A and B are two spherical isolated conductors placed at large distance having radius ratio r =

Transcription

1 Excis * MARK IS MORE THAN ONE CORRECT QUESTIONS. SECTION A : DEFINITION OF CAPACITANCE A. A. Whn 0 C chag is givn to an isolatd nducto of capacitanc 5 F. Find out followi Potntial of th nducto Engy stod in th lctic fild of nducto (iii) If this nducto is now nnctd to oth isolatd nducto of total chag 50 C and capacity 0 F thn find out on potntial of both th nductos. (iv) Find out hat dissipatd dui th pocss of chag distibution. (v) Find out atio of final chags on nductos. (vi) Find out final chags on ach nducto. A A and B a two sphical isolatd nductos placd at lag distanc havi adius atio = and B QA chag atio Q =. Find out followi if thy a joind by a nducti wi B A Ratio of final chag dnsitis. B Calculat th capacitanc of a paalll plat capacito havi 0 c 0 c squa tal plats which a spaatd by a distanc If th plats ntain qual but opposit chag of agnitud 0 C. thn find out ngy stod btwn th plats of capacito. A. Q' A Ratio of final chags Q'. B An ai-filld paalll-plat capacito is to b nstuctd which can sto C of chag whn opatd at 00 V. What can b th iniu plat aa of th capacito? Th dilctic stth of ai is 06 V/. A 5. Plat A of a paalll ai filld capacito is nnctd to a spi havi foc nstant k and plat B is fixd. If a chag + q is placd on plat A and chag q on plat B thn find out xtnsion in th spi in quilibiu. Assu aa of plat is A. A 6. Th capacity of an isolatd nducti sph of adius R is popotional to : R (/R) /R R A 7. Wok don in placi a chag of C on a ndns of capacity 00 ifaad is 6 0 J. 0 6 J 0 0 J 0 J A 8. If two nducti sphs a spaatly chagd and thn bought in ntact: Th total ngy of th two sphs is nsvd Th total chag of th two sphs is nsvd Both th total ngy and chag a nsvd Th final potntial is always th an of th oiginal potntial of th two sphs A 9. Th adii of two tallic sphs a 5 c and 0 c and both cay qual chag of 75 C. If th two sphs a shotd thn chag will b tansfd 5 C fo ll to bigg 5 C fo bigg to ll 50 C fo ll to bigg 50 C fo bigg to ll A 0. Two isolatd chagd tallic sphs of adii R and R havi chags Q and Q spctivly a nnctd to ach oth, thn th is: No cha in th ngy of th syst An incas in th ngy of th syst Always a dcas in th ngy of th syst A dcas in ngy of th syst until q R = q R a A.

2 A. A thin tal plat P is instd btwn th plats of a paalll plat capacito of capacity C in such a way that its dgs touch th two plats [Fig.]. Th capacity now bs: C/ C Zo A. Two paalll tal plats cay chags +Q and Q. A tst chag placd btwn th plats xpincs a foc F. Th plats a thn ovd apat so that th spaation btwn th is doubld. Th foc on th tst chag will now b F/ F F/ F A. 6 idntical cuy dops bin to fo on bigg dop. Th capacitanc of bigg dop, as pad to that of ll dop will b 8 tis 6 tis tis 6 tis A. Th foc of attaction btwn th plats of a chagd ndns is q/ 0A q/ 0A qa/ 0A Non of th abov On incasi th plat spaation of a chagd ndns (batty is not nnctd), its ngy incass dcass ains unchad Non of th abov A 6. A paalll plat capacito is chagd and thn isolatd. On incasi th plat spaation Chag Potntial Capacity ains nstant ains nstant dcass ains nstant incass dcass ains nstant dcass incass incass incass dcass A 7. Two isolatd tallic solid sphs of adii R and R a chagd such that both of ths hav chag dnsity. Th sphs a locatd fa away fo ach oth, and nnctd by a thin nducti wi Thn th nw chag dnsity on th bigg sph is a A SECTION B : CIRCUITS WITH CAPACITOR AND USE OF KCL AND KVL A capacitanc C, a sistanc R and an f a nnctd in sis at t = 0. What is th axiu valu of (a) th potntial diffnc ass th sisto, (b) th cunt in th cicuit, (c) th potntial diffnc ass th capacito, (d) th ngy stod in th capacitos. () th pow dlivd by th batty and (f) th pow nvtd into hat. B. A paalll-plat capacito with th plat aa 00 c and th spaation btwn th plats.0 c is nnctd ass a batty of f volts. Find th foc of attaction btwn th plats. B. Find th chag on th capacito shown in figu B. Find out valus of i, i and i in stady stat B. Find th final chags on th fou capacito of capacitanc F, F, F and F shown in figu (Assui initially thy a unchagd).

