ESE-2018 PRELIMS TEST SERIES Date: 29 th October, 2017 ANSWERS. 61. (d) 121. (a) 2. (a) 62. (c) 122. (c) 3. (c) 63. (c) 123. (d) 4. (b) 64.

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1 ESE- PREMS TEST SERES Dte: 9 th Octobe, 7 ANSWERS. (). () 6. (d) 9. (b). (). (). () 6. (c) 9. (d). (c). (c). (d) 6. (c) 9. (c). (d) 4. (b) 4. () 64. (b) 94. (b) 4. (d) 5. (c) 5. () 65. () 95. () 5. (c) 6. (b) 6. (d) 66. (c) 96. (d) 6. (d) 7. () 7. () 67. (d) 97. () 7. (c). (). (c) 6. (c) 9. (). () 9. (c) 9. (b) 69. (c) 99. (c) 9. (b). () 4. (d) 7. (d). (b). (). () 4. (b) 7. (c). (c). (c). (b) 4. (b) 7. (b). (d). (b). (d) 4. (d) 7. (d). (b). (c) 4. (c) 44. (b) 74. () 4. (c) 4. (c) 5. () 45. (d) 75. (b) 5. () 5. (b) 6. (b) 46. (c) 76. (d) 6. (d) 6. (b) 7. (d) 47. (d) 77. (d) 7. () 7. (b). (d) 4. () 7. (). (). (b) 9. () 49. () 79. () 9. (c) 9. (d). () 5. (b). (b). (c) 4. (b). (b) 5. (c). (c). (d) 4. (). (d) 5. (c). (c). () 4. (d). (c) 5. (). (c). () 4. (c) 4. (b) 54. (d) 4. (b) 4. (c) 44. (c) 5. () 55. (b) 5. (b) 5. (c) 45. (c) 6. () 56. (c) 6. (d) 6. (b) 46. (c) 7. () 57. (c) 7. (d) 7. (c) 47. (d). (c) 5. (). (). (c) 4. (b) 9. (c) 59. (c) 9. (c) 9. (c) 49. (d). (c) 6. (b) 9. (c). () 5. ()

2 () (Test - 6)-9 Octobe 7. () Bndgp enegy (E g ) of diffeent mteils is given below : R Metls : Eg e s both the conduction bnd nd vlnce bnd ovelp nsultos : E g > e Semiconductos: E. () g e The popety of mteil by which mteil gets polized in the diection of extenl field nd emin polized even fte emovl of extenl field is clled spontneous poliztion. Among dielectic mteils only feoelectic nd pyoelectic mteils show spontneous poliztion; But feoelectic mteils hve stong spontneous poliztion s comped to pyoelectic mteils.. (c) Mteil Feoelectic Pyoelectic P electic Spontneous Poliztion Stong eo Wek eo Elements lose (o gin) nd she electons to fom ionic nd covlent bonds espectively nd these bonds e stble bonds. onductivity in ionic cystls depends on i) ie concenttion ii) ie mobility, : This in tun, depends on tempetue nd is given by the Aenhius 4. (b) expession exp E kt Whee. E ctivtion enegy T Tempetue k Boltzmnn s constnt The eltion between dielectic loss nd fequency is P f P v f so s fequency is doubled, the powe loss is doubled. 5. (c) Thee is lwys dielectic losses occuing in condense contining lossy dielectic nd this losses my be ccounted s ohmic loss occuing in esistnce R. So, the condense cn be epesented s 6. (b) Steps to find Mille indices : i) Find the intecepts of the plne on the thee cystl xes (OX, OY, O) s (p, qb, c); whee, b, c e coesponding pimitives nd p, q, be intege. ii) Wite the ecipocl of the numbe p, q, s,, p q. iii) Find the M of thei denominto. iv) Multiply the ecipocls by the M, to get Mille ndices. Hee i) ntecepts e (4,, ) ii) ecipocls :,, 4 iii) M of 4,, is 4 iv) Mille indices e 4, 4, 4,4, 4 7. (). () 9. (c) ystl system Unit cell dimension Angle between Axis Othohombic b c 9 Ticlinic b c 9 Hexgonl b c 9, ubic b c 9 Mgnetic mteil Dimgnetic Pmgnetic Feomgnetic Antifeomgnetic Feimgnetic Mgnetic susceptibility Negtive nd smll Positive nd smll Positive nd vey lge Positive nd smll Positive nd lge Pemnent mgnetic mteils e difficult to demgnetize. Popeties of pemnent mgnetic mteils :- High etentivity High coecivity High pemebility Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

