleaton a Lkoga aeleeae öelse x x t at x t Fo onstant eloty. x t onstant aeleaton a : Lkoga aeleeae öelse at splaeent x ; Constant aeleaton a Gälle konstant aeleaton ä s ä stäka ä utgångshastghet (begynnelsehastghet), a ä aeleaton oh t ä t: at s t Fo onstant eloty. Gälle konstant hastghet ä ä hastghet s ä stäka t ä t: s t nstantaneous eloty : oenthastghet onstant aeleaton a : aeleaton Gälle konstant aeleaton ä s ä stäka ä utgångshastghet (begynnelsehastghet), a ä aeleaton oh t ä t. ax aeage eloty : eelhastghet [ / s] a [ / s ] aeage aeleaton a t t t t t t x a [ / s ] t t Gatatonal aeleaton g 9.8 / s always ownwas.: aeleaton tt all. x nstantaneous aeleaton a t t F g [N] he weght o an objet o ass [kg] whee the gatatonal aeleaton s g [ / s ]. yngkaten so ett öeål e assan känne a joytan. behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 5

6 a b a sn os b tan a b a Newton s st law F net F net a t Newton s th law: Aton an eaton Vekan oh åteekan F F N Lutane plan: tan V b I the total oe on a gen objet s zeo, the objet shall stay at est t was ntally at est, othewse t wll ontnue ong at a onstant eloty on the eton t was ognally ong. Vaje kopp öbl I stt tllstån a la elle lkog oh ättlnjg, o en nte tngas a ytte kate att äna etta öelsetllstån. Newton s seon law: Net oe on a ee patle o ass. Newtons ana lag ä F net ä en esulteane katen, ä assan, oh a ä aeleatonen. Fo any aton thee s a eaton equal but n the opposte o the atng oe. å koppa påeka aana e lka stoa en otktae kate. Fton oe: F ; : oeent o ton: ktonstal; Lutane plan: tan o an nlne plane o the angle o nlnaton an onstant eloty. F N : Noal (oe) to the suae: noalkat Densty : Denstet, ass : assa an olue V : oly F behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 6

7 L g V g Ahees pnple: an objet subege wholly o patally n a lu s buoye up by a oe L equal to the weght o the lu t splaes. Akees pnp: ett öeål en ätska elle en gas å en lyt kat L so ä lka e en unantänga ätskans elle gasens tyng. F Pessue P ; oe F ; aea A P A F ä tykkat P ä tyk oh A ä aean P g h he Pessue P at a epth h n a lqu whose ensty s. Vätsketyket beäknas e oeln ä ä ätskans enstet F [N] Fsn F l [N] sn F g ä en konstant oh h ä jupet (höjen a ätskepelaen) oque s ene as the pout o oe F tes lee a (pepenula stane o the lne o aton o the oe to the axs o otaton) Då en hästång utsätts ö en kat, uppstå ett sk oent, F l. Stoleken ä popotonell ot häaens läng l oh en nkeläta katkoposanten F. axs o otaton Enegy an wok Eneg oh abete W F x F xos Wok W F x F x os, whee F s the apple oe, W E [J], [N] splaeent x an angle between the oe an splaeent. O ett öeål utsätts ö en esulteane kat F å en ölyttas stekan x, utös abetet W, oh enegn so käs ä E. Katen åste aa paallell e ölyttnngen (annas anäns en paallella koposanten). E PE g h E PE g h s the gatatonal potental enegy o a ass whh s at a heght h aboe an abtay eeene (zeo) leel. g 9.8 / s s the gatatonal aeleaton. EKE E P [W], [ J / s ] t E E P, P t t P F F os Ett öeåls lägeseneg (potentella eneg) so benne sg på höjen h oanö en gen nollnå. Knet (tanslatonal) enegy s enegy o oton. An objet o ass an spee has tanstonal knet enegy EKE. Röelseenegn (knetsk eneg) so ett öeål öelse ha. Powe s ene as the ate at whh wok s one, o the ate at whh enegy s tansoe. Enegoanlngen E på ten t ge en genosnttlga eekten P. behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 7