3 B 5. Find th chag supplid by th batty in th aant shown in figu Find out chag on ach capacito. Find th potntial diffnc Va Vb btwn th points a and b shown in ach pat of th figu B 7. Th unchagd capacitos of capacitanc C = F, C = F and C = F a nnctd as shown in figu to on anoth and to points A, B and D potntials A = 0 V, B = 5 V and D = 0 V. Dtin th potntial ( 0) at point O. B 8. A capacito with stod ngy.0 J is nnctd with and idntical capacito with no lctic fild in btwn. Find th total ngy stod in th two capacitos finally. B 9. A 5.0 F capacito is chagd to V. Th positiv plat of this capacito is now nnctd to th ngativ tinal of a V batty and vic v. Calculat th hat dvlopd in th nncti wis. B 0. Fiv capacitos a nnctd as shown in figu blow. Initially S is opnd and all capacitos a unchagd. Whn S is closd, stady stat is obtaind. Thn find out potntial diffnc btwn th points M and N. B. Th low plat of a paalll plat capacito suppotd on a igid od. Th upp plat is suspndd fo on nd of a balanc Th two plats a joind togth by a thin wi and subsquntly disnnctd. Th balanc is thn untpoisd. Now a voltag V = 5000 volt is applid btwn th plats. Th distanc btwn th plats is d = 5 and th aa of ach plat is A = 00 c. Thn find out th additional ass placd to aintain balanc [All th lnts oth than plats a asslss and nonnducti] B. Th final potntial diffnc btwn th plats of ndns C in th givn figu will b a B 6. B. V R R R R R V R R R VR R R K V Th agnitud of chag on ith of th plats of ndns C in th adjoini cicuit is CE CER (R ) CER (R ) CER (R )

4 B *. In th cicuit shown in figu th switch is closd at t = 0. A lo ti aft closi th switch voltag dop ass th capacito is E E cunt though th batty is R R B 5 R E ngy stos in th capacito is C R R cunt though th capacito bs zo Th plat spaation in a paalll plat ndns is d and plat aa is A. If it is chagd to V volt thn th wok don in incasi th plat spaation to d will b 0 AV d 0 AV d 0 AV d 0 AV d In th adjoini diaga, th ndns C will b fully chagd to potntial V if S and S both a opn S and S both a closd S is closd and S is opn S is opn and S is closd. B 7. Two ndnss of capacitancs C and C a chagd to potntials V and V spctivly. Engy will not b xchad btwn th whn ths a nnctd in paalll, if (plats of polaity nnctd togth) V = V C = C CV /= CV B 6. C C V = V A 0 F ndns is chagd to a potntial of 00 volt. It is now nnctd to anoth unchagd ndns Th on potntial achd is 0 volt. Th capacitanc of snd ndns is F 5 F 0 F F B 9. A paalll plat ndns of capacity C is nnctd to a batty and is chagd to potntial V. Anoth ndns of capacity C is nnctd to anoth batty and is chagd to potntial V. Th chagi battis a ovd and now th ndnss a nnctd in paalll in such a way that th positiv plat of on is nnctd to ngativ plat of anoth Th final ngy of this syst is 5CV 6 CV 9CV Two paalll plat ndnss of capacity of 0F and 0F a chagd to th potntials of 0V and 0V spctivly. If likly chagd plats a nnctd togth thn th on potntial diffnc will b 00 V 50 V V 0 V B 0. zo a B 8. B. A capacito of capacitanc C 0 is chagd to a potntial V 0 and thn isolatd. A capacito C is thn chagd fo C 0, dischagd and chagd again ; th pocss bi patd n tis. Du to this, potntial of th lag capacito is dcasd to V valu of C is : C0 [V0/V]/n C0[(V0/V) /n ] C0 [(V0/V) ] C0 [(V/V0)n + ] SECTION C : COMBINATION OF CAPACITORS C. Th capacitos havi capacitancs 0 F, 0 F and 0 F a nnctd in sis with a V batty. Find th chag on ach of th capacitos. How uch wok has bn don by th batty in chagi th capacitos?

5 Consid th situation shown in th figu Th switch S is opn fo a lo ti and thn closd. (a) Find th chag flown though th batty whn th switch S is closd. (b) Find th wok don by th batty. (c) Find th cha in ngy stod in th capacitos. (d) Find th hat dvlopd in th syst C. Find th potntial diffnc btwn th points A and B and btwn th points B and C of figu in stady stat C. If you hav sval.0 F capacitos, ach capabl of withstandi 00 volts without bakdown, how would you assbl a bination havi an quivalnt capacitanc of; (a) 0.0 F o of (b). F, capabl of withstandi 000 volts. C 5. A capacito of capacitanc C =.0 F chagd upto a voltag V = 0 V is nnctd in a paalll to th tinals of a cicuit nsisti of two unchagd capacito nnctd in sis and possssi th capacitanc C =.0 F and C =.0 F. What chag will flow though th nncti wis? C 6. Tak th potntial of th point B as shown in figu to b zo. (a) Find th potntials at th point C and D. (b) If an unchagd capacito is nnctd btwn C and D, what chag will appa in this capacito? C 7. Find th potntial diffnc Va Vb btwn th points a and b shown in ach pat of th figu C 8. Convinc youslf that pats (a), (b) and (c) of figu a idntical. Find th capacitanc btwn th point A and B of th assbly. a C.

