6. CURRENT ELECTRICITY

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1 Synopss : 6. CUNT LCTICITY. lectc cuent : a) Net chage flowng acoss the coss secton of the conducto n one second s called electc cuent. =Q / t o Q = t b) S.I. unt of cuent s ampee coulomb ampee = sec ond c) The cuent flowng though a conducto s sad to be one ampee when one coulomb of chage passes though t n one second. d) If electons pass acoss the coss-secton of a conducto n one second, the stength of the cuent flowng acoss the conducto s one ampee. t. Dft velocty ( d ) : t a) The aveage velocty of the chage s called as Dft velocty ( d ). b) Dft velocty s the aveage velocty and not nstantaneous velocty of the chage. = A d ρ c whee A s aea of coss secton of the conducto ; d s dft velocty; ρ c s chage pe unt volume. = A d ne whee n s numbe of electons pe unt volume. Dft velocty pe unt feld s temed as moblty (μ). μ = d 3. Two temnologes ae used fo cuent egadng the decton of flow. They ae ) lectonc cuent : Hee the decton of ths cuent s taken as the decton n whch the electons ae tansfeed. ) Conventonal cuent : The decton of ths cuent s taken as opposte to that of electonc cuent. 4. a) Fee electons ae chage caes n metals. b) Postve and negatve ons ae chage caes n lquds. c) Postve ons and electons ae chage caes n gases. d) Holes and electons ae chage caes n semconductos. 5. The cuent n dffeent stuatons s calculated as follows: a) Due to tanslatoy moton of chage : If n patcles, each of chage q passes though a gven aea nq n tme t seconds then = t b) Due to otatoy moton of chage : If a pont chage q s movng n a ccle of adus wth speed q e qv v, constant fequency f and tme peod T then = = = qf = t T π 6. AC and DC : a) If the magntude and decton of cuent does not vay wth tme. It s known as dect cuent DC.

2 Cuent lectcty b) If a cuent s peodc.e. magntude vaes peodcally and polaty eveses afte each half cycle, t s known as altenatng cuent (AC). 7. lectc cell : a) It s a devce whch convets chemcal enegy nto electcal enegy. b) Thee ae two types of cells ) Pmay cell ) Seconday cell c) compason of pmay and seconday cells: Pmay cell ) Convets chemcal enegy nto electcal enegy ) Ths cannot be echaged. ) The e.m.f s less and ntenal esstance s moe v) In ths the conveson of chemcal enegy nto electcal enegy s an evesble pocess g: Denal cell, voltac cell, cadmum cell, dy cell, Laclanche cell etc. Seconday Cell lectcal enegy s fst stoed n the fom of chemcal enegy and then agan gets conveted nto to electcal enegy on dawng cuent fom t. Ths can be echaged The e.m.f s moe and ntenal esstance s less In ths the conveson of chemcal enegy n to electcal enegy s a evesble pocess. g: Lead accumulatos, dson cell 8. lectomotve foce (e.m.f) of a Cell : a) The wok done s cayng a unt postve chage once n the whole ccut ncludng the cell, s defned as the electomotve foce. b) lectomotve foce s the potental dffeence between the temnals of a cell n open ccut. c) lectomotve foce depends on () natue of electolyte () metal of the electodes. d) lectomotve foce does not depend on () aea of plates () dstance between the electodes (3) Quantty of electolyte (4) sze of the cell. e) lectomotve foce s the chaactestc popety of the cell. The decton of cuent nsde the cell s always fom negatve to postve electode. f) The unt of electomotve foce s volt. 9. Intenal esstance () : The ntenal esstance of a cell s the esstance offeed by the column of the electolyte between the postve plate and the negatve plate. ) The ntenal esstance of a pefect cell o deal cell s zeo. ) Intenal esstance depends on a) stength of electolyte ( stength) b) dstance between plates ( d) c) aea of the plates A d) tempeatue of electolyte t

