UNIT # 08 CURRENT ELECTRICITY

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1 XS UNT # 8 UNT LTTY. j uent density n hage density j nev d v d j v d n e, n n n v d n n : v n n d. j nev d n j n e 9. Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 d nev 6...(i) d nev '...(ii) Fom equation (i) & (ii) v v' v 6 v i. v d s so v ne d v P > v Q. i nev d ; L L L env ( nev) L m L L L d nev d, same fo all as the mateial is same fo all. : : 5 : 9 : 5 : 5 : 5 L L L L L alanced Wheatstone idge s 7 6 So ()() This is balanced wheat stone bidge Fom maimum powe tansfe theoem ntenal esistance tenal esistance 6 6 P nitially, Powe acoss P X P Y Finally,, Powe PX, P 9 y Pz 9 Hence P inceases, P y deceases. ltenative method : ightness i when S is closed cuent dawn fom battey inceases because eq deceases. i.e. cuent in X inceases. So bightness of X inceases and cuent in Y deceases. So bightness of Y deceases. i S eq X X Y Y. P ( ) is constant and (+ ) inceases apidly Then P (+ ) P. P i i 5 i i 5 i i 5 i P, P 5 (i )5 P P5 P P5 5 5, P cal/s 5

2 ., s < so > n seies H t H ; H > H n paallel H t H ; H < H Fom (i) & (ii) 676 S S 65 (676) (65) S S 65. & ' ' /. + i().5 + () (s the battey is a stoage battey it is getting chaged) () 5. The coect answe is. Potential gadient ( ) ccoding to question () 9 5L L 9 9 L (i) (ii) fom eq. () 5 voltage diffeence acoss any of the battey. ) a a +. 5 b a b olt. 7.. () g. (though the galvanomete) g (i i g )S (.) () (.)S S. 8. v 9 9 i g b No. of divisions f i, potential diffeence is equal of MF of cell. P Q S 65 Q P S 676 P S...(i) Q 65 P 676 Q S...(ii). Potential gadient () m.5.5 Hee () () - m.5 5. Potential gadient () m 8 6 ffective emf of and ( ) volt / / alancing length N 6. P same 7. (5W ) P, 96 5 ( W ) P, 8 n Seies ( same) m 5cm H t, H so if > then H > H is likely to fuse Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 8

3 Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 8. P L...(i) P L 9L L...(ii) fom eq. (i) & (ii) P P 9 P P P 9.% P P 9 9. n paallel combination the equivalent esistance is less than the two individual esistance connected and in seies combination equivalent esistance is moe than the two individual components.. ) 8 8 volt and. Theefoe. ns. (). iven cicuit can be educed to eading of ammete ( ) eading of voltmete ( ). wie. 5.. Potential diffeence acoss voltmete, () sint. 5 cost (cost) cm/s O,,,5,6 7,8 ',',' ',5',6' 7',8' (let) Points,,...8 ae of same potential and ', ', '...8' ae of same potential. (,,...8 ', ', '...8' ) eq 8 5. Total length of wie () m ; 6. Total esistance of wie () 8/5 s n.5 n O Total numbe of cells equied 5 6 () n. 5 n n.7 6 eq 6 9

4 XS. Fee electon density and the total cuent passing though wie does not depend on 'n'.. (n ) eq 7 i eq ; i / dq 6t dt Powe : P ( 6t) Heat poduced 56 t 6 t t 8 Pdt ( 56 t 6 t)dt / 8 6. t is the concept of potentiomete. joules 6 () 7. y applying node analysis at point b / / a b. 8 > Fom Figue : + i ; i 6 ; ;, H + + i H O / 7 9. Fo wheat stone idge condition is ( ) Theefoe null point is independent of the battey voltage. () eq ; i 7 volt. oth '' and '6' esistos ae shot cicuited theefoe eq of the cicuit in is. ('' '6' eq.) Powe () watt Potential diffeence acoss both '' and '' ('' '' ) 5. i i + Slope of gaph '' and 'i' gives '' intecept of gaph '' and 'i' gives tan y. ('' 'i' '' '' 'i' tan y.). + i and in chaging cuent flows fom positive teminal to negative teminal. ( + i ) Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65