8 E E E E O Nyttg otal P P QQ k E PE Nyttg otal Eeny s ene as the ato o the useul (output) enegy (o powe) to the total nput enegy (powe) o the syste. Veknngsgaens enton: koten ellan nyttg (anänba) eneg oh tllö eneg. Gälle äen eekt. he potental enegy o a syste o two pont hages Q an QQ Q at a stane o eah othe: E PE k whee 9 k 9 N C : Coulob s onstant. E PE QV he potental enegy E PE QV o a hages Q at a potental eene: V. Haon Osllatons: F k x Hook s law: F k x ; whee k : spng onstant; x : splaeent o equlbu E PE k x Potental enegy: E PE k x ; whee k : spng onstant; x : splaeent o equlbu. Peo o osllaton: ; whee k : spng onstant; k k : ass. Fequeny o osllaton: ; whee : peo. Angula equeny o osllaton: ; whee : peo. behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 8

9 Ch 3 Pojetle oton: Kastöelse Physal Quantty Intal eloty Angle o pojetle Hozontal oponent o the ntal eloty Denton- Sybol Intal eloty o the pojetle s a eto o agntue at angle wth the poste hozontal axs,.e. at angle aboe the goun Hozontal oponent o the ntal eloty Foula x os Vetal oponent o the ntal eloty Hozontal oponent o the ntal eloty y sn x-eton (Hozontal) y-eton (etal) x os sn y x x os y y g t sn g t x x t os t y y t g t sn t g t Range: Kast Maxu heght eahe: Stghöj R sn g y ax sn g g y Pojetle s equaton: Kastpaabolens ekaton : g y x tan x os behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 9

10 Ch 5 Cula Moton; Gataton: Physal Quantty Uno Cula Moton: Centpetal Aeleaton Centpetal Foe Centpetalkat Unesal Gataton Denton- Sybol An objet ong n a le o aus wth a onstant spee has a entpetal aeleaton a C (o a R aal aeleaton) that s ete aally towa the ente o the le whose agntue s a C. Een though eton o entpetal (aal) aeleaton as well as the eloty ontnuously hange, they ae pepenula to eah othe une the ente oton. 4 FC ac 4 : aus: ae : peo: oloppst : equeny: ekens : angula eloty: nkelhastghet wo asses an at a stane attat eah othe wth the oe F G, whee G 6.67 N / kg s Newton s Unesal Gatatonal Constant. he eton o the oe s along the lne jonng the two asses. All patles n the unese attat eah othe! Foula a C F C a F G C Keple s Law Keple s 3 law o planetay oton 3 Eath 4 Mass: 5.98 kg, 3 Raus R 6.38 k Sun 3 Mass:.99 kg, 5 Raus R 6.96 k Moon Mass: 7.35 kg, 3 Raus R.74 k Eath-Sun stane 6 ES 49.6 k Eath-Moon stane 3 EM 384 k behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

11 Ch 7 Lnea Moentu, Cente o Mass (CM): Physal Quantty Denton- Sybol Foula Cente o Mass x CM : x-oonate o the CM x x... x CM y CM : y-oonate o the CM... y y... y CM... Lnea P : Lnea Moentu P Moentu : Mass Röelseäng [ kg / s ] : Veloty (hastghet) Ipulse Ipulse s the hange n the t Ipuls lnea oentu. I F t t F t t F [ kg / s ] : aeage oe: eelkaten I P P Ipuls ä änngen a öelseängen Conseaton o Lnea Moentu Peetly Elast Collson Fullkolgt elastsk stöt e Peetly Inelast Collson Fullkolgt oelastsk stöt e I the net oe on a syste s zeo,.e. F, then the total lnea oent o the syste s onsee: Lagen o öelseängens beaane: I ett slutet syste ä konstant. Stuskoeent: e Lnea Moentu o the syste s onsee. (Mehanal/knet) enegy o the syste s onsee. Lnea Moentu o the syste s onsee. (Mehanal/knet) enegy o the syste s not onsee. Fullkolgt oelastsk stöt : geensa sluthastghet P P.. P P.... Rak ental stöt:, stöten : patklanas hastghet öe, : patklanas hastghet ete stöten P P.. P P.. e... P P.. P P behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