6 C 9. Find th quivalnt capacitancs of th binations shown in th figu btwn th indicatd points. C 0. Find th quivalnt capacitanc of th infinit ladd shown in th figu btwn th points A and B. If now ach capacito is placd by a capacito which is doubl in capacitanc thn pat th qustion. Find th chag appai on ach of th th capacitos shown in figu Find out total wok don by th batty dui chagi pocss. C. Th ndnss C, C and C a nnctd to a 00 Volt D.C. souc as shown in th figu If th chags stod on th plats of C, C. and C a qa, qb and qc, qd and q, qf spctivly, thn C. 00 Coulob 9 qb + qd + qf = 0 qb = qd = qf qa + qc + q = 50 Coulob a C.. n th followi figu, th chag on ach ndns in th stady stat will b C 6 C 9 C C qb + qd + qf = Th iniu nub of ndnss ach of capacitanc of F, in od to obtain sultant capacitanc of 5 F will b C 5. How th svn ndnss, ach of capacity F, should b nnctd in od to obtain a sultant capacity of 0 F? C. C 6. Th potntial diffnc btwn th points P and Q in th adjoini cicuit will b- (CC C C ) E (C C ) (C C ) C C E C C (C C ) (C C CC ) E (C C ) (C C ) (C C CC ) E (C C C C )

7 C 7. Th sultant capacity btwn th points A and B in th followi cicuit will b- C C C C Th quivalnt capacity btwn th points A and B in th adjoini cicuit will b C C C C C 9. In th abov pobl th quivalnt capacity btwn th points C and D will b C C C C C 0. In th abov pobl th quivalnt capacity btwn th points A and D will b C C 8C/5 5C/8 C. Th sultant capacity btwn th points A and B in th adjoini cicuit will b C C C C C. Th ffctiv capacity in th followi figu btwn th point P and Q will b F 5 F F F ) Th potntial diffnc btwn th plats of.5 F capacito in th followi cicuit will b8 6 volt C. A a ( 8 volt Th quivalnt capacitanc of th bination shown in Figu is. C C C 5. volt C. C 8. C C In th givn cicuit, th P.D. btwn th points A and B is 0 V. Also C = C = C = C = C5 = F. Chag on C : 0 C 0 C 50 C 5 C Chag on C5 : 0 C 0 C 50 C 5 C (iii) P.D. ass C : 5 V.5 V 7.5 V 0 V

8 C 6. Th capacitanc of th bination btwn 'a' and 'b' is C C C C C 7. Th quivalnt capacitanc btwn th tinals X and Y in th figu shown will b 00 pf 00 pf Fiv capacitos togth with thi capacitancs a shown in th adjoini figu Th potntial diffnc btwn th points A and B is 60 volt. Th quivalnt capacitanc btwn th point A and B and chag on capacito 5 F will b spctivly F, 0 C 6 F, 50 C 5 F, 00 C F, 50 C C pf 00 pf C Non of ths In th aant of th capacitos shown in th figu, ach C capacito has capacitanc of F and ach C capacito has capacitanc of F thn, Equivalnt capacitanc of th ntwok btwn th points a and b is : F (iii) F C F If Vab = 900 V, th chag on ach capacito nast to points 'a' and 'b' is : 00 C C. C 8C a C. In th batty of capacitos shown, all th capacitos hav qual capacitancs. Thn th quivalnt capacitanc of th syst ass th tinals A and B : C 0. C 9. Th quivalnt capacitanc btwn point A and B is C/ C/ C C 600 C 50 C 900 C If Vab = 900 V, thn potntial diffnc ass points c and d is : 60 V 00 V 0 V 00 V A bination aant of th capacitos is shown in th figu C = F, C = 6 F and C = F thn quivalnt capacitanc btwn 'a' and 'b' is : F 6 F F F If a potntial diffnc of 8 V is applid ass points a and b, thn chag on th capacito C at stady stat ndition will b : 8 F 6 C C 6 C

9 C. Each dg of th cub ntains a capacitanc C. Th quivalnt capacitanc btwn th points A and B will b 6C 5 C 7 5C 6 7C SECTION D : EQUATION OF CHARGING AND DISCHARGING D. By valuati i R dt, show that whn a capacito is chagd by nncti it to a batty though a sisto th ngy dissipatd as hat quals th ngy stod in th capacito. How any ti nstants will laps bfo th cunt in a chagi RC cicuit dops to half of its initial valu? Answ th qustion fo a dischagi RC cicuit. D. A capacito of capacitanc 00 F is nnctd ass a batty of f 6.0 V though a sistanc of 0 k fo.0 s. Th batty is thn placd by a thick wi What will b th chag on th capacito.0 s aft th batty is disnnctd? D. Th lctic fild btwn th plats of a paalll plat capacitanc.0 F dops to on thid of its initial valu in. s whn th plats a nnctd by a thin wi Find th sistanc of th wi D 5. A capacito chagd to 50 V is dischagd by nncti th two plats at t = 0. If th potntial diffnc ass th plats dops to.0 V at t = 0 s, what will b th potntial diffnc at t = 0 s? D 6. A 5.0 F capacito havi a chag of 0 C is dischag though a wi of sistanc 5.0. Find th that dissipatd in th wi btwn 5 to 50 s aft th nnctions a ad D 7. A capacito of capacity F is nnctd in closd sis cicuit with a sistanc of 0 7 ohs, an opn ky and a cll of V with ngligibl intnal sistanc: Whn th ky is switchd on at ti t = 0, find; (a) Th ti nstant fo th cicuit. (b) Th chag on th capacito at stady stat (c) Ti takn to dposit chag qual to half that at stady stat If aft fully chagi th capacito, th cll is shotd by zo sistanc at ti t = 0, find th chag on th capacito at t = 50 s. D 8. A 00 F capacito is chagd to 00 volt. It is dischagd though a oh sistanc Th aount of hat gnatd will b Joul Joul 0. Joul 0. Joul D 9. A ga oh sisto and F capacito a nnctd in a sil loop cicuit with a nstant souc of volt. At on snd aft th nnction is ad what a th ats at which; th chag on th capacito is incasi. a D. ( / ) C/s / C/s / C/s ( / ) J/s 6 ( / ) J/s ngy is bi stod in th capacito. 6 ( / ) / J/s 6 / J/s Non of ths

10 (iii) (iv) joul hat is appai in th sisto. 6 / J/s / J/s 6 ( / ) J/s 6 ( / ) J/s ngy is bi dlivd by th souc 6( / ) C/s 6 C/s 6 / C/s 6 ( / ) J/s D 0*. Th chag on th capacito in two diffnt RC cicuits and a plottd as shown in figu Choos th ct statnt(s) latd to th two cicuits. q Both th capacitos a chagd to th agnitud of chag qax Th f's of clls in both th cicuits a qual. Th f's of th clls ay b diffnt t Th f E is o than E O D *. Th instantanous chag on a capacito in two dischagi RC cicuits is plottd with spct to ti in figu Choos th ct statnt(s) (wh E and E a f of two DC soucs in two diffnt chagi cicuits). q RC > RC R C R C R > R if E = E C > C if E = E O t qax A paalll-plat capacito with plat aa 0 c and plat spaation.0 is nnctd to a batty. Th sistanc of th cicuit is 0 k, thn th ti nstant of th cicuit is : 0.8 s 0.6 s s Non of ths D. A 0 F capacito is joind to a batty of f 6.0 V though a sistanc of 00, thn th chag on th capacito.0 s aft th nnctions a ad is : 0 C 66 C 76 C 6 C D. Th plats of a capacito of capacitanc 0 F, chagd to 60 C, a joind togth by a wi of sistanc 0 at t = 0, thn a D. C th chag on th capacito in th cicuit at t = 00 s is : 0 C 60 C C 8 C (iii) th chag on th capacito in th cicuit at t =.0 s is : 0.00 C 60 C C 8 C th chag on th capacito in th cicuit at t = 0 is : 0 C 60 C 0 C D 5. A capacito of capacitanc C is nnctd to a batty of f at t = 0 though a sistanc R, thn th axiu at at which ngy is stod in th capacito is : R R R ti at which th at has this axiu valu is CR ln CR ln CR ln R CR ln