3 Cuent lectcty 0. elaton between MF and PD: ) In case of chagng of a cell a) The cuent flows fom +ve to ve temnal nsde the cell. b) > c) = + ) In case of dschage of a cell a) The cuent flows fom ve to +ve temnal nsde the cells b) < c) = 3) The dffeence between and s called lost volts lost volts = = 4) A cell of emf and ts esstance s connected to esstance. a) = + b) P.D. acoss esstance s gven by = = + c) Facton of enegy useful = = + d) % of factonal useful enegy= 00 = 00 + e) Facton of enegy lost = = = + f) % of lost enegy = 00 + ( ) g) = h) Fo sngle cell, the condton fo maxmum cuent s =.. Back emf : a) The coppe electode gets coveed wth a laye of hydogen and ths hndes flow of cuent. In the neghbouhood of both electodes, the concentatons of ons get alteed. Ths esults n an emf actng n a decton opposte to the emf of the cell. Ths s called back emf. b) Ths fomaton of hydogen aound the anode s called polazaton. c) To educe the back e.m.f manganese doxde and potassum dchomte ae added to electolyte of cell. These ae called depolazes.. Sees combnaton of cells : a) = n b) = n c) When cells of e.m.f. s,, 3. and of ntenal esstances,, 3.. ae connected n sees acoss an extenal esstance, the cuent s gven by I I I I I 3

4 = + ( ) 3 d) If the e.m.f s of all the n cells and the ntenal esstances ae same, then = Cuent lectcty n ( + n) e) If n >>, then = /,.e the cuent obtaned fom n cells s equal to that obtaned fom a sngle cell. f) If n << then = n /. g) Ths type of combnaton s used when the ntenal esstance of battey s neglgble n compason to the extenal esstance and e.m.f equed s hgh. h) In ths combnaton same cuent flows though all the cells. 3. Wongly connected cells : Suppose by mstake m cells ae wongly connected n above ccut then a) Total emf = emf due to popely connected cells emf due to wongly connected cells = (n m) m = (n m) b) Total ntenal esstance of cells = n c) Total esstance n the ccut = + n (n m) d) The cuent n ccut = + n 4. Cell n paallel : ) = n ) The e.m.f of the combnaton s equal to the e.m.f of a sngle cell.e. = = = 3 = = + m ) If >> then I = m/ = n (cuent obtaned fom a sngle cell) v) If << then = / Ths type of combnaton s used when >> and moe cuent s equed n the ccut. v) If the e.m.f of m cells and the ntenal esstance ae dffeent then m m ) = n m ) I= n ) = total 4) total = n = + 4

5 Cuent lectcty 5. If two cells of emf and havng ntenal esstances and ae connected n paallel to an extenal esstance, then ) + + a) The effectve emf, = + + b) The effectve ntenal esstance, = c) Cuent though the ccut, = + + d) = + e) = and = ) + + a) The effectve emf, = + b) The effectve ntenal esstance, = c) Cuent though the ccut, = + + d) = e) = and 6. Mxed goupng of cells : + = n mows ) The e.m.f of cells n a ow = n. ) Total e.m.f of the combnaton = n 5

6 Cuent lectcty ) The total ntenal esstance = m n v) The total esstance of the ccut = + m n v) The cuent flowng though the extenal esstance () n mn = = n m + n + m v) Fo maxmum cuent to flow though the extenal ccut, the extenal esstance should be equal to the total ntenal esstance. o = m n o, m = n 7. Two cells f e.m.f.s and be connected n a ccut. Let and be the ntenal esstance of the cells. + a) The cuent though the ccut I = + b) The temnal voltage acoss the cells = I = I 8. Let two cells of e.m.f.s and be connected n paallel n a ccut. Let and be the ntenal esstance of the cells. a) The decton of the esultant cuent s detemned by the decton of the hghe e.m.f. b) If <, the cuent though the ccut s I =. + I I c) Whle the cell s dschagng, the cell s n the chagng. The temnal voltage acoss the cells = I and = + I. 9. Ohm s law : At constant tempeatue, the cuent () flowng though a conducto s dectly popotonal to the potental dffeence () between ts ends. α o = whee s the electcal esstance of the conducto a) Ohm s law s not a unvesal law. b) Conductos whch obey Ohm s law ae called ohmc (o) lnea conductos. x. metals. c) The gaph between and I fo ohmc conducto s staght lne passng though the ogn. d) Conductos whch do not obey Ohm s law ae called Non ohmc (o)non lnea conductos. x:cabon compounds, electolytes, tansstos, dodes, semconductos, dschage tubes, Themonc valves, vacuum tubes. e) The gaph between and fo non ohmc esstance s a cuve f) Metal conducto acuum tube lectolyte Themsto 0. Themsto : a) It s a themal essto. b) It s a heat senstve nonohmc devce. 6