12 Copae the lnea oton to the ula oton: Lnea Moton: Constant aeleaton a : Cula Moton: Constant angula Lkoga aeleeae öelse aeleaton Sybol-oula Physal Quantty Sybol-oula Physal Quantty x Dsplaeent angula splaeent Veloty angula eloty a Aeleaton angula aeleaton ntal eloty ntal angula eloty x x t at t t at t x t t aeage eloty aeage angula eloty ass I oent o neta ass I oent o neta F a Foe, Newton s I toque seon law F toque P Lnea oentu L Angula oentu Foe, Newton s toque F a P t seon law I L t F Conseaton o lnea Conseaton o oentu angula oentu P CONSAN L CONSAN anstonal knet Rotatonal knet E KE enegy E KE I enegy An objet ong n a le o aus wth a spee has a entpetal aeleaton a C (o a R aal aeleaton) that s ete towa the ente o the le whose agntue s a C. Een though eton o entpetal (aal) aeleaton as well as the eloty ontnuously hanges, they ae pepenula to eah othe une the ente oton. he elaton between the tangental eloty, aeleaton an splaeent to those o the angula eloty, aeleaton an splaeent o a ula oton ae: Sybol-oula Physal Quantty Sybol-oula Physal Quantty s Lnea Dsplaeent angula splaeent (seto) angental Veloty angula eloty a angental aeleaton angula aeleaton behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

13 Ch Mehanal Waes Physal Quantty Denton Foula Hook s law Hookes lag F estong oe poues SHM k spng onstant: jäekonstant F k x Potental enegy (SHO) Potentell eneg en jäe Deental equaton (SHO) Apltue Apltu Angula eloty nkelhastghet Phase angle asnkel Peo Sple penulu Plan penel Fö en plan penel gälle så utslagsnkla x splaeent o the equlbu Potental enegy o a sple haon osllaton. Elast potental enegy. o a stethe o opesse spng, whee x s the splaeent o the equlbu an k s the spng onstant. Potentell eneg en jäe he soluton o the eental ay be expesse as: x Asn t Maxu splaeent SHO: Sple Haon Osllato SHM: Sple Haon Moton : he peo o baton o a : ass on the en o a spng o k : spng onstant ö en ullstäng sängnng SHO: Sple Haon Osllato : he peo o baton o a L : Length o the sple penulu: Penelns läng g : gatatonal aeleaton E PE A k x x kx t k k g Con penulu Konsk penel Peo Sängnngst [s] Fequeny Fekens [Hz] o [ s ] : he length o the penulu : he angle o the on penulu : he te a wae takes to epeat tsel. : waelength : eloty o the popagaton o the wae : equeny Nube o osllatons pe seon. os g behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 3

14 Veloty utbenngshastghet [/s] Wae length Poston oonate Lägeskoonat [] Elongaton elongaton [] Wae equaton Vågekatonen [] Wate wae Vattenågo Veloty o popogaton [/s] Wae on a stng Veloty o popagaton o the wae he stane between two sla eents, o ex. he stane between two onseute axus. Elongaton, akelse ån jäktsläget Deep wate (wate epth s uh lage than the waelength): Djupattenågo (attenjup >> åglängen) utbee sg e g aten Shallow wate (wate epth s salle than the waelength): På gunt atten, ä attenjupet ä ne än åglängen, utbee sg ågona e aten gh he eloty o a wae on a stethe stng o ass an length L une whh s une tenson F. x y y Aos x t y Aos x t g gh F / L behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 4