11 An unchagd capacito of capacitancs.0 F is nnctd to a batty of f 6.00 V and intnal sistanc.00 though sistanclss lads. At.0 s aft th nnctions a ad : th cunt in th cicuit is :. A 6 A. A 0 A th pow dlivd by th batty is : 6. W. W.87 W 0 (iii) th pow dissipatd in hat is : 6. W. W.87 W 0 (iv) th at at which ngy stod in th capacito is incasi is : 6. W. W.87 W 8.7 W D 7. Th chag on ach of th capacitos 0.0 s aft th switch S is closd in figu is : C 6.8 C 0.7 C.5 C D 8. Chag on th capacito in th givn cicuit in stady stat ndition is: C 5 C 8 C 6 C D 9. A ntwok of capacitos and sistancs is shown. Cunt in th cicuit idiatly aft ky K is closd and aft a lo ti intval is : E Zo, R E R R R R R E R R, E E R, R R a E E R R, R R R R 5 Fig. shows two idntical paalll plat capacitos nnctd to a batty with switch S closd. Th switch is now opnd and th f spac btwn th plats of th capacitos is filld with a dilctic of dilctic nstant (o lativ pittivity). Thn th atio of th total lctostatic ngy stod in both capacitos bfo and aft th intoduction of th dilctic. D 0. D D *. Two capacitos of F & F a chagd to 50 volt & 0 volt spctivly. Th plats of a capacito a nnctd as shown in th fig. A dischagd capacito of capacity.5 F falls to th f nds of th wi Thn: Chag on th.5 F capacito will b is 80 C. Chag on th F capacito will b 0 C. +V chag flows though A fo lft to ight. +V chag flows though A fo ight to lft. D. An lctic cicuit is as shown in th figu Th clls a of ngligibl intnal sistancs. Find : (in stady stat) Th cunts in sistanc and th cll of 8 volt. Th chag on th capacito.

12 D. Each capacito shown in figu has a capacitanc of 5.0 F. Th f of th batty is 50V. How uch chag will flow though AB aft th switch S is closd? SECTION E : CAPACITOR WITH DIELECTRIC E. Th two paalll plats of a capacito hav qual and opposit chags Q. Th dilctic has a dilctic nstant K and sistivity. Show that th "lakag" cunt caid by th dilctic is givn by th lationship i = Q. K o Th paalll plats of a capacito hav an aa 0. and a 0 apat. Th oiginal potntial diffnc btwn th is 000 V, and it dcass to 000 V whn a sht of dilctic is instd btwn th plats filli th full spac Coput: ( 0 = 9 x 0 S.. units) Oiginal capacitanc C 0. Th chag Q on ach plat (iii) Capacitanc C aft instion of th dilctic. (iv) Dilctic nstant K. (v) Pittivity of th dilctic. (vi) Th oiginal fild E 0 btwn th plats. (vii) Th lctic fild E aft instion of th dilctic. E. A paalll plat isolatd ndns nsists of two tal plats of aa A and spaation 'd'. A slab of thicknss 't' and dilctic nstant K is instd btwn th plats with its facs paalll to th plats and havi th sufac aa as that of th plats. Find th capacitanc of th syst If K =, fo what valu of t/d will th capacitanc of th syst b / tis that of th ndns with ai filli th full spac? Calculat th atio of th ngy in th two cass and acunt fo th ngy cha E. Had ubb has a dilctic nstant of.8 and a dilctic stth of 8 x 0 6 volts/t If it is usd as th dilctic atial filli th full spac in a paalll plat capacito. What iniu aa ay th plats of th capacito hav in od that th capacitanc b 7.0 x 0 f and that th capacito b abl to withstand a potntial diffnc of 000 volts. a Two paalll plat ai capacitos filli th full spac C w nnctd in sis to a batty with.f.. Thn on of th capacitos was filld up with unifo dilctic with lativ pittivity k. How any E 5. E. tis did th lctic fild stth in that capacito dcas? What aount of chag flows though th batty? A paalll-plat capacito of capacitanc 5 F is nnctd to a batty of f 6 V. Th spaation btwn th plats is. (a) find th lctic fild btwn th plats. (b) Find th lctic fild btwn th plats. (c) A dilctic slab of thicknss and dilctic nstant 5 is instd into th gap to occupy th low half of it. Find th capacitanc of th nw bination. (d) How uch chag has flown though th batty aft th slab is instd? E 7. Find th capacitancs of th capacitos shown in figu Th plats aa is A and th spaation btwn th plats is d. Diffnt dilctic slabs in a paticula pat of th figu a of th thicknss and th nti gap btwn th plats is fild with th dilctic slabs. E 6.