7 Cuent lectcty c) Made of semconducto compounds as oxdes of nckel, on, cobalt and Cu. d) It s enclosed n a capsule wth an epoxy suface. e) Symbol s o f) One type of themsto has hgh postve tempeatue co-effcent (PTC) of esstance. g) Anothe type of themsto has hgh negatve tempeatue co-effcent (NTC) of esstance. h) () NTC themsto s used as esstance themomete fo measung low tempeatues of the ode of 0 K. () Hgh esstance at low tempeatue makes t possble to measue low tempeatue vey accuately. ) Themstos one n the fom of beads, dscs o ods to whch a pa of platnum wes ae povded at leads. j) A tny bead fom themsto seves as themomete and can measue tempeatue changes of the ode as small s 0 3 K. k) Themsto used n measung the ate of enegy (powe) n a mno wave beam. l) Themsto used n ado ccuts to avod sudden and lage suge of cuent. m) Themsto s used as themostat.. esstance : a) The popety by vtue of whch a conducto opposes the flow of chage n t s known as esstance. b) It s measued as the ato between potental dffeence between the ends of the conducto and cuent flowng n the conducto = /. c) SI unt of esstance s Ohm. ohm = volt / amp d) Ohm s the esstance of a conducto though whch a cuent of ampee flows when the potental dffeence between ts ends s volt. e) Dmensons fomula s ML T 3 I. f) Fo good conductos esstance s vey low and fo nsulatos o bad conductos t s hgh.. Conductance : a) The ecpocal of esstance s known as conductance G = /. b) SI unt of G s semen (S) (o ohm o mho) c) Conductance deceases on nceasng tempeatue 3. Dependence of esstance : a) esstance of a conducto s dectly popotonal to ts length and nvesely popotonal to ts aea of coss secton. = S o ρ A A A Hee S o ρ s known as esstance o specfc esstance ρ = Whee s adus of coss secton. π 7

8 8 Cuent lectcty ρl ρl ρ ρm ρl d b) = = = = = A A A d m c) esstance does not depend on cuent and potental dffeence. Though esstance of a lnea conducto s ndependent of appled voltage, fo a gven body t s not unque and depends on length and aea of coss secton. (.e how the potental dffeence s ρ appled)if,b, h denote length, beadth and thckness of a slab, ( >b>h), max = and bh ρh mn = b 4. Specfc esstance : a) It s equal to esstance of the conducto of unt length and unt aea of coss secton. s A b) α o = o s = A A c) S.I. unt : Ohm mete d) It depends only on the mateal of the conducto and tempeatue. e) It s ndependent of dmensons of the conducto. f) Fo slve and coppe specfc esstance s small g) Fo Nchome, constantan, Magann t s lage. 5. Conductvty : (o) specfc conductance (σ) : a) It s ecpocal of esstvty. σ = = s A b) S.I unt : semen / m c) Fo nsulatos σ = 0 d) Fo pefect conductos, σ = nfnty 6. Tempeatue co-effcent of esstance (α) : a) It s defned as the change n specfc esstance (o esstance) pe C se of tempeatue to the ognal specfc esstance (o esstance) at 0 C. ρt ρ0 b) α = ρ0 t y t α = +ve 0 c) α = 0t α 0 α = ve c) ρ t = ρ0( + αδt) () x t d) t = 0 ( + αδt) () ρ 0 and 0 ae the specfc esstance and esstance at 0 C, ρ t and t ae the coespondng values at t C. e) If and ae esstances at t C and t C then α =. t t f) Fo small tempeatue vaaton, ρ T = ρt [ + α(t To )] whee ρ o T and ρ o T ae the esstvtes at tempeatues T o and T espectvely and α s a constant fo a gven mateal and s called the tempeatue coeffcent of esstvty. dρ α = ρ dt