3 (Test - 6)-9 Octobe 7 (). (). () Tll nd wide Hysteesis loop High stution mgnetiztion High uie tempetue High hysteesis loss becuse of lge e of hysteesis loop Pmgnetic mteil e chcteized by ndom ngement of dipole. Due to ndom dipole ngement the vlue of spontneous mgnetiztion is zeo. When these mteils e plced in mgnetic field, they cquie wek mgnetiztion in sme diection of the field. Hydogen molecule is dimgnetic mteil whee s hydogen tom is pmgnet. n pinciple ny system tht contins toms, ions o molecules with unpied spin cn be clled pmgnet. A system with unpied spins tht do not intect with ech othe e system with miniml intection. Ech hydogen tom hs one non-intecting unpid electon.. (b). (d) Mgnetic susceptibility Reltive pemebility Totl poliztion of polytomic gs, P P e + P i + P o e E Npp E NeE NiE KT E y p p Ne i E KT Np p e i K T N i.e. y mx + c This is n eqution of stight line, hving slope m 4. (c) Np p K Fce cented cubic : c m x whee dius of n tom n fce-cented cubic lttice, toms e locted t ech cone nd t the cente of ech fce of unit cell. So, () We know tht J J D (b) 7. (d). (d) hence it is good conducto. Feomgnetic mteils obey uie - Weiss lw, m T whee, is the cuie constnt nd is clled the pmgnetic cuie tempetue. Above the cuie-tempetue feomgnetic mteils, behv es like pmgnetic mteils. Hlf-coefficient of semiconducto mteils R H ne Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

4 (4) (Test - 6)-9 Octobe 7 whee n is the cie-concenttion, 9. (). (). (b). (d) n 4 RA R B B A n 4 : Supeconducto shows dimgnetism. Hence, it expels mgnetic flux fom within its volume. A supeconducto becomes noml metl when citicl mgnetic field is pplied. B H H B Supeconducto (T < T ) Supe Noml Stte onducting Stte T T At equilibium, qe y q x.b z x E B y z...() nd, J x Nq x...() So, Hll coefficient, R H Ey x B J Nq. Nq z x x Hll effect occus when tnsvese mgnetic field is pplied to conducto cying cuent. Due to the cuent, longitudinl electic field nomlly pesent in the diection of flow of cuent. The conductivity t ny given tempetue (except t bsolute zeo) is due to both electons nd holes, nd it is given by whee n e i i e h e nie me m h h i conductivity of intinsic mteil e, elxtion time fo electons nd h holes m,m mss of electon nd holes e. (c) 4. (b) 5. () e h, mobility of electon nd holes h The semiconducto in its puest fom is clled intinsic semiconducto e.g. Si, Ge When some impuity is dded to the intinsic semiconducto, it is clled extinsic semiconducto. N-type semiconducto nd P-type semiconducto e clssified on the bsis of type of impuity dded. f impuity is dono (o Pent vlent) e.g. P, A, Sb, etc. it is clled N-type semiconducto. f impuity is ccepto (o ti vlent) e.g. B, Al, G etc. et x is the displcement of electon nd E is pplied electic field coss conducto. F d x me ee dt dx ee dift velocity dt me As, mobility, µ dift velocity Electic field intensity ee m e E e me Fo supeconducto, citicl field H vies with tempetue s, H T H T whee, H is the citicl field t bsolute zeo nd T is the tnsition tempetue So, t T T ; H Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