5 . Slope of '' vs 'i' gaph give intenal esistance 5 ('' 'i' 5 ntecept gives the value of e.m.f. volt ( volt ) Maimum cuent is () i ma. f n batteies ae in seies than the cicuit can be made n as i n n n i.e. independent of n. (n n n n ) n i n. f n batteies ae in paallel than the cicuit can be n made as i n i ) (n /n i () Fo voltmete g ( + ) 5 ( + ) + k 8. i min i ma k ma min mp 5 5 Potential i min PM coss potentiomete i ma PM f e.m.f of c is geate than the e.m.f. of the '' So does not play any ole of zeo deflection in galvanomete. '' i is diectly popotional to n. n Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 5. n paallel combination cuent gets divided theefoe paallel combination suppots i i + i is in seies cuent emain same theefoe the seies combination suppots i. ( i i + i i ) 6. s powe in is maimum when the cuent in it is maimum. uent in it will maimum when the value of eq is minimum ( eq ) Heat i T(6)() 7 W 7. Fo mmete g ( g ) g g. oth ae in paallel / i i i / /. ssume + Means balance wheat stone bidge P ; Q S 5

6 i/6 i/ i i/ i/ i/ i/6 i/ i/6 F i/ i/6 H i i/6 So cuent in F etween and ( 9 +.9) ( m). 99 m m m 7. When S open (S ) ssume esistance of ( ) esistance of wie pe unit length. () L. X Y X X When Y shoted + +. ;( + ) ( + ) < ( + +) Now in L 6 L When S closed 5L L + + < + ; ( + ) < On solving we get > ( + ) 5. f all wee in seies all of them would have being getting dischaged. ut since, ae in opposite polaity, they will be getting chaged. ( ) (n ) +i getting chaged i n as (n ) as batteies will be cancelled out n +, + n n n slope So P P P Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 5

7 Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 9. eaanged cicuit between & is :. ( ) (due to symmety) 7 Total esistance of cicuit () 7. i 9 Heat poduced in cell () () 6W uent in esistance connected diectly between 7 7 &. 5 5 ( d 7 7. ) ( + ) d d d ( ) d, ( ) d ( ) Fo null point + m. P Q () () P.5.5 T Q S U, (), + 8 XS Match the column. Fo potentiomete shot cicuit () epends only on pimay cicuit ( ) ( ) if seconday cicuit emain same ( ) if seconday cicuit emain same ( ) S. if emain same S.. fte closing the switch net esistance deceases theefoe thee will be inceases in the cuent. fte closing the switch becomes zeo hence. ( S ) S v v fte shot cicuiting cuent in the esistance becomes zeo theefoe powe become zeo. ( ) ompehensi on. Powe though fuse () P h h heat enegy lost pe unit aea pe unit time () cuent. h / / / 8. P kw volt < volt. t maimum powe delivey, so 5% () 5

8 ompehensi on. s potential of, and ae same potential diffeence acoss them 'zeo'. (, ) o. s, and ae having same potential theefoe we can daw it. (, ) O,, / ; /; /. s point,, ae equipotential (, ) and Now as ompehensi on 5 & n balancing condition, cuent in the cicuit should be zeo which happens at cm accoding to gaph. ( cm ). t balance point () 6. theefoe fo,, ompehensi on. uent is maimum when esistance in the cicuit is minimum. i.e. when S,S,S 5 ae closed because then all esistances will be shotcicuited ma. ( S, S, S 5 ma.. fte egula closing of switches, total esistance deceases gadually. ( ). P ompehensi on, P 7 7., + so P 7 P t, applying kichhoff's nd law in the cicuit containing cell, (, ) whee is the cuent at, & is the emf of the cell.. (. ) ompehensi on 6. + i + (.) (5) +. ns. () Loss in powe (). ns. () 5. i (5) (.) W Total input () Loss in powe () Useful powe (), nput powe (5) 7 w Loss in powe () w, ate of convesion () 6 watt Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 5

9 . XS J-Physics 5. y applying pependicula is Symmety () (7).5 volt y symmetic path method Points, F and, ae quipotential, F, ) y applying pependicula ais symmety. Points lying on the line '' have same potential theefoe esistance between and can be emoved 9 '' 9 7. (i) When switch S is open 6 a (S ) 6 b 6. y pependicula is symmety all points,, ae at same potential theefoe junction on this line can be edawn as 5 (,,. a b (6 6 ) (6 ) 6 (ii) Total cuent though cicuit 9 () 6 Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 5.) / + / + / / + / + / 55 6 a 6 b Theefoe 6 8. (i) hemical enegy consumed watt () (ii) ate of enegy dissipation i. watt () (iii) ate of enegy dissipation in esisto ( ) ( i).6 watt (iv) The output enegy to the souce.6 watt ()