15 Stanng Wae: Resonane Funaental waelength Both-en-lose stng Nth equeny Stanng wae: Open en ppe Stanng wae: Funaental waelength One-lose-en stng Stanng Wae Haony. Both-en-lose stng Stanng wae: Haony. One-lose-en stng Both-en-lose stng o length L. Funaental o st haon, : L he lowest equeny s alle unaental equeny whh oespons to one antnoe (o loop) L o Fst oetone o seon haon L n th oetone o n th haon L n n n n n n n n n n L L Open en ppe L. Stanng wae L One-lose-en stng (o ppe) o length L. L 4 Both-en-lose stng o length L. Stanng wae L Haony. One-lose-en stng o L L length L. Stanng wae 4 Ch : Soun: Physal Quantty Denton Foula Leel o soun he leel o soun (n B) log Ljunå Ljuntenstetsnå uttyk ebel I : ntensty o soun I W ä ljuntensteten / höbahetsgänsen ö ekensen Reeene Intensty he ntensty o the eeene leel I W Soun eloty n gases Ljuet hastghet I gase : epeatue 73 K : hastgheten khz I I / behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 5

16 Heat an heoynas: Heat an heoynas Q Q Q L Q L Q L Q L V eoynak Heat absobe o gen o : Q Whee: : spe heat; : tepeatue nease o eease; : the ass o the substane. Fö att åstakoa en tepeatuöänng hos en assa åste enegn E tllöas elle ages ä änets speka äekapatet Heat eque o gen o ung the phase hange: Q L Whee: L : Latent heat o patula poess an substane: ( L V : heat o apozaton; L F : heat o uson); : the ass o the substane. Heat eque o gen o ung the phase hange o the sol to lqu o V esa : Q L (seltng) whee L F : heat o uson; : the ass o the substane. Eneg so käs ö att sälta ett äne elle eneg so ages å ett äne stelna, ä ä assan oh ä änets speka sältentalp Heat eque o gen o ung the phase hange: Q L Heat eque o gen o ung the phase hange o the lqu to gas o V esa : Q L V whee L V : heat o apozaton; : the ass o the substane. Eneg so käs ö att öånga ett äne elle eneg so ages å ett äne konensea ä ä assan oh ä änets speka ångblnngsentalp behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 6

17 Eletostats an Det Cuent (DC) Lannga 9 9 e.6 C Elet hage o an eleton: e.6 C e kg. Mass o an eleton: e 9. kg. p kg Mass o a poton: p.67 kg k Q Q F k 9 9 N C Coulob s onstant Coulob s Law: Foe between two pont hages Q an Q at a stane o eah othe: QQ F k. 9 Coulob s onstant: k 9 N C. Katen e lken tå lannga påeka aana. k ä en 9 konstant. k = 8,99 E PE QV. he potental enegy o a pont hage Q n an (extenal elet) potental (eene) V : E PE QV. E q U Enegn so käs ö att öa en lanng q geno en spännng U. Detta ä äen enegn so oanlas (tll knetsk) å lanngen å alla tt geno spännngen. F QE. Elet Foe ae by a hage Q n an elet el E : F QE. Q Q E. E k Elet el o a pont hage, Q, at a stane : k QQ k E PE Q V k he potental enegy o a syste o two pont hages Q an QQ Q at a stane o eah othe: E PE k he (Elet) potental o a pont hage, Q, at a stane : Q V k. EKE he knet enegy spee. EKE o a (pont) ass ong at behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 7

18 Elet uent, Potental eene, Powe Q Q I ; I t t Q I [A] o [C/s] t V RI U R I R S l R A P VI RI P U I E U I t R eq R R V R R R3 R R ot R n Stö, spännng, oh eekt Q Q (Elet ) uent: I, o I s the ate o low o t t elet hage. Dentonen på elektsk stö. Antal lannga (nte elektone) so passea en ss punkt une en ss t. O lanngana ä negata gå stöen åt otsatt håll. Oh s Law states that the uent n a goo onuto s popotonal to the potental eene apple to ts two ens. he popotonalty onstant s alle the esstane R o the onuto: V RI Kaptlets est anänbaa saban: Ohs lag. O en koponent en elektsk kets ha otstånet R, oh genolyts a stöen I, et att spännngen öe koponenten åste aa U. Resstane R o a we o length, oss seton S aea S an esstty : Resstty epenene o tepeatue: Whee s the esstty at tepeatue, s the esstty at tepeatue an s the tepeatue oeent o esstty,. Alla leae ha en ss essttet, oh äe en ss esstans, R. Vae beo esstansen på leaens läng l oh ess täsnttsaea A. Obseea att konstanten ä anpassa så att A ska anges, tll skllna ån e lesta ana ole ä äena ska anges SI-enhete. he (Elet) powe sspate n a essto R, when two ens o t s at the (elet) potental (eene) V an uent I V passes though t: P VI RI. R Eekten (ölje a oanståene saban). E E Powe: P o P whee P : powe; E : enegy (o t t wok) an t : te. Den äng elektsk eneg so osätts en koponent, ex. otstån, lapa, oto. Equalent esstane o esstos n sees: R eq R R R... 3 En seekopplng a esstanse (n st.) å öljane totala otstån (esättnngsesstans). Den totala spännngen öe enna see elas upp öe alla otstånen. behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 8