5 (Test - 6)-9 Octobe 7 (5) 6. () 7. (). (c) 9. (c). (c). () A good electic contct should offe low esistnce to flow of cuent. This educes the voltge dop nd lso het geneted t contct points. Supeconductos e used fo geneting vey stong mgnetic field. f supeconducto cies cuent, then developed mgnetic field H whee is the dius of supeconducto wie. Mgnetic bubble memoies e built using feites. The tempetue below which noml mteil behves s supeconducto, is clled tnsition tempetue of tht mteil. Expeimentlly, it is found tht tnsition tempetue of mecuy is 4. K. Fo ny intinsic semiconducto, the intinsic concenttion is diectly popotionl to T /. As conductivity of the instinsic semiconducto is diectly popotionl to intinsic concenttion. So, / T. Fo the semiconducto mteil, The Hll s coefficient, R x As, ne So, R H Ey J B ne ne Since, Hll coefficient, R H x ne Whee n is numbe of chge-cie pe unit volume; m. nd e is the chge of electon; coulomb. So unit of R H : (mete) (coulomb) So, option () z. (). (d) The cuent equied to flowing though supe conducto of dius to poduce citicl mgnetic field H c is c Hc d Hc 7 7 Ampee As, femi level fo P-type semiconducto, whee, E F E n KT loge N E mximum enegy of vlence bnd in e. i.e. 4. () 5. () 6. (d) n no. of electons in vlence bnd, N A concenttion of ccepto toms. A onduction bnd Femi level fo P-type semiconducto lence bnd Accoding to the Messene s ef f ect, supeconductos expels the mgnetic field flowing though it. So, eltiv e pemebility is zeo f o supeconducto. Tnsfome oil cts s insulto nd cooling medium fo tnsfome coes nd chokes. ts dielectic stength should be high to wok s good insulto. Flsh point nd viscosity e lso impotnt pmetes fo tnsfome oil. Flsh point is the lowest tempetue t which it vpoize. Fo bette tempetue stbility it Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

6 (6) (Test - 6)-9 Octobe 7 should be high. iscosity is mesue of its esistnce to gdul defomtion by stess so its should lso be high fo tnsfome oil. 7. () Powe loss of dielectic in ltenting electic. (c) field E So powe loss Tempetue hs no effect upon ionic polizbility nd electonic polizbility. 9. (b) Sodium is pmgnetic. 4. (d) Feites fom mgnetic would be in fom of MO.Fe O (M divlent metl) it cn be epesented s AB O 4 (A, B metls) 4. (b) Neel tempetue is the tnsition tempetue between nti-feomgnetism nd pmgnetism behviou of mteil. 4. (b) 4. (d) 44. (b) Boh mgneton is the unit of pemnent dipole moment due to spin of electons in obit. Boh mgneton whee, eh 4m mpee.m h plnk s constnt joule sec. m mss of electon e chge of electon As we know, men fee pth, v nd T d Accoding to wiedemnn Fnz lw Theml conductivity Electicl conductivity whee, KT k Boltzmnn s constnt e Electonic chge T Tempetue k.t e The tio of theml conductivity nd electicl conductivity is popotionl to tempetue nd this lw holds good bove debye tempetue. 45. (d) 46. (c) 47. (d) 4. () 49. () f supe conducting mteil is plced in mgnetic field (H) it emins supeconducto upto citicl field (H c ) bove tht it tuns into noml stte. Similly it emins supeconducto below tnsition tempetue nd bove tht tempetue it convets into noml stte. Mgnetic impuities cn lso contibute towds citicl field. Rochelle slt is piezoelectic cystl, which is used s piezoelectic tnsduce. Piezoelectic tnsduces convet mechnicl motion to electicl signl. Dimgnetic mteil is the only mgnetic mteil which hs no dipoles. d ib d i b m dt dt cd 5 cos t 5 5 cos t 4cos t 7.5cos t volt..5 cos t volt. d icd di cd M dt dt b 4 5 cos t 5 5 cost cos t 7.5cos t.5cos t volt. Whee d / s. Hee, the instntneous v oltge nd instntneous cuent e in phse which indictes tht the cicuit is in esonnce so, the net impednce z R. R m m At esonnce, Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

7 (Test - 6)-9 Octobe 7 (7) 5. (b) 5. (c) 5. (c) H 6 Since the cuent flowing in the loop is i, Hence, i 5 i i 5 i.5a So, the voltge coss the 5i volt 5 esisto. Fom the cicuit, we cn obseve tht voltge t point b is b Also, b b + + i.e. nd, b 5 c 5 5 Given cicuit is, 4A 5 5 uent though i i (i i ) 5 esisto, i 4A Applying K is loop (), we get i + (i i ) i i i i 4A So, voltge coss esisto 4 5. () R B Y B et RY YB BR f ll the esistnce e pesent is lod Powe, P Ph Ph cos R R cos, esistive Y R f one of the esistnces of the lod gets open cicuited, Powe P Ph Ph cos R R % eduction in powe P P P.% 54. (d) n powe mesuement of lod, W cos ( ) W cos ( ) nd, tn W W W W When, ie. Pf is unity W W > When, 6 ie. pf.5 (lg) W but W > When, 9 ie. pf is zeo W.5 l nd W.5 ie. W W o, W + W. unblnced 55. (b) A. Fo R cicuit voltge lods cuent by n ngle tn R B. Fo R cicuit voltge lgs cuent by n ngle tn R Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