10 Taking point '' as efeence potential and its potential to be '' : ('' ) Powe supplied by cell W. y applying node nalysis () ('' ' ' + ( )() '' eq ( ) y solving above equation. n loop i i i i 5 i i+5 ii i F i i i n loop F i i i i+5 n loop F i (i i i ) Put the values of i & i i (+i 5+i 5) ) i i+ i 5 5. icuit can be edawn as 5, eq 5. P P ( ) ( ), eq ; e q uent n + ; 5. y taking 'O' as a efeence potential as cuent though '' is zeo thee should be no potential dop acoss it ('O' '' ) 6 6 alue of '' fo this condition ''. '' and ' ' ae in seies theefoe + and it is in paallel with ( )() '' eq ( ) (i) i ; i t i T i T i T Q i T t (ii) i i T i t dq dt idt T t (iii) Heat i dt [ i i T ] Heat T i T i t i dt tdt T i T i T i T T it Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65

11 Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 7. Submission of cuent at the Node 'X' is (Node 'X' ) / uent 5 8. Potential diffeence acoss voltmete is same as that of 9. 5 i i (i); ( ) +...(ii) y solving (i) and (ii) ; 5. (i) uent due to pimay cicuit (ii) () p i mp pm PM 9volt 9 Potential gadient () 9 ( ).5 6m p i 9 PM et i PM 9.5 volt Potential gadient.5 L.5 S. 8 i, i i Powe developed in it is maimum when etenal esistance intenal esistance. ( ) n 9n n / n. pplying KL ( + ), + ( + ), Powe supplied by a W Powe supplied by b W Theefoe a + b W. Heat developed will be maimum fo the esisto '' because (P..) will be maimum fo the banch containing '5' and '' 5. ('' '5' '' ) 9 ' ' ' ' y applying K..L (i) y applying K..L. in loop ''''' 9 + ( ) (ii) y solving (i) and (ii) uent in esistance is.5. 6.(i) J.d (ii) J d J J J d J J Jd d 6 J d J J

12 7. Potential gadient..5 (.) 7.5m (a) i, i 5 S m 7 (b) S S...5. ( ) 6.5m XS olt 5,M.5 olt. y applying nodal analysis at note '' and ''. ('' '' ) 7 7 and i.e. times the length of any side. O. y symmety and F ae at same potential and and. nd by symmety and ae at same potential. So we can emoved F and ( F F ). y path symmety potential of points,,, is same. (,,, ) eq a a e q ( ) 8. / eq + ( ) (5 ) eq (5 ) ( )(5 ) ( ) ( )(5 ) 5 5 ( )(5 ) eq eq eq (ma) ( )(5 ) d d eq t sin T T / dq t T s so Q dt sin dt T Total heat geneated T T t dt sin dt T T t cos dt T Q T T L / L e d Q 8T d T L L(e ) e e e L e Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65

13 7. uent with both switches opened is - ().5 i 5 e q fte closing the switch (), i 8 i.5 volt y kichoffs fist law () 7 i ; i i (.).( + + ) ( + + )...(i). 5. (.) ( + )...(ii). 5 (.)...(iii). 5 (i) divided by (ii) fte solving.. S S ; (+ +.99) g (+) ; g S ( g ); g (S +) y solving the above equation we get the answes. XS -. n ode to convet an ammete into a voltmete, one has to connect a high esistance in seies with it.. The emf of the standad cell The emf of the seconday cell e Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 9. y solving quation (i), (ii) and (iii).78 ;.5;.5 ssume division have ampee When 9 / 9... (i) When / 5...(ii) e e e. g ;.8; g S g.8 9 ; S S

14 5. On edawing the cicuit between and we get.5 6. Fo a given volume, the esistance of the wie is epessed as olume 8. Let esistances be and then S + and P S n P 9. iven that. n min n paallel : hence & 9 l 9 y So, the change in esistance of wie will be % % cm y 8 y 8cm y On edawing the diagam, we get Now a -a y a 5 cm a a oltage acoss Hence, voltage acoss uent though Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 6