19 R eq R R R R R R ot R n I ot Equalent esstane o esstos n paallel:... R R R R eq 3 En paallellkopplng a esstanse (n st.) å öljane totala otstån (esättnngsesstans). Saa spännng lgge öe alla otstån. I I Khho s st law: At any pont, the su o all uents enteng the junton ust equal to the su o all uents leang the junton. O en leae ela upp sg tå gena, gå en el a stöen geno en ena genen oh esten a stöen geno en ana. Ch 6 Foulas. Elet Chage an Elet Fel: Physal Quantty Denton- Sybol Foula Coulob s Law he agntue o the oe one pont hage, QQ F k Q exets on anothe pont hage Q at a stane o eah othe. whee 9 k 9 N/ C n SI [MKS] unts. Elet el he agntue o the Elet el ue to a sngle pont hage Q at a stane o the pont s gen by: Q E k behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 9

20 Ch 7 Foulas. Elet Potental an Elet Enegy; Capato: Physal Quantty Denton- Sybol Foula potental enegy he hange n the potental enegy EPE o a PE QV ab hage, Q, when t oes though a potental eene V ab V s PE QVab E PE QV potental eene elet potental he potental eene V between two ponts whee a uno elet el E exsts s V E, whee s the stane between the two ponts. he elet potental ue to a sngle pont hage Q, elate to zeo potental at nnty Q s V k whee s the stane o the pont o the hage. V E Q V k hage he total hage stoe n a apato s Q CV elet enegy he elet enegy stoe n a hage apato: U QV CV Q C apatane he apatane o a paallel-plate apato whose plates hae a oon aea A an sepaate by a stane o a s gen by: I the sepaate stane s lle by a elet el, the apatane s gen by: A A C K whee, K s elet onstant. C C A A A K behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

21 Ch 8 Foulas. Elet Cuent: Physal Denton- Sybol Quantty Elet he elet uent n a we I s ene as the net uent aount o hage Q that passes though t pe unt te t at any pont. Oh s law Powe, Elet enegy Resstane, Resstty he uent, I, n a goo onuto s popotonal to the potental eene, V, apple to ts two ens. he popotonalty onstant s alle the esstane R o the onuto: he ate at whh enegy s tansoe (.e. the powe tansoe) n a esstane R o elet enegy to the othe os o enegy s gen by: V P VI RI. R Elet enegy whh s tansoe to othe o o enegy n a essto, engnes, lght bulbs,.. ung a gen te: E Pt V I t he esstane R o a etal we s etly popotonal to ts length an nesely popotonal to the ossseton aea A. he onstant o popotonalty s alle esstty an epens on the ateal use. Foula I Q t Q I t V RI Q t V P VI RI R E Pt V I t R A Ch 9 Foulas. DC Cuts: Physal Denton- Sybol Foula Quantty Resstos n Equalent essto sees: R eq R R R3... otal uent Beause o the onseaton o elet hages the uent lowng nto a junton ust equal to I I I I3... the lowng out o the junton pont. Resstos n paallel: Capatos n sees: Capatos n paallel: Chagng a apato: te onstant Dshagng a apato: Equalent essto Equalent apatane R eq C eq R R R C C C Equalent apatane C C C... In an RC ut ontanng a esstane R n sees wth a apato C s onnete to a DC soue o e, V, the oltage aoss the apato ses exponentally n te: In an RC ut ontanng a esstane R n sees wth a hage apato C to an ntal oltage V, the oltage aoss the apato eeases exponentally n te: C eq V V e V RC V e 3 3 t RC RC t behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