8 () (Test - 6)-9 Octobe (c) 57. (c). Fo pue cpcitive cicuit cuent leds voltge by n ngle. D. Fo pue inductive cicuit cuent lgs voltge by n ngle. 5 Hete A hoke, 5Hz Given : A, H (dop coss hete) 5 R ( Resistnce of choke) 5 s R H (Resistnce of hete) 5 5 Hence, net esistnce of the cicuit is, R R H + R R H (dop coss R H ) R H 5 5 R R 5 R (dop coss X, the inductive ectnce of the choke) X X. Howeve, the supply voltge being the vecto sum of the dops R nd. j R RH () X This gives the impednce of the choke s R X 5 (7.) Given voltge souce, v +sint 5. () 59. (c) i v i i v i v.9 (+sint) The cicuit shown in question, cn be edwn s, b n c d Hee, R bn R cn R dn uent, Given cicuit is, 4A 6 Req [(4) 5] + (4 ) 9 9 R eq ( / 9) 9.4 A + 5 ( ) A b + v t we see tht,, i v Hee, v the voltge coss the non line oltge coss the non line esisto v i v i i (v i) uent in esisto A Applying k in loop (i), we get 5 + 5A So, cuent in section b, Ι b 5 4A Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

9 (Test - 6)-9 Octobe 7 (9) 6. (b) Given cicuit is, (+6) 6A et cuent deliveed by voltge souce Applying k in loop-, we get 6 4 ( + 6) A 6. (d) So, powe deliveed by voltge souce 6 6 ( ) 6W Now, voltge coss cuent souce ( 6) ( + 6) volt So, powe deliveed by cuent souce Since, 6 6 W cost cos²t sin²t sin²t sin²t ( cost) s [sin²t] s s s 4 s s(s 4) 6. (c) 64. (b) 65. () ie. cpcitive ectnce X c inceses if both nd f deceses. Given cicuit is unde esonnce, so cuent will be mximum, ms ms R ( / ) Avege powe will be dissipted only in esisto. So, P vg ( ) R ms /.5 W 5 mw Since, cuent will leve the dot in fist inducto nd ente the dot in second inducto, hence. equivlent inductnce will be, eq + M H So, esonnce fequency, Fo R Th 6.77 d/sec. eq 6. (c) 4 s(s 4) s(s 4) Since, cpcitive ectnce X c c fc R b (4) 6. b Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

10 () (Test - 6)-9 Octobe 7 A 66. (c) 67. (d) i.e. R Th. Fo Th : By tnsfomtion theoem, the cicuit cn be edwn s, b 4A + 4 b 4 ( 4) 4 4 i.e. Th 4 Fo lttice netwok, the z-pmetes e, z z nd z z z z So, z z nd, z z z z z z z z z (5 5) ( ) 4 Then, h z 4 z 5 z h z 5 Fo T-netwok, (c) Fiven, ie. R So, 4+R 4 6 nd + R 5 Fo the given cicuit ( + ) And, z b ( )z zb z b () nd (z + z b ) + z z z z b () Fo ABD pmetes A B D A B D 69. (c) The fequency t which the voltge coss the cpcito is mximum, R f c mx which is below the esonnce fequency, f The fequency t which the voltge coss the inducto is mximum f mx R which is bove the esonnce fequency, f 7. (d) Qulity fcto, Q esonnt fequency Bndwidth f f 4 R R R R 6 Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

11 (Test - 6)-9 Octobe 7 () 7. (c) 7. (b) Symmety Recipocity. pmete. Y pmete Y Y Y Y. h pmete h h h h h h 4. ABD pmete A D AD B 7. (d) 74. () Tnsmission Pmetes Netwok b Fo ecipocity, [AD B] A B 9 4 D o / Fo z-pmete, we get 5...() nd...() Fo the given netwok, Fom () nd (), 5...() [Fo eqn. ()] 5 [Fo eqn. ()] 45 in (b) Fo pssive netwok, the output powe cnnot be gete thn the input powe. 76. (d) Fo nd, put, then Fo nd, put, then -pmetes e 77. (d) 7. () in A B in AB in in in 5 in When in seies, we hve to dd the -pmetes to combine the two, two netwok. 79. () - netwok hs only enegy stoge element. Powe dissiption elements R is not thee, so the poles nd zeos lie on the imginy xis. Netwok function should be detemined by zeo initil condition.. (b) A 6A 4A A A i Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