13 E 8. Th distanc btwn th plats of a paalll plat ndns is d. If a pp plat of but thicknss d is placd btwn th plats thn th nw capacitanc will b half doubl on fouth unchad Th capacitanc of a ndns A is F. It is filld with a diu of dilctic nstant 5. Th capacitanc of anoth ndns B is F. Both a spaatly chagd by a batty of 00V. Aft chagi th two ndns a nnctd in paalll without batty and without dilctic. Th on potntial will b 00 V 800 V 00 V 600 V E 0. Two tal plats fo a paalll plat ndns Th distanc btwn th plats is d. A tal plat of thicknss d/ and of th aa is instd pltly btwn th plats. Th atio of capacitancs in th two cass (lat to initial) is : : : : : E. On placi a dilctic slab btwn th plats of an isolatd chagd ndns its Capacity Chag Potntial Diffnc Engy stod dcass ains dcass incass unchad incass ains incass incass unchad incasd ains dcass dcass unchad dcass ains dcass incass unchad Elctic fild incass dcass dcass ains unchad E 9. a E *. Th plats of a paalll plat capacito with no dilctic a nnctd to a voltag souc Now a dilctic of dilctic nstant K is instd to fill th whol spac btwn th plats with voltag souc aini nnctd to th capacito. th ngy stod in th capacito will b K fold th lctic fild insid th capacito will dcas to K tis th foc of attaction btwn th plats will incas to K tis th chag on th capacito will incas to K tis In th adjoini diaga th capacitos C and C a nnctd to a batty. Ai is filld btwn th plats of C and a dilctic is filld btwn th plats C, thn q < q q > q q + q Non of ths E. A batty of 00 V is nnctd to a sis bination of two siila paalll plat ndnss. If dilctic of nstant is slippd btwn th plats of snd ndns, thn th potntial diffncs on th ndnss will spctivly b 75 V, 5 V 50 V, 80 V 80 V, 0 V 0 V, 80 V. E 5. In th abov pobl if th batty is disnnctd bfo insti th dilctic, thn potntial diffnc will b- E. V V V V A paalll plat ndns with plat spaation d is chagd with th hlp of a batty so that U0 ngy is stod in th syst A plat of dilctic nstant K and thicknss d is placd btwn th plats of ndns whil batty ains nnctd. Th nw ngy of th syst will b E 6. KU0 KU0 U0 K U0 K

14 E 7. Th ffctiv capacitanc of th syst in adjoini figu will b C = 0 A d d d d K K K K d C = A 0 C = 0 A d C = K K K K d Th capacitanc of a paalll plat ai ndns to 0 F. Two dilctic dia of qual siz a filld of lativ pittivity and a filld in it. Th ffctiv capacity of th syst will b 0 F 0 F 0 F 0 F E 9. A paalll plat capacito without any dilctic has capacitanc C 0. A dilctic slab is ad up of two dilctic slabs of dilctic nstants K and K and is of dinsions as that of capacito plats and both th pats a of qual dinsions aad sially as shown. If this dilctic slab is intoducd (dilctic K nts fist) in btwn th plats at nstant spd, thn vaiation of capacitanc with ti will b bst psntd by: Th ti nstant of th cicuit shown is : RC RC RC 5 E 0. a E 8. RC SECTION F : MISCELLANEOUS F. A vaiabl ai capacito is ad of sicicula aluiniu plats c in diat Find its axiu capacitanc in F, if altnat plats a nnctd togth fo positiv polaity and th aini plats fo th ngativ polaity. Assu th ai gap btwn th plats to b 0.. F. Two paalll plat capacitos with diffnt distancs btwn th plats a nnctd in paalll to a voltag souc A point positiv chag Q is ovd fo a point that is xactly in th iddl btwn th plats of a capacito C to a point (o a capacito C ) that lis at a distanc fo th ngativ plat of C qual to half th distanc btwn th plats of C. Is any wok don in th pocss? If ys, calculat th wok don by th fild if potntial at and a V and V.

15 F. A sphical ndns has 0 c and c as th adii of inn and out sphs. Th spac btwn th two sphical is filld with a dilctic of dilctic nstant 5. Find th capacity whn; th out sph is athd. th inn sph is athd. F. Paalll plat capacito is nstuctd usi th diffnt dilctic atials as shown in th figu Th paalll plats, ass which a potntial diffnc is applid a of aa A and a spaatd by a distanc d, find th capacitanc ass P and Q. F 5. In th followi figu th ffctiv aa of ach plat of a ica ndns is A and distanc btwn two nscutiv plats is d. If th dilctic nstant of ica is k, thn th capacity of ndns will b 0KA d 0KA d 0KA d Two squa tallic plats of sid a kpt 0.0 apat, lik a paalll plat capacito, in ai in such a way that on of thi dgs is ppndicula, to an oil sufac in a tank filld with an insulati oil. Th plats a nnctd to a batty of.f. 500 volt. Th plats a thn lowd vtically into th oil at a spd of 0.00 /s. Thn th cunt dawn fo th batty dui th pocss is : 0 = 8.85 x 0 C/N ] 8. 0 A A 5. 0 A A i l c t i c c o n s t a n t o f o i l =, Two sphical nductos A and A of adii and a placd ncntically in ai. Th two a nnctd by a pp wi as shown in figu Thn th quivalnt capacitanc of th syst is 0k. a F 7. d [ F 6. 0KA d 0 0 A paalll plat capacito is filld with a dilctic up to on half of th distanc btwn th plats. Th ann in which th potntial btwn th plats vais with distanc is illustatd in th figu Which half ( o ) of th spac btwn th plats is filld with th dilctic and what will b th distibution of th potntial aft th dilctic is takn out of th capacito povidd that; (a) (b) F 8. 0 ( + ) Th chags on th plats a nsvd o Th potntial diffnc ass th capacito is nsvd. F 9. Consid th situation shown in figu Th width of ach plat is b. Th capacito plats a igidly clapd in th laboatoy and nnctd to a batty of f. All sufac a fictionlss. Calculat th valu of M fo which th dilctic slab will stay in quilibiu. F 0. Consid th situation shown in figu Th plats of th capacito hav plat aa A and a clapd in th laboatoy. Th dilctic slab is lasd fo st with lth a insid th capacito. Nglcti any ffct of fiction o gavity, show that th slab will xcut piodic otion and find its ti piod. K a d