9 Cuent lectcty 7. Sees connecton : ) Cuent s the same though all the esstos ) Total p.d.= sum of ndvdual p.d.s acoss each essto. ) Indvdual p.d. s dectly popotonal to ndvdual essto. v) Total esstance s geate than the geatest ndvdual esstance. v) Total esstance = sum of the ndvdual esstances. = v) Two esstances n sees : 3 a) The total esstance S = + b) = + c) = d) = + = v) A conducto and Sem conducto ae connected n sees. If the esstance of the combnaton s same at all tempeatues then α = α whee, ae esstances of conducto and sem conducto. 8. Paallel connecton : ) Potental dffeence emans the same acoss each essto. ) Total cuent=sum of the ndvdual cuents. ) Indvdual cuents ae nvesely popotonal to the ndvdual esstances. v) ffectve esstance s less than the least ndvdual esstance. v) When a numbe of conductos ae connected n paallel, the ecpocal value of the esultant esstance s equal to the sum of the ecpocal values of the ndvdual esstances. = v) Two esstances n paallel a) The total esstance P = + b) I = c) I = I + I + 3 ; = I = I 3 3 I I 9. If S and P be the esultant esstance of esstances and, when connected n sees and paallel then = S + S 4sP = S + S 4sP 9

10 Cuent lectcty 30. If n equal esstances each of esstance ae connected to fom tangle (o) Squae (o) Polygon then effectve esstance between any two adjacent cones s n =. n 3. When twelve dentcal esstos each of esstance Ω ae connected n the fom of a skeleton cube, the effectve esstance acoss () the ends of a sde s (7/)Ω, () the opposte vetces on the same face s (3/4)Ω and () the dagonally opposte vetces s (5/6)Ω. 3. Kchhoff's laws : a) Fst law : ) The algebac sum of electc cuents meetng at a juncton s zeo. fo the juncton 'P' ; = 0 (o) + = ) Kchhoff's fst law s known as juncton law o pont law of kchhoff's cuent law ) Kchhoff's fst law obeys law of consevaton of electc chage. b) Second Law : ) the algebac sum of emfs o potental dffeences aound a closed ccut s zeo. Fo the closed ccut ABCDA = 0 ) Second law s known as loop theoem o kchhoff's voltage law. ) Kchhoff's second law obeys law of consevaton of enegy. c) Sgn conventon n kchhoff's laws: ) Whle gong fom +ve of a battey to the negatve though a cell, emf s negatve. ) Whle gong n the decton of the cuent though a conducto, potental dffeence s negatve. 33. Wheatstone bdge : ) Wheastone bdge s a ccut used to compae the ato of nealy equal esstance. It B conssts of fou ams, each consstng a essto. P ) If two of the esstos of the fou ae known, the othe two can be compaed. ) If thee esstances ae known the fouth one can be calculated. A G v) If the cuent though the galvanomete n a Wheastone bdge s made zeo, then the bdge s balanced. D v) Unde balanced condton : a) P = Q S b) The same cuent passes though the P& Q. c) The same cuent passes though the & S d) The P.D. acoss the ends of the galvanomete s zeo. e) When galvanomete and cell ae ntechanged, the balance pont s not effected. ( P + Q )( + S ) f) The effectve esstance = P + Q + + S v) Wheatstone s bdge s moe senstve f P = Q = = S v) The numbe of closed ccuts n bdge = Q S ( ) C 0

11 Cuent lectcty 34. Mete bdge : ) It woks on the pncple of Wheastone Bdge. It s the smplfed fom of Wheatstone Bdge. ) It s used to fnd a) unknown esstance of a we b) specfc esstance of the we c) and also to compae esstances. esstance n the left gap ) When the Mete bdge s balanced then = esstance n the ght gap 00 Whee s the balancng length fom the left end. v) A hgh esstance box s connected n sees to the galvanomete to potect t fom hghe cuents. v) The bdge we (mangann we) ha low α-value. v) Mete bdge s moe senstve f = 50 cm v) The esstance of coppe stp s called end esstance. v) The esstance n two gaps (x and ) ae ntechanged to educe the effect of end esstance. x) If a conducto s connected n the left gap and t s heated then blanchng pont shfts towads ght. x) If a semconducto s connected n the left gap and t s heated then balancng pont shfts towads left. 35. Potentomete : ) It s a devce whch s used to a) compae the e.m.f.s of two cells, b) to detemne the e.m.f of a cell c) detemne the ntenal esstance of a cell d) calbate a voltmete and an ammete e) detemne the cuent n a ccut, f) detemne unknown esstance, g) measue themo emfs. ) A cell of and ntenal esstance n the pmay ccut mantans unfom potental gadent along the length of ts we. ) Cuent though the potentomete we, = + v) Potental gadent o potental dop pe unt length = whee 'l' s the total length of potentomete we, '' s the total esstance of the we and '' s the cuent though potentomete we due to pmay ccut. v) If a esstance s s connected n sees wth the potentomete we then =. + + v) potental dop pe unt length = + + S v) Compason of emfs usng potentomete : S