15 Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65. 5 s 5 and ae in seies value of 5 / 5,, 5 5 uent in the cicuit () potential diffeence acoss cell with esistance ut potential diffeence. uent supplied by the souce to the etenal esistance f () >>; which will be constant() 5. The intenal esistance of a cell e l v l T 6. Kichoff's fist law is based on law of consevation of chage.kichoff's second law is based on law of consevation of enegy. 7. Specific esistance ( ) ; diamete d d ( ) ; d d? esistance fo esistance dia dia 8. iven that 9.. T T? [+()]...(i) T]...(iii) On dividing eq. () by eq. (), we get T T On solving, we get T P Q S S Unde balanced condition () P P S S Q SS Q SS S S 5 5 On edawing the cicuit, we get () 5 5 t is a balanced Whetstone bidge having eff as eff 5 5 6

16 5 5 Fo paallel combination () ( t) ( t) eq 5 The cuent deliveed by the souce is 5.5. Let the esistance of the wie at is also let the tempeatue coefficient of esistance is. 5 [+(5 )]...(i) Similaly [+( )]...(ii) On dividing equation (ii) by equation (i), we get. 5 5 ; / On eplacing 5 5 / in equation (i), we get hoosing as oigin,( ) ( t) ( t) pt ( + p t) ( + t) + ( + t) using binomial epansion () p t t + t p [.].% incease Fo combination 5%. i., 7 -m, 8 7 m 7 i. 7. /m 8. ue to geate heating as H 5W get fused.. H 5W 6 5. j a b d a b a a a b a 7. Fo seies combination () S (given) S () bulb Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65

17 () heate So change in voltage. olt. To incease the ange of ammete, esistance should be deceased (So additional shunt connected in paallel) so total esistance to ammete deceases. ( ) Single hoice XS -. Net esistance of the cicuit is 9. cuent dawn fom the battey, 9. uent can be independent of 6 only when,,, and 6 fom a balanced wheatstone s bidge. Theefoe,,,, 6 6. n the fist case () H t t mst..(i) When length of the wie is doubled, esistance and mass both ae doubled. Theefoe, in the second case ( N ividing eq. (ii) by (i), we get N 8 N 6 N6.t (m)st..(ii) 5. The cicuit can be edawn as follows Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 i cuent though esisto 8 i i 8 i i i Potential diffeence between and is 9 (+) 8i i.5 i i.5 Similaly, potential diffeence between and ( ) i (+) i (.5) 8i i.5 Theefoe, i i i.5.5 i.5. s thee is no change in the eading of galvanomete with switch S open o closed. t implies that bidge is balanced. uent though S is zeo and S S, P Q. P P 6. P so, P Now, W W 5 5 Q Q and P P + Q & 6 W and 5 W :W :W 5:5 :6 W <W <W 7. mmete is always connected in seies and voltmete in paallel. ( 8. The atio will emain unchanged. Q 6

18 9. Pi uent is same, so P. n the fist case it is, in second case it is (/), in 6. case it is & in case the net esistance is Pi P., (/),. PQ < < < P < P <P < P 5, Q and P PQ is maimum., and ae known esistance. The unknown esistance is connected between and., > > pplying P Q S We have..(i) 8...(ii) Solving eq. (i) and (ii) we get 7. iven cicuits can be educed to P 9W P 9W P 8W. ab i g.(i i g )S i i g S S (i-i ) g i a i g b Substituting the values, we get i. m. W. Theefoe, fom fist law of themodynamics, W. U Q i t () () (5 6) J kj. uent in the espective loop will emain confined in the loop itself. Theefoe, cuent though esistance. uent always flow in closed path. 5. H t same So H So H H H, same P and W > 6W > W 6 6 [Note : lthough () 6 + so at oom tempeatue () (pplicable 6 6 Only at oom tempeatue) ()] L L independent of L Lt t Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65

19 Multiple hoice. v e q amp K p The heostat is as shown in figue. attey should be connected between and and the load between and 9. K m () uent () is 7.5 m () oltage dop acoss L is 9 volt L 9 volt () P P v () fte intechanging the two esisto and P. 7.5 m eq (8) P L 9 ssetion - eason. ns. L (v ) 9 v v Subjective Poblems. (i) Thee ae no positive and negative teminals on the galvanomete because only zeo deflection is needed. (ii).. Slide wie bidge is most sensitive when the esistance of all the fou ams of bidge is same. Hence, is the most accuate answe. 5. Node-6\:\ata\\Kota\J-dvanced\SMP\Phy\Solution\Unit-7 & 8\-uent lecticity.p65 J (iii) J 6 cm J cm f no deflection is taking place. Then, the Wheatstone s bidge is said to be balanced, Hence, X J J X 8 6 J J and J as.5 / J so.5 65

Phys 1215, First Test. September 20, minutes Name:

Phys 1215, First Test. September 20, minutes Name: Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo