fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics ELECTRONICS AND EXPERIMENTAL METHODS NET/JRF (JUNE-2011)

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1 ELETONIS ND EPEIMENTL METHODS NET/J (JUNE-). sgnal of frequency khz s beng dgtalzed by an /D converter. ossble ns. : (b) samlng tme whch can be used s (a) s (b) 4 s 6 s s Soluton: f f 5s f S TS 3 T 5s. onsder the dgtal crcut shown below n whch the nut s always hgh (). Z S (hgh) The truth table for the crcut can be wrtten as Z The entres n the Z column (vertcally) are (a) (b) ns. : Soluton: Z. H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

2 3. tme varyng sgnal n s fed to an o-am crcut wth outut sgnal o as shown n the fgure below. K The crcut mlements a (a) hgh ass flter wth cutoff frequency 6 Hz K (b) hgh ass flter wth cutoff frequency Hz n K K low ass flter wth cutoff frequency 6 Hz K o low ass flter wth cutoff frequency Hz ns. : Soluton: Snce crcut has and combnaton, ts a Low Pass flter and cutoff frequency 6Hz. NET/J (DE-) 4. In the oeratonal amlfer crcut below, the voltage at ont s K K K 5 5 (a). (b).5 5. ns. : (b) Soluton:.5. H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

3 5. counter conssts of four fl-flos connected as shown n the fgure: 3 LK J K J K J K J K ns: (b) Soluton: If the counter s ntalzed as 3, the state after the next clock ulse s (a) (b) 3 LK J K J J J K K K 6. The ns,, and 3 of art of a mcrocontroller are connected wth resstors to drve an LED at varous ntenstes as shown n the fgure. or = 4. and a voltage dro of. across the LED, the range (maxmum current) and resoluton (ste sze) of the drve current are, resectvely, (a) 4. m and. m (b) 5. m and. m 7.5 m and.5 m 4. m and.5 m ns: 3,,, Soluton: or Maxmum current,,, 3.75 k.5k 3k 6k Thus, I m.75k.5k 3k 6k 5 max H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

4 or Ste sze,,, 3. Thus m,,, I k 5 7. The fgure below shows a voltage regulator utlzng a Zener dode of breakdown voltage 5 and a ostve trangular wave nut of amltude. 5 t(s) or > 5, the Zener regulates the outut voltage by channelng the excess current through tself. Whch of the followng waveforms shows the current assng through the Zener dode? (a) (b) (m) (m) t(s) t(s) t(s) ns: (a) Soluton: When zener s O zener current s zero when zener s ON zener current wll flow. K (m) (m) (m) t(s) H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

5 NET/J (JUNE-) 8. In the o-am crcut shown n the fgure below, the nut voltage s. The value of the K outut s K K K o (a) -.33 (b) ns. : (b) n Soluton:. 5 where K and K 9. n LED oerates at.5 and 5 m n forward bas. ssumng an 8% external effcency of the LED, how many hotons are emtted er second? (a) 5. x 6 (b).5 x 6.8 x 6.5 x 6 ns. : Soluton: Pn ext 3 Pn 5 hf, number of hoton ext e hf e.6. The transstor n the gven crcut has h fe = 35Ω and h e = Ω. If the load resstance L = Ω, the voltage and current gan are, resectvely. (a) -35 and + 35 O 6 (b) 35 and and.97 I L.98 and - 35 ns. : (a) H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

6 . The outut, O, of the gven crcut n cases I and II, where ase I:, = ;, D = ; E, = and G = ase II:, = ;, D = : E, = and G = are resectvely (a), (b),, D, ns. : O D E G E Soluton: G O NET/J (DE-). lve musc broadcast conssts of a rado-wave of frequency 7 MHz, amltudemodulated by a mcrohone outut consstng of sgnals wth a maxmum frequency of khz. The sectrum of modulated outut wll be zero outsde the frequency band (a) 7. MHz to 7. MHz (b) 6.99 MHz to 7. MHz 6.99 MHz to 7. MHz MHz to 7.5 MHz ns: (b) Soluton: Sectrum conssts of f c f m and c f m f. 3. In the o-am crcut shown n the fgure, s a snusodal nut sgnal of frequency Hz and s the outut sgnal. The magntude of the gan and the hase shft, resectvely,. close to the values (a) 5 and / (b) 5 and / and zero and π K K o ns: Soluton: v v n v v n H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