12 () (Test - 6)-9 Octobe 7 Applying K t node, we get 6A A 4A A. (c). (c) i A Fo obtining equivlent esistnce,we hve to shot cicuit the independent voltge souce nd open cicuit indepdent cuent souce. Theefoe the cicuit is, R Th R Th Using supeposition theom, cuent in esisto due to A cuent souce is A 5A 5 5 A uent in esisto due to A cuent souce is A 5 5 Now powe bsoubed is.5w, so 4. (b) 5. (b) 6. (d) R.5W.5A Fom ineity, ma s 5 S 5mA Applying supeposition theom, it is known tht if ll cuent souce vlue e doubled, then node voltges lso e doubled. Powe obsebed by R is, s R P R R s fom the expession, powe is mximum when R s. Thevenin equivlent of unknown cicuit is Th R Th by voltge division substituting vlues fom tble, 6 Th Th RTh RTh...()...() Th R R R R Solving the eqution () nd (), we get R Th 7. (d) nd Th Th. (c) 5 A 5A Totl cuent A Fom lineity we known tht s tio emins constnt. [Y] Y Y Y Y [Whee ] Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

13 (Test - 6)-9 Octobe 7 (). () 9. (c) When switch ws open, totl chge q et fte closing the switch; voltge coss pllel combintion is. t As chge will be conseved. Now, q eq. ie. Powe P i msr Hee ms 9. (c) 9. (b) A i it dt T ms T i R 7W t dt 7 R 7 7 t di t d M i t i t dt dt d di t t i t i t M dt dt Multully induced voltge occus due to othe cuent. f t Self induced voltge occus due to self cuent. T t A f t t T A T f(t) f t.f t t f t ut ut T T t 9. (d) 9. (c) 94. (b) A t u t u t T T A A tut tut T T T A A tut t T Tut T T T A A tut t Tut T Aut T T T The single voltge souce my be consideed to be equivlent to two identicl souces in pllel. So option () nd option (4) e equivlent. Option (4) nd option () e equivlent since connection fom the positive teminls of the two souces does not ffect the netwok becuse thee would be no cuent in such connection. Note: The single cuent souce my be consideed to be equivlent to two identicl souces in seies. 5 mh, mh N t the numbe of tuns e doubled the new vlue of 4 5 mh 4 mh Totl nductnce eq + M (Fo negtive polity) M K eq mh Applying K in st loop we get 6 6.mA Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

14 (4) (Test - 6)-9 Octobe () 96. (d) k Applying K t node +.ma 9 oltge coss 5K esiste v k v 5. i A Applying K, we get b i + b i 4 Given 4i v...() Applying K we get i v...() Fom eqution () nd (), we get 4i ( i) 4i 4 + 4i i i + i i i i + 9 (i 7) ( 4) i 7, 4 A 97. () i + v 9. () ms 99. (c) 64 Avege Powe loss in 9 esisto P v 9 ms W Electic field is given by : Q Q E ˆ ˆ 4 4 whee â nd â e unit vectos long nd. ˆi ˆj kˆ Hee, ˆi j ˆ kˆ ˆi 6 ˆj 6 kˆ And, i ˆ 6ˆj 6kˆ E,, ˆ i j ˆ k ˆ i ˆ 6j ˆ 6k ˆ 9 ˆ ˆ ˆ ˆ ˆ ˆ E i j k i j k m E ˆ i ˆ i j ˆ j ˆ k ˆ k m E 4 ˆj kˆ k m T ms t dt T 64 T T Hee T Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