22 Ch Magnets Physal Quantty Denton Foula Magnet Foe on A agnet el B exets a oe F I B a uent F I B on an elet uent. Fo a staght F I Bsn Magnet Foe on a ong hage Magnet Fel B esla Magnetska löestäthet Magnet Fel B esla Apee s law oque on a uent Loop we o length ayng uent I the oe has the agntue F I Bsn. A agnet el B exets a oe F Q B on a ong elet hage. Fo a hage Q ong at a eloty the oe has the agntue F QBsn. I the hage oes n a eton noal to the eton o the agnet el,.e. sn sn9 F QB Magntue o the agnet el at a stane o a long staght we ayng a uent I s Magnetska löestätheten kng an oänlgt lång, ak leae akuu. ä astånet tll leae Magntue o the agnet el nse a soleno ayng a uent I. he soleno s ae o n loop we. I B F I B F QBsn B B I n I B I NIA B NIAB sn Magnet Moent Magnet Dpole Moent M NIA behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes

23 Ch Inuton an AC uts: Elektoagnetsk nukton Physal Quantty Denton Foula Magnet lux Magnet lux ue to agnet el, BA os Magnetskt löe whh passes though a oss seton aea Wb. he angle between an s a. : agnetlöet geno slngan Eletooto oe. Faaay s law o nuton sel-nutane Elet el poue by a hangng agnet lux Enegy stoe n a agnet el ansoe Powe..s. Ipeane LRC sees n AC Cuts esonane equeny Eletooto oe: (Elet Potental) ue to the hange n the agnet el w..t. te. N: nube o tuns. : nuea es I en sluten t slnga (ett a) Inue e o an nuto L : sel-nutane: I : Cuent Spolens själnuktans A hangng agnet lux poues an elet el. N N t t B I L t F Q B E B Q Q Enegy stoe n a agnet el U L I N P : Nube o tuns n the pay VS N S N S : Nube o tuns n the seonay VP N P V P : Voltage n the pay (nput) I S N P V S : Voltage n the seonay (output) I P N S I P : Cuent n the pay (nput) B VS NS I S : Cuent n the seonay (output) t he powe lost an hgh oltage P VI tanssson P L RI Root ean Squae û U s V V V V R L C Z P powe ato os I V s s LC X L X C tan R Inute eatane (peane) X L L LR Cut L In an nuto the te onstant V R I e uent lags the R R X L X C t behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 3

24 oltage by 9 I ax V V s V R I I X L s X L I I ax e t RC Cut Capatane eatane (peane) Vs Is X C ; In a apato the uent leas the oltage by 9 X C C Geoet Opts Ch3: Optks n whee, : spee o lght ay n a eu wth nex o eaton n 8 an s the spee o lght n the auu: 3. / s. n, sn n sn n sn() = n sn(b) he law o eaton (Snell s law): n sn n sn, whee n an ae the nex o eaton an angle wth noal to suae o the nent ay (nent angle) an, n an ae o the elete ay. n n n n = Bytnngslagen ä n n e tå änenas bytnngsnex oh ä nallsnkeln oh b ä bytnngsnkeln Angle o nent s the sae as the angle o eleton Relektonslagen ä nallsnkel oh ä elektonsnkleln behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 4

25 O a b Lens equaton (Gauss lnsoel): O whee : oal length o the lens, O : objet stane an, Lens equaton (Gauss lnsoel): whee : oal length o the lens, O : objet stane an, age stane. O : : O h O h Conegng lens Lnsoeln ä ä bännen a ä astånet lns öeål oh b ä astånet bl lns O Mo equaton:, O whee : oal length o the o, O : objet stane an, : age stane. Conae o h ho b G a O Magnaton: h h, O whee O : objet stane an, heght, h : age heght. O : age stane; h O : objet Föstongen G ä a ä astånet lns öeål oh b ä astånet bl lns behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 5

26 Ch, 3, 4, 5 Eletoagnet Waes (lght): Ch Eletoagnet Waes Physal Quantty Denton Foula Spee o lght Spee o lght n the auu s onstant an s the uppe lt o the spee any physal quantty ay ahee. he waelength an equeny o EM waes (lght) ae elate to the spee Ch 3 Lght: Geoet Opts: Physal Denton Foula Quantty Inex o eaton Inex o eaton n Inex o eaton Inex o eaton n Veloty Veloty o popagaton o the wae n the eu Veloty Veloty o popagaton o a wae (equeny n n an waelength ) n a eu o nex o eaton n Foal length : the stane o the oal pont o the lens s the oal length o the o an whee s the aus o uatue o the o. Mo o : Objet stane equaton : Iage stane Magnaton h : Objet heght o h : Iage heght : agnaton o h h o Snell s law Law o eaton n sn n sn lens equaton o : Objet stane : Iage stane Magnaton h : Objet heght o h : Iage heght : agnaton o h h o o o Waelength Gatng s onstant Gatng s oula Waelength o the wae n a eu wth nex o eaton n Gatng s onstant (Gttes konstant) Gatng oula. Constute nteeene (Gttes oula) n n n n sn behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 6

27 Ch 4 he wae natue o Lght Physal Quantty Denton Foula Inex o eaton Inex o eaton n Inex o eaton Inex o eaton n Veloty Veloty o popagaton o a wae (equeny n n an waelength ) n a eu o nex o eaton n Waelength Waelength o the wae n a eu wth nex o eaton n n n n Young s ouble slt: Constute nteeene Young s ouble slt: Destute nteeene Young s ouble slt: Constute nteeene Gatng s oula : Constute nteeene (Föstäknng) Sngle slt aton (Enkelspalt) Dakton en kulä öppnng Bagg s law Baggs lag Wae length o : waelength o the wae (lght) : poste ntege:,,, 3, : he sepaaton o slts. : waelength o the wae (lght) : poste ntege:,,, 3, : he sepaaton o slts. (spaltastån) (Dubbelspalt Utsläknng) : waelength o the wae (lght) : poste ntege:,,, 3, : he sepaaton o slts. (spaltastån) (Dubbelspalt Föstäknng) Gatng oula. Constute nteeene (Gttes oula, Föstäknng) : Gatng s onstant (Gttes konstant) : oe o spetu: (onngstal),,, 3,... : he angle between the noal to the plane o the gatng an the spetu: (nkel ot gtteplanets noal) Fst nu sn D Fösta böjnngsnu: sn D :,, 3, na D : wth o the sngle slt Vllko ö östa böjnngsnu Constute nteeene: Vllko ö östäknng : astån ellan tå atoplan : nallsnkel,, 3,... 4 n olet sn sn sn sn D sn D sn. sn n behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 7

28 Vsble lght: Ina e (IR) Ulta olet (UV) 46 n blue 55 n geen 575 n yellow 65 n oange 75 n e 75 4 n n Dopple s eet: soue : obseea ekens : Utsän ekens : ågens utbenngshastghet : obseatöens hastghet obs soue : källans hastghet Physal Quantty Denton Foula Dopple eet he wae soue s at est. Doppleeekt Obsee s eloty obs s taken poste t appoahes the soue. Dopple eet Doppleeekt Dopple eet Doppleeekt Vågkällan la: Obseatöens hastghet obs äknas so poste å obseatöen näa sg ågkällan. he obsee s at est he eloty o the soue soue s taken poste t appoahes the soue. Mottagaen la: Källans hastghet soue äknas so poste å ågkällan näa sg obseatöen I both the soue an the obsee ae n oton, takng the sgn o the elotes as those entone aboe: O båe ågkällan oh obseatöen ä öelse gälle e oanståene tekenegle: obs soue obs soue behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 8