12 Cuent lectcty a) and ae balancng lengths when two cells of emfs, and ae connected n the seconday ccut. one afte the othe then, = b) By sum and dffeence method, + L L + L = o =. L L L v) Intenal esstance of a cell = = When = balancng length fo the cell connected n the seconday ccut. = balancng length when a esstance s connected n paallel to the cell. = emf of the cell n the seconday ccut = Temnal voltage x) The senstvty of potentomete can be nceased by deceasng the potental gadent..e., by nceasng the length of potentomete we fo a gven B. x) The best nstument fo accuate measuement of the e.m.f of cell s potentomete because t does not daw cuent fom cell. x) Potentomete acts lke a voltmete of nfnte esstance. x) b (emf of battey n the pmay ccut ) must be geate then c ( emf of cell n the seconday ccut) othewse e.m.f wll not be balanced even ove the complete length of we. x) + ve temnals of both battey and cell must be connected at same pont othewse I b and I c wll be n same decton and null pont s neve obtaned. 36. LCTICAL POW: The ate at whch wok s done n mantanng the cuent n electc ccut. lectcal powe W P = = I = I = watt (o) joule / sec t 37. lectcal negy : The electc enegy consumed n a ccut s defned as the total wokdone n mantang the cuent n an electc ccut fo a gven tme. t lectcal negy = t = Pt = I t = S.I. unt of electc enegy s joule whee Joule=watt sec = volt ampee sec Kwh = 000Wh = J Bulbs connected n Seees:

13 Cuent lectcty If Bulbs (o electcal applances) ae connected n sees, the cuent though each esstance s same. Then powe of the electcal applance P & = P t.e. In sees combnaton; the potental dffeence and powe consumed wll be moe n lage esstance. When the applances of powe ae n sees, the effectve powe consumed (P) s = e. effectve powe s less than the powe of ndvdual applance. P P P P3 If n applances, each of equal esstance ae connected n sees wth a voltage souce, the powe dsspated Ps wll be Ps = n. 39. Bulbs connected n paallel: If Bulbs (o electcal applances) ae connected n paallel, the potental dffeence acoss each esstance s same. Then P and I..e. The cuent and powe consumed wll be moe n smalle esstance.. When the applances of powe P, P, P 3... ae n paallel, the effectve powe consumed (P) s P = P+ P + P e. the effectve powe of vaous electcal applcance s moe than the powe of ndvdual applance. 3. If n applances, each of esstance ae connected n paallel wth a voltage souce, the powe dsspated Pp wll be S n PP = = ( /n) PP = n ( o) P = n P P P S Ths shows that powe consumed by n equal esstances n paallel s n tmes that of powe consumed n sees f voltage emans same. 4) In paallel goupng of bulbs acoss a gven souces of voltage, the bulb of geate wattage wll gve moe bghtness and wll allow moe cuent though t, but wll have lesse esstance and same potental dffeence acoss t. 5) Fo a gven voltage, f esstance s changed fom to, powe consumed changes fom P to n 3 np P = whee = n, then n P = = = np. ( /n) 6) Flament of lowe wattage bulb s tnne thnne that of hghe wattage bulb.e. flament of 60 watt bulb s hghe than that of 00 watt bulb. 7) If I s the cuent though the fuse we of length l, adus, specfc esstance P and Q s the ate of loss of heat pe unt aea of a fuse we, then at steady state, I IPl = QA o = Q π l π π Q I = 3 3/ I P Hence cuent capacty of a fuse s ndependent of ts length and vaous wth ts adus as.

14 Cuent lectcty 8) If t,t ae the tme taken by two dffeent cols fo poducng same heat wth same supply, then If they ae connected n sees to poduce same heat, tme taken t = t+ t tt If they ae connected n paallel to poduce same heat, tme taken s t =. t + t 4

Physics Exam II Chapters 25-29

Physics Exam II Chapters 25-29 Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do