15 (Test - 6)-9 Octobe 7 (5). (b) Hee, A A d d 4 A 4A d d A 4A d d nd e in pllel : 7A d Now, nd e in seies. eq A d A A d d Mgnetic flux is given by B A webe. (c) B Webe. A m Mgnetic field intensity unit is Ampee/m. Ampee lw sttes tht line integl of tngentil component of H ound closed pth is the sme s net cuent enclosed by the pth. H dl enc Applying Stokes Theoem: enc enc. (d) H H dl HdS S J ds Guss w is given by : s J (in point o diffeentil fom) D ds Q ene B p Mgnetic field lines lwys exist in closed pths nd mgnetic monopole does not exists.. (b) E Electic field lines neve exist in closed pth Hence, E Mgnetic monopoles does not exist nd hence mgnetic field lines e lwys closed. So, it hs no sinks o souces. 4. (c) S B ds o B Hence, B is solenoidl but it is nonconsevtive s H. M H Hee, 5 nd H H H H is due to A t M nd H is due to A t N. H cos nd H cos will cncel ech othe. Net field intensity H sin H sin H H sin 5 5 A m. N Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

16 (6) (Test - 6)-9 Octobe 7 5. () Q E Fig. P KQ E Q Fig. Applying Guss s lw fo fig- E ds Q ' Q E 4 ' E Q KQ E' E 4 6. (d) 7. () E' E m/m ˆ ˆ ˆ z z P...() z z z 5e sin ˆ 5e cos ˆ e sinˆ z,, 5 ˆ 5 ˆ ˆ z 4.ˆ.5ˆ 7.ˆ z B W Q E dl A Q AB Q ( B A ) sin9º cos 6º sinº cosº 4. z J E 9. (c) z (e )( ) e A / m Q. (c). (d) (given d.m) z z H.dl ( H).ds H.dl enclosed D.ds v D.ds (stoke s theoem) (Ampee s lw) (.D)dv (Guss divegence theoem We know velocity P (Guss w) (s it is fee spce substituting in bove eqution) P E / H, the chcteistic mpednce of the medium ().5 Joule oltge (v) E distnce between plnes (d) z A Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

17 (Test - 6)-9 Octobe 7 (7). (). () 4. (c) 5. (c) / A hee 6 P P One my ive t the coect choice by comping the two sides dimensionlly. Since hs the dimension of velocity squed the petinent choice is: Ey Ey t x The electomgnetic wve eqution is given by E E E t t Fo fee spce nd e ech zeo hence nd e flse hence sttements nd 4 e coect H J, D given efctive index ( ).5 fequency 4 H elocity of light in vcuum elocity of light in glss ( ) o 6. (b) 7. (c) We know f 4 6 m f(x) - t) fowd epesents wve motion in fowd diection f(x) + t) evese epesents wve motion in evese diection dv E d 5 given 6, m 5 d 6 E d 4 We lso know equting both 4 q 4 6 q 4 q E 4 (by oloumb s lw) Refctive index ( ) o.5.5. (c) 6 q ( ) q coloumbs given E (.5x ye )e E x.5 j / jst Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

18 () (Test - 6)-9 Octobe 7 9. (c). (). (). (c). (d) y E cos / sin / So, E x E y nd phse 9 hence it is ellipticlly polised wve Fo unifom plne wve E nd H must be in plne But both e pependicul to ech othe. ntinsic impednce, Fo fee spce,, j j j j, Fo conducting medium, ; so, j 45 Fo pefect dielectic;, j j.kichoff s cuent lw : Rte of flow of chge enteing t node is equl to te of flow of chge leving the node..ampee s w : H.d l d d.fdy s w : E BA dt dt 4.Guss w : D.ds q As the wve is popgting in Y-diection. So the component of electic field will be eithe in x-diection o in z-diection but neve in Y- diection. W hen chged pticle is moving it expeiences foce due to both mgnetic nd electic field. 4. (d) 5. (c) 6. (d) 7. (c). () Numbe of evolutions /6.p.s t sec e t 5 /. 4 Since, thee is no electic field inside the conducto, hence thee will be no tngentil component t the sufce of conducto. Only noml component of electic field will be thee. Hence electic lines of foce will be lwys pependicul to the sufce of conducto. As A nd B e t the sme potentil, the wok done will be zeo. Since chge density Accoding to Guss s w, Fo < 4 D.4 D Fo Fo qute wve in in in D.ds Q Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