29 Ch 6 Speal heoy o Relatty: Physal Quantty Denton Foula Pope length he length easue n the est ae. L Pope te he te easue n the est ae t Rest ass he ass easue n the est ae Gaa ato / e laton: Mong loks ae easue to un t slowly. t t Length ontaton: he length o a ong objet s easue to be shote (n ts eton o L L oton) than when t s at est. Mong ass he ass o a boy s easue to nease wth spee. Equalene o ass he aount o enegy an objet has E an enegy beause o ts ass. Knet enegy he Knet enegy o an objet ong E K at spee Enegy & otal enegy (assung no potental 4 E p oentu enegy) s elate to the lnea oentu p o the objet. Relatst aton o elotes along the sae lne. : he eloty o the st objet wth espet to the statonay obsee; : he eloty o the seon objet wth espet to the statonay obsee; : he eloty o the seon objet wth espet to the st. behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 9

30 Ch 7 Ealy Quantu heoy: Physal Quantty Denton- Sybol Foula J. J. hoson an B : agnet el, : aus o the bea; e E hs athoe ay tube E : elet el; B Plank s quantu E nh hypothess Photon s enegy E E h Wen s law P : waelength at the peak, : epeatue P.9 Fequeny Pnple o : (e Bogle) waelength, : oentu h h Copleentaty P Angula oentu L : Angula oentu o the ato eletons n h Boh s oel L Copton eet : waelength o the nent photon. : waelength o the sattee photon at the angle. : the est ass o the taget (eleton) h 3 os K Enegy o the eleton n the nth exte state n H. n,, 3,... Rybeg onstant 7 R.97 Lyan sees n, 3, 4,... Bale sees n 3, 4, 5,... Pashen sees n 4, 5, E n n R.97 e 7 R n R n R 3 n n n n3 Funaental onstants Quantty Sybol Appoxate alue Spee o lght n auu 8 3. / s Eleton s hage e 9 e.6 C Eleton s est ass 3 e e 9. kg Poton s est ass 7 p p.676 kg Neuton s est ass 7 n n.6749 kg Ato ass unt u 7 u.665 kg Plank s onstant h 34 h 6.63 J s Peeablty o ee spae 7 4 / A / 8.85 C / N Pettty o ee spae Stean-Boltzann onstant W / K behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 3

31 Physs B Ch 8 Quantu Mehans o Hyogen Ato Physal Quantty Denton- Sybol Foula Hesenbeg x unetanty n easueent o poston. x p Unetanty Pnple p unetanty n easueent o oentu. Hesenbeg E unetanty n easueent o enegy. E t Unetanty Pnple t unetanty n easueent o te. Boh Moel Enegy o the eleton n the nth exte Z state n H. n,, 3,... E n 3. 6 n e Boh Moel Boh aus.59 n n Z Pnpal Quantu n,, 3,... n,, 3,... Nube Obtal Quantu Relate to the agntue o the angula,,..., n Nube oentu L Magnet Quantu Nube Spn Quantu Nube Relate to the eton o the angula oentu: Spae quantzaton: L Z n Relate to the ne stutue an the angula oentu assoate wth the spn o eletons:,,..., s Seleton ule Allowe tanston Paul exluson pnple Photon s enegy Pnple o Copleentaty No eletons n an ato an oupy the sae h quantu state. os E enegy, : equeny : (e Bogle) waelength, : oentu E h h h P Funaental onstants Quantty Sybol Appoxate alue Spee o lght n auu 8 3. / s Eleton s hage e 9 e.6 C Eleton s est ass 3 e e 9. kg Poton s est ass 7 p p.676 kg Neuton s est ass 7 n n.6749 kg Ato ass unt u 7 u.665 kg Plank s onstant h 34 h J s &.55 J s Peeablty o ee spae 7 4 / A h / 8.85 C / N Pettty o ee spae Stean-Boltzann onstant W / K Boltzann s onstant k 3 k.38 J / K Aogao s nube N 3 6. ol A N A behza.assouzaeh@hunge.se Not o sale. Fee to use o euatonal puposes 3