7 4. The logc crcut shown n the fgure below Imlements the oolean exresson HIGH y (a) y (b) y y y ns: (a) Soluton: Outut of each Ex-O gate s and. Thus y 5. dode D as shown n the crcut has an -v relaton that can be aroxmated by ns: vd vd, for v D, for v The value of v D n the crcut s (a) (b) 8 5 D D Soluton: v v v v D D D D 6. and-ass and band-reject flters can be mlemented by combnng a low ass and a hgh ass flter n seres and n arallel, resectvely. If the cut-off frequences of the low ass and hgh ass flters are LP and HP mlement the band-ass and band-reject flters are, resectvely,, resectvely, the condton requred to HP LP HP LP HP LP HP (a) and (b) and D LP D v D ns: HP LP HP LP HP LP HP and and (b) LP H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

8 NET/J (JUNE-3) 7. slcon transstor wth bult-n voltage.7 s used n the crcut shown, wth 9.7, 3k, and k. Whch of the followng fgures correctly reresents the load lne and quescent ont? (a) E m 6 (b) E m E 9.7 E ns: (b) E Soluton: I 3 and I 3 3, sat If the analog nut to an 8-bt successve aroxmaton D s ncreased from. to., then the converson tme wll (a) reman unchanged (b) double decrease to half ts orgnal value ncrease four tmes ns: (a) m H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

9 sn where, 9. The nut to a lock-n amlfer has the form t t ns:, are the amltude, frequency and hase of the nut sgnal resectvely. Ths sgnal s multled by a reference sgnal of the same frequency, amltude r and hase r. If the multled sgnal s fed to a low ass flter of cut-off frequency, then the fnal outut sgnal s (a) cos r r (b) cos cos r r t r sn cos cos t (a) r r r Soluton: sn t sn t cos cos t r r Outut of low ass flter= r cos. our dgtal oututs, P, T and H montor the seedv, tyre ressure, temerature t r r and relatve humdty h of a car. These oututs swtch from to when the values of the arameters exceed 85 km/hr, bar, r r 4 and 5%, resectvely. logc crcut that s used to swtch ON a lam at the outut E s shown below. Whch of the followng condton wll not swtch the lam ON? (a) v 85km / hr, bar, t 4, h 5% (b) v 85km / hr, bar, t 4, h 5% v 85km / hr, bar, t 4, h 5% P r r E v km hr bar t h 85 /,, 4, 5% T ns: H H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

10 J/NET-(DE-3). onsder the o-am crcut shown n the fgure. If the nut s a snusodal wave 5snt, then ns: Soluton: the amltude of the outut s (a) 5 5 v v o n, (b) where, 3 6 j j K K o v v o n 3 3 v o 5 snt 5 snt. If one of the nuts of a J-K fl flo s hgh and the other s low, then the oututs and ns: (a) oscllate between low and hgh n race around condton (b) toggle and the crcut acts lke a T fl flo are ooste to the nuts follow the nuts and the crcut acts lke an S fl flo 3. samle of S has electron and hole mobltes of. 3 and.5 m /-s resectvely at 3 K. It s doed wth P and l wth dong denstes of 3.5 / m and 3.5 / m resectvely. The conductvty of the doed S samle at 3 K s (a) 8 m (b) 3 m.8 m 83. m ns: (a) 3 3 Soluton: esultng doed crystal s -tye and.5.5 / m / m e 9 n e.6. 5 n 8 m H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

11 4. Two dentcal Zener dodes are laced back to back n seres and are connected to a varable D ower suly. The best reresentaton of the I- characterstcs of the crcut s (a) I (b) I I I ns: 5. 4-varable swtchng functon s gven by f 5, 7, 8,, 3, 5 d,,, where d s the do-not-care-condton. The mnmzed form of f n sum of roducts (SOP) form s (a) D (b) D D D D ns: D D D D D D H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

12 NET/J (JUNE-4) 6. The nner sheld of a traxal conductor s drven by an (deal) o-am follower crcut as shown. The effectve caactance between the sgnal-carryng conductor and ground s Sgnal (a) unaffected (b) doubled halved made zero ns: (a) 7. n o-am based voltage follower (a) s useful for convertng a low medance source nto a hgh medance source. (b) s useful for convertng a hgh medance source nto a low medance source. has nfntely hgh closed loo outut medance has nfntely hgh closed loo gan ns: (b) 8. n network roduces a hase-shft of o 3. How many such networks should be cascaded together and connected to a ommon Emtter amlfer so that the fnal crcut behaves as an oscllator? (a) 6 (b) 9 3 ns: (a) Soluton: Total hase shft must be or 36. ommon Emtter amlfer has hase change of 8 so we need 6 network for next 8 hase shft. H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

13 9. or the logc crcut shown n the below smlfed equvalent crcut s (a) (b) ns: Soluton:. H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

14 NET/J (DE-4) 3. onsder the amlfer crcut comrsng of the two o-ams and as shown n the fgure. K r M If the nut ac sgnal source has an medance of 5 k, whch of the followng statements s true? (a) s requred n the crcut because the source medance s much greater than r (b) s requred n the crcut because the source medance s much less than can be elmnated from the crcut wthout affectng the overall gan s requred n the crcut f the outut has to follow the hase of the nut sgnal ns: (a) Soluton: s requred n the crcut because the source medance s much greater than r 3. The I characterstcs of the dode n the crcut below s gven by.7/ 5 for.7 I for.7 where s measured n volts and I s measured n ameres. K I The current I n the crcut s (a). m (b) 9.3 m 6. m 6.7 m ns: Soluton: lyng K..L. I.7 / olts Thus I.7 / / 5 3./ 5 6. m H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

15 3. In a measurement of the vscous drag force exerenced by shercal artcles n a lqud, ns: the force s found to be roortonal to artcle. If s measured to be / 3 where s the measured volume of each 3 3mm, wth an uncertanty of relatve ercentage uncertanty n the measured force s (a). 8 (b) (b) 3.7 mm, the resultng Soluton: The relatve ercentage uncertanty n the measure force s where s the uncertanty n the measurement of volume. /3 / / / /3 33. onsder a Low Pass (LP) and a Hgh Pass (HP) flter wth cut-off frequences f LP and ns: f HP, resectvely, connected n seres or n arallel confguratons as shown n the gures and below. f HP () Inut L Outut () Inut Outut f HP f LP L Whch of the followng statements s correct? f LP (a) or f f, acts as a and Pass flter and acts as a band eject flter (b) or HP HP wthout flterng or or LP f f, stos the sgnal from assng through and asses the sgnal HP LP f f, acts as a and Pass flter and asses the sgnal wthout flterng HP LP f f, asses the sgnal wthout flterng and acts as a and eject flter LP 34. The ower densty of sunlght ncdent on a solar cell s mw / cm. Its short crcut current densty s m / and the oen crcut voltage s.7 3 cm. If the fll factor of the solar cell decreases from.8 to.5 then the ercentage effcency wll decrease from (a) 4. to 6. (b) 4. to 6.8. to to.5 H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

16 ns: Soluton: The effcency of a solar cell s determned as the fracton of ncdent ower whch s converted to electrcty and s defned as ocisc and Pmax ocisc P where n oc s the oen crcut voltage, I sc s the short crcut current densty, s the ll factor, P n s the nut ower and s the effcency of the solar cell. Gven Pn mw / cm, Isc 3 m/ cm, oc.7 Let s the effcency of solar cell when.8 3 cm.7 3 / W / cm Let s the effcency of solar cell when.5 3 cm.7 3 / W / cm Thus effcency decreases from 6.8% to.5% NET/J (JUNE-5) 35. The concentraton of electrons, n and holes, for an ntrnsc semconductor at a temerature T can be exressed as 3 Eg n T ex kt, where E g s the band ns. ga and s a constant. If the moblty of both tyes of carrer s roortonal to then the log of the conductvty s a lnear functon of T, wth sloe Eg Eg Eg (a) (b) k k k E ne T ex T kt Soluton: e ln 3 3 g Eg Eg ln sloe s kt k Eg ex kt E k g T 3, H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

17 Pa 36. The vscosty of a lqud s gven by Poseulle s formula 8l ns. 4. ssume that l and can be measured very accurately, but the ressure P has an rms error of % and the radus a has an ndeendent rms error of 3%. The rms error of the vscosty s closest to (a) % (b) 4% % 3% 4 Soluton: ka n a P a a 4Pa 4 3 a a n n a n % n 37. onsder the crcuts shown n fgures (a) and (b) below K K K K.7 5 (a) (b) If the transstors n gures (a) and (b) have current gan of and resectvely, then they oerate n the (a) actve regon and saturaton regon resectvely (b) saturaton regon and actve regon resectvely saturaton regon n both cases actve regon n both cases ns. (b) Soluton: In both case nut secton s or fgure (a) I m I I m dc H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

18 Thus.7 ve outut secton s.. snce both secton are.. so t s n saturaton regon. 5.7 or gure (b) I.43 m I I 4.3 m 4.3.7) ve Thus out ut secton s.. Thus t s n actve regon 38. In the crcut gven below, the thermstor has a resstance 3 k at decreases by 5 er uon heatng. The outut voltage of the crcut at T 5. Its resstance 3 s K out ns. (a) 3.75 (b) Soluton: t 3 esstance v.5 volts H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

19 NET/J (DE-5) 39. If the reverse bas voltage of a slcon varactor s ncreased by a factor of, the corresondng transton caactance ns.: Soluton: (a) ncreases by a factor of (b) ncreases by a factor of decreases by a factor of decreases by a factor of T T T T T 4. If the arameters y and x are related by y log x roduce an outut voltage varyng lnearly wth x s T T, then the crcut that can be used to (a) y o (b) y o y o y o ns.: Soluton: () Integrator () Logarthmc mere y y (3) nt-log e x (4) Dfferentator log H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

20 4. The state dagram corresondng to the followng crcut s x y LOK D l lo (a),, (b),,,,,,,,,,, ns.:,,, Soluton: D xy Inut Present l-lo Next State x y State Inut D H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

21 4. snusodal sgnal of eak to eak amltude and unknown tme erod s nut to the followng crcut for 5 second s duraton. If the counter measures a value 3E 8 H n hexadecmal, then the tme erod of the nut sgnal s. K bt counter K ns.: (a).5ms (b) 4ms ms 5ms Soluton: 3E H In 5 sec, number of counts s Then count er sec s count/sec So, T sec 5 ms NET/J (JUNE-6) 43. The deendence of current I on the voltage of a certan devce s gven by I I where I and are constants. In an exerment the current I s measured as the voltage aled across the devce s ncreased. The arameters and I can be grahcally determned as (a) the sloe and the y -ntercet of the I grah (b) the negatve of the rato of the y -ntercet and the sloe, and the y -ntercet of the I grah the sloe and the y -ntercet of the I grah the negatve of the rato of the y -ntercet and the sloe, and the y -ntercet of the ns: I grah H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

22 Soluton: I I I I I I Sloe I I I I Intercet on y -axs I 44. In the schematc fgure gven below, assume that the roagaton delay of each logc gate s t gate. 5 I ns: Soluton: The roagaton delay of the crcut wll be maxmum when the logc nuts and make the transton (a),, (b),,,,,, Inut Outut NOT O ND O 3t 3t t 4t H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

23 45. Gven the nut voltage, whch of the followng waveforms correctly reresents the outut voltage n the crcut shown below?.5 K.5 t.5 5 K 5 K K (a) t.5.5. t ns: (b) Soluton: When, when..8, when The decay constants f of the heavy seudo-scalar mesons, n the heavy quark lmt, are ns. : related to ther masses m by the relaton t f (b) a m, where a s an emrcal arameter to be determned. The values m 64 6 Me and f corresond to uncorrelated measurements of a meson. The error on the estmate of a s (a) 75 Me 3 (b) 9 Me 3 Me 3 4 Me 3 t Me H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

24 Soluton: a f m / a a a f m f m a f m / a f and m m f f a m a m f m 4m a f m / / 3/ a f m Me Me Me f f 8 3 m f a a f m m 6 and.56 m 64 3/ 3 4 / 3 / 3/ 887 Me a 88 Me Me 3/ a NET/J (DE-6) 47. Whch of the followng crcuts mlements the oolean functon,,,,4,6? 4 (a) I I I 4 MU (b) I I I 4 MU I3 S S I3 S S I I I 4 MU I I I 4 MU I3 S S I3 S S ns. : (b) H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

25 Soluton: a 48. The I characterstcs of a devce can be exressed as I Is ex T, where T s the temerature and a and I s are constants ndeendent of T and. Whch one of the followng lots s correct for a fxed aled voltage? (a) ns. : log I log I 3 3 a / T 3 3 a / T Soluton: Let av x T or large x ; x I Is e loge I loge Is x loge I x (b) log I log I 3 3 a / T a / T H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