16 . Th agnitud of lctic fild E in th annula gion of a chagd cylindical capacito. Is thoughout Is high na th out cylind than na th inn cylind Vais as /, wh is th distanc fo th axis wh is th distanc fo th axis. [JEE - 96,] V a i s a s / Th capacitanc of a paalll plat capacito with plat aa 'A' and spaation d is C. Th spac btwn th plats is filld with two wdgs of dilctic nstant K and K spctivly. Find th capacitanc of th sulti capacito. [JEE - 96,]. A batty of 0 volt is nnctd to a capacito of capacity 0. F. Th batty is now ovd and this capacito is nnctd to a snd unchagd capacito. If th chag distibuts qually on ths two capacitos, find th total ngy stod in th two capacitos. Futh, pa this ngy with th initial ngy stod in th fist capacito. [REE - 96,5]. A paalll bination of 0. M sisto and a 0 F capacito is nnctd ass a.5 volt souc of ngligibl sistanc Th ti quid fo th capacito to st chagd upto 0.75 volt is appoxiatly (in snds): log log 0 zo [JEE - 97,] 5. A laky paalll plat capacito is filld pltly with a dilctic havi dilctic nstant k = 5 and lctical nductivity = 7. x 0. If th chag on th plat at t = 0 is q = 8.8 C, thn calculat th lakag cunt at th instant t = s. [JEE - 97,5] 6. An lcton nts th gion btwn th plats of a paalll plat capacito at a point quidistant fo ith plat Th capacito plats a x 0 apat and 0 lo. A potntial diffnc of 00 volt is kpt ass th plats. Assui that th initial vlocity of th lcton is paalll to th capacito plats, calculat th lagst valu of th vlocity of th lcton so that thy do not fly out of th capacito at th oth nd. [JEE - 97,5] 7. Two capacitos A and B with capacitos µf and µf a chagd to a potntial diffnc of 00 V and 80 V spctivly. Th plats of th capacitos a nnctd as shown in fig. with on wi fo ach capacito f Th upp plat of A is positiv and that of B is ngativ An unchagd µf capacito C with lad wis falls on th f nds to plt th cicuit. Calculat Th final chag on th th capacitos and Th aount of lctostatic ngy stod in th syst bfo and aft th pltion of th cicuit. [JEE - 97,5] 8. A dilctic slab of thicknss d is instd in a paalll plat capacito whos ngativ plat is at x = 0 and positiv plat is at x = d. Th slab is quidistant fo th plats. Th capacito is givn so chag As x gos fo 0 to d. [JEE - 98,] Th agnitud of th lctic fild ains th Th diction of th lctic fild ains th Th lctic potntial incass ntinuously Th lctic potntial incass at fist, thn dcass and again incass. 9. In th cicuit shown in th figu, th batty is an idal on, with.f. V. Th capacito is initially unchagd. Th switch S is closd at ti t = 0. (a) Find th chag Q on th capacito at ti t. (b) Find th cunt in AB at ti t. What is its li valu as t? [JEE - 98,8] a.

17 0. Th cicula plats A and B of a paalll plat ai capacito hav a diat of 0. and a x 0 apat. Th plats C and D of a siila capacito hav a diat of 0. and a x 0 apat. Plat A is athd. Plats B and D a nnctd togth Plat C is nnctd to th positiv pol of a 0 volt batty whos ngativ is athd. Calculat Th bind capacitanc of th aant and Th ngy stod in it. [REE - 98,5]. Fo th cicuit shown, which of th followi statnts is tu? With S closd, V = 5 V, V = 0 V With S closd, V = V = 5 V With S and S closd, V = V = 0 With S and S closd, V = 0 V, V = 0 V. Calculat th capacitanc of a paalll plat ndns, with plat aa A and distanc btwn plats [JEE - 99,] d, whn filld with a dilctic whos dilctic nstant vais as; (x) = 0 + x d ; 0 < x < (x) = 0 + (d x) d < x < d. Fo what valu of would th capacity of th ndns b twic that whn it is without any dilctic? [REE 000,6] [ Not : In this pobl th xain has usd wo notation of dilctic nstant. Assu (x) as th absolut pittivity of th diu at x.] In th givn cicuit with stady cunt th potntial dop ass th capacito ust b: V V/ V/ V/ [JEE - 00,]. Consid th situation shown in th figu Th capacito A has a chag q on it whas B is unchagd. Th chag appai on th capacito B a lo ti aft th switch is closd is zo q/ q q [JEE - 00,] a. Two idntical capacitos hav th capacitanc C. On of th is chagd to potntial V and th oth to V. Th ngativ nds of th capacitos a nnctd togth Whn th positiv nds a also nnctd, th dcas in ngy of th bind syst is: C (V V) C (V + V) C (V V) C (V + V) [JEE 00,] 6. Dottd lin psnts th chagi of a capacito with sistanc X. If sistanc is ad X thn which will b th gaph of chagi P Q R S [JEE Sc. 00] 7. In th givn cicuit th capacito C is unchagd initially and switch S is closd at t = 0. If chag on capacito at ti t is givn by quation Q = Q0 ( t ). Find valu of Q0 and?[jee Mains 005, ] 8. An unchagd capacito of capacitanc µf, a batty of f volt and a sisto of.5 M a nnctd c = vr is (tak n = 0.69) 6.9 snds.86 snds not availabl not availabl [JEE Sc. 005] 5. i n s i s. T h t i a f t w h i c h v