19 given in 5 (Test - 6)-9 Octobe 7 (9) whee no eflected wve exists nd eflection co-efficient is zeo. oltge is unifom long the line 5 mx min 9. (b). (b) SWR :. (). (c) given 75 f 6MHz (75 j4) s is cpcitive in ode to hve cncelling effect n inductnce should be connected t lod so tht lod mtching tkes plce. We know eflection co-efficient E E i nd [ fo non-mgnetic mteil] fo fee spce 5 Tnsmission of powe to lod ove tnsmission line chieves optimum vlue when SWR becomes : This is possible when. (c) 4. (c) Given 4 m / s P We know f H P f 4 4m length of line l m Since the length of the line is hlf the wve length theefoe in l. We know tht R j G j with s pue esistnce we hve R,, G oss less line R G Distotion less line : R, G hence it is not lossless line nd not distotionless line We know eflection co-efficient Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

20 () (Test - 6)-9 Octobe 7 j6 6 j (b) Avege powe is given by P Hee, Gd db log Gd G P d d ve 4 5. (b) fo SWR fo line in line 4 in () 5 5 / line nd / 4 line e pllel 6. (b) in fo / line, in f chnge of polistion diection is equied, twist section my be used extending ove two o moe wvelengths. Tpes e used to couple wveguides of diffeent dimensions. Bends & cones e used to chnge diection.. (b) d Gd P w nd m P 9. (d) 4 ve 6 W Hon ntenn, n exmple of n petue ntenn is tpeed section of wveguide poviding tnsection between wveguide nd the suoundings. t finds its ppliction in icft. Pbolic dish Reflecto eflects EM wves by conducting sheet. Wied ntenns e led by tnsmission lines. The wve is popgting in +z diection. The expession of electic field fo TM mode is given by : mx ny E E sin sin e b E comping with 4. (b) iz i z sin 5x sin 6y e m 5 i z sin 6y e m n 6 b n 6 5 Mode is TM4 A wveguide behves s high pss filte. Thee is hevy ttenution fo fequencies below cut-off lthough the wveguide itself is vitully lossless. Such ttenution is due to eflection t the mouth of the guide nd some tke plce in evnescent modes. Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og

21 (Test - 6)-9 Octobe 7 () 4. () long the wve popgtion is given by: 4. (d) 4. (c) 44. (c) The wvelength of the wve popgting in wveguide is given by m whee Fee spce wvelength. Hence is lwys gete thn A. Phse velocity is the velocity with which the wvechnges phse t pln foundy nd not the velocity with which it tvels long the boundy this ppent velocity which is gete thn velocity of light in spce is clled phse velocity. A psitic element shote thn the diven one o dito tends to incese dition in its own diection nd behves s convegent convex lense which is clled Diecto. Reflecto Rdito Diecto A psitic element longe thn the diven one nd which educes signl stength in its own diection nd inceses in opposite diection is clled eflecto. TEM (Tnsvese Electomgnetic Mode) does not hve ny cut-off fequency nd hence it will be suppoted t ny fequency. ut-off fequency is given ly: mode m) mc nd (fo E z 47. (d) 4. (b) 49. (d) mx ny E sin sin e b Fo m, Fo n, n, E z m, E z z TM nd TM will not exist nd TEM mode cnnot popgte in ectngul wveguide. Only TM cn popgte. oop Antenn consists of wie with one o moe tuns. They e lso clled wie Antenns nd used in Buildings, ships, Automobiles, etc. Hon Antenn is n exmple of Apetue Antenn is tpeed section of wve guide. t is used in Aicft s it cn be conveniently flush mounted. Pbolic dish eflecto eflects EM wve by conducting sheet. t is used in communiction, Rd & Astonomy. Ygi Ud Ay is used fo shot wve tnsmissions by Rdio Amteus. At bsolute tempetue, intinsic semiconducto behves like on insulto s thee is no fee electons vilble. n intinsic semiconducto, the totl electicl conductivity. ne ne e h e h Although the numbe of electons in conduction bnd nd holes in vlence bnd e equl in intinsic semiconducto, the conductivity due to electons is moe thn the conductivity due to holes. Becuse the mobility of electons is highe thn tht of holes. 45. (c) 46. (c) A wveguide my consist of one o moe conductos, o no conductos t ll nd will suppot wveguide modes. Fo Tnsvese mgnetic wve popgting in wveguide, the electic field component 5. () Alloying elements lwys inceses the esistivity of the metl to which they e dded. One eson behind this is, the tomic size of pent tom nd lloying element, e diffeent which leds to the vition in the lttice pmete nd thus, the electon sctteing occus. Regd. office : F-6, (owe Bsement), Ktwi Si, New Delhi-6 Phone : Mobile : 9955, 9759 E-mil: info@iesmstepublictions.com, info@iesmste.og