26 49. The actve medum n a blue LED (lght emttng dode) s a Ga In N alloy. The band gas of GaN and InN are 3.5e and.5e resectvely. If the band ga of Ga In vares aroxmately lnearly wth x, the value of x requred for the emsson of blue lght of wavelength 4nm s (take hc e -nm ) (a).95 (b) ns. : (b) Soluton: E 3.5e and E.5e g GaN g InN E e x x x x N and Ga energy of GaxIn xn s E x or blue lght of wavelength 4nm, the band ga.5 hc e. nm energy s 3.e 4nm. x? Thus equatng sloes we get; x.5 x.75 x 5. In the crcut below, the nut voltage s, cc 6, k and L k x L The value of requred to delver mw of ower across L s (a) k (b) 4k 8k 4 k ns. : v v v v Soluton: ly kl ; I I IL v L mw v L L I I I L L o 8 8k k H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

27 5. Two snusodal sgnals are sent to an analog multler of scale factor followed by a low ass flter (LP). 5cos t Multler LP f 5Hz out cos t / 3 If the roll-off frequency of the LP s f 5 Hz c, the outut voltage out s (a) 5 (b) 5 5 ns. : (b) Soluton: fter multlyng 5cos cos 3 t t 5 cost 3 cos t cos 3 3 fter ass L.P.. v The resstance of a samle s measured as a functon of temerature, and the data are shown below. T The sloe of vs T grah, usng a lnear least-squares ft to the data, wll be 6 (a) ns. : (b) 4 (b) 8 H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

28 NET/J (JUNE-7) 53. In the n -channel JET shown n fgure below,,, 6 and DD D k. DD D D O G S If the dran D - source S saturaton current I DSS s m and the nch-off voltage P s 8, then the voltage across onts D and S s (a).5 (b) ns. : Soluton: I D GS I DSS GG GS P z m 5.63m 8 I z 4.8 DS DD D D z 54. The gan of the crcut gven below s. n b a out The modfcaton n the crcut requred to ntroduce a dc feedback s to add a resstor (a) between a and b (b) between ostve termnal of the o-am and ground n seres wth arallel to ground H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

29 ns. : decoder wth an enable nut can functon as a (a) 4 multlexer (b) 4 demultlexer 4 encoder 4 rorty encoder ns. : (b) 56. The exermentally measured values of the varables x and y are..5 and ns. : (a) 3.. resectvely. What s the error n the calculated value of z 3y x from the measurements? (a). (b) Soluton: z 3y x z z z y x 9 y 4 x y x. 57. Let I be the saturaton current, the dealty factor and v and v the forward and reverse otentals resectvely, for a dode. The rato / of ts reverse and forward resstances and, resectvely, vares as (In the followng k s the oltzmann constant, T s the absolute temerature and q s the charge.) (a) v v qv ex kt (b) v v qv ex kt v v qv ex kt v v qv ex kt ns. : (a) I I e, T / Soluton: T KT q / I I / I I / T Ie q ex I KT H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

30 58. In the fgures below, and Y are one bt nuts. The crcut whch corresonds to a one bt comarator s (a) Y Y Y Y Y (b) Y Y Y Y Y Y Y Y Y Y ns. : Y Y Soluton: (a) Y, Y,3 (b). Y, Y,3 Y,,3 Y Y Y Y Y (equalty comarator ) Y, Y, Y 3 H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

31 59. oth the data onts and a lnear ft to the current vs voltage of a resstor are shown n the grah below. I (ams) If the error n the sloe s grah s (a) , then the value of resstance estmated from the (b) ns. : (b) Imax Imn Soluton: Sloe m (let) 5 5 max mn I m 5 where m m m 4 Error n s m 4 m m m m m volts 5 6. In the followng oeratonal amlfer crcut n, k, k and n n. n out The magntude of the gan at a nut sgnal frequency of 6kHz s (a) 67 (b) H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /

32 ns. : Soluton: / z Jc Jc n z Jc o / Jc jc / o j c j c j c j c n o c, f n c c ln H.No. 4 D, Ground loor, Ja Sara, Near IIT, Hauz Khas, New Delh 6 Phone: /