18 Excis - C. (a) fiv C capacitos in sis (b) paalll ows; ach nsisti of fiv.0 F capacitos in sis C C SECTION A : A. 6 V 90 J (iii) Q5 F (v) Q0 F 6 5 V (iv) J C 6. (a) 50/ V at ach point (b) zo C Q 0 F = C (vi) Q 5 F = A = B Q' A A. Q' = B A 8. B A. D A 9. A A. B A. C A 6. B A. A A 7. A A 5. A C 5. C C 6. C C 8. A C 9. B C. C C. D C. B C 5. A C 6.D C 7. B C 9. D C 0. A C. A D (iii) B C. A A 7. D A 0. D A 6. D Q A 5. k 0 A A. 0.5 SECTION B : (d) C () (f) R R B N 0 C B 6. (a) zo B 7. 0 = Q6 F = 60 C, Q5 F = 50 C (b) 0. V] B 5. B. C, 8 C, 9 C and C A C B C D C = 0 V C C C B 8..0 J B..5 g B *. BCD B 7. B B 9.. J B. B B 5. D B 8.B B 0. C B. B B 0. B. C B 6. C B 9. AC (iii) B D C. A D ( /)CV D. 70 C D..0. D V D 6..7 J. D 7. (a) 0 s (b) C (c) 0 ln = 6.9 s q = ( 5 ) C =.8 x 0 8 C D 8. A D 9. C A (iii) D (iv) D D. 0, /5 A, /5 A C C D SECTION D : a B. C C 7. C 0. C. D C 8. (c) R B. (a) (b) C 8..5 F C 9. (a) 8 F (b) 8 F C 0. F, F C. 8 C on th 8 F capacito and C on ach of th F capacitos 576 J C. C C. D C. A A. 0 pf 5 J V (b) 8 V C 7. (a) D. D 0. AC D. C D. AC D. A D 5. A C D 7. C D 0. C D. A B (iii) C D 6. C B (iii) C (iv) D D 8. C D. AC D 9. A 76 = 0.7 A to th lft, = 0.5 A to th lft 6.9 C D. SECTION C : COMBINATION OF CAPACITORS D.. 0 C C. 0 C on ach,. 0 J SECTION E : E. 80 pf C (iii) 50 pf (iv) (v) 7 x 0- C N (vi) 05 v/ (vii) x 05 v/ C. (a) C /, (b) C / (c) C / (d) C / C. 5 V and 75 V. E. t wi =, = d wf E. 0.6

19 Excis - k ( + k), q = CE k E 6 (a) 0 µc (b) 0 V/ (c) K K 0 A E 7. (a) d(k K ) (b) 5 µf (d) 0µC 0 A K K K d (K K K K K K ) 0 A (c) d (K + K) E 8. B CK K K. (K K ) n K. C. Uinitial 5.5 J, U = =.5 final. D E 9. B E 0. A E. C E. ACD E. A E. C E 7. A E 0. A E 5. A E 8. D E 6. A E 9. B 5. i = /s B, C 9. (a) q = CV [ t/rc] (b) i = V V t / RC ; i = as t R R F..8 pf F. wok don by th fild = Q (V V). D F 5. B. a F 6. D F 7. C F 8. st pat has di-lctic; (a) xtnd gaph of (b) staight lin joini points A and B ( a) d 0 A (K ) F b (K ) F 9. dg 7 pf. nj 0 A k k k d k k F 0 d d 0 n 0, C = F F 7. 0 C 8 J 8. SECTION F : MISCELLANEOUS F. q / 0 K 0. A k 0 E 5.. C. A A d n 0 5. C R VC (R R ) 7. Q0 = R R & = CR R 6. B 8. B