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VISVESVARAYA NATIONAL INSTITUTE OF TECHNOLOGY, NAGPUR DEPARTMENT OF MATHEMATICS Sessional-II Examination (October, 2022) Max. Marks: 15 Duration: 1 hour (6 x3 = 15 Marks) III Semester, B.Tech. (MEC, EE Subject: Integral Transforms and Partial Differential Equations-MAL201 Note: any five of the following questions. Eich question carry equal weightage. NS 4 ; 1, Find the the frequency spectrum of the function f(z) = | and also plot it. afte . Find Fourier integral of the function f(x) “10, 1 (CO-2) your answer, What is the value of this integral? Justif F(A), exists. Then, for any constants Ag and is Aad e(\ =X). (CO-2) Fourier tr 3. Let f bea function defined on ® such tha fy, Show that the Fourier transform of the function g(t) = « veconstant. (CO-2) 4. Find Fourier cosine transform of the function f(z) 0, where eis a po: 5. Solve the differential equations y’ — 4y = d(t—3), -co << os. (CO-2) Furst, is hyperbolic, aGttation +. ifs equation ss, Uyy = 6. (a) Find the region(s) of 2? in which the partial diff parabolic or elliptic? (b) Find the D Alembert solution of the u(z,0) = e7,w(2,0) = cos2z,-co << t < ow. cose
Owith {CO-3) SVARAYA NATIONAL INSTITUTE OF TECIINOLOGY, NAGPUR DEPARTMENT OF MATHEMATICS Sessional-I Examination II Semester, B.Tech. (MEC, EEE) Max. Marks: 15 Subject: Integral Transforms and Partial Differential Equations-MAL201 ___Duration: 2 hour Note: Answer any five of the following questions. Each question carry equal weightage. (3 <3 = 15 Marks 1. State the first shifting (shifting along t—axis) property of Laplace transforms. i bt Let f bea function defined on (0, 0) such that L{ f(#)} = F(s), then show that L-'{F(as+b} = : eal : where a,b € R. (CO-1) 2. Without finding the inverse Laplace transform, is it possible to say that a function of s, say F(s), is Laplace transform of some function of ¢ ? Justify your answer. Find the inverse Laplace transform of the function cot"? (+). ; pe (c0-) 3. (a) State the sufficient conditions for the existence of Laplace transform of a given function, and also prove this result, 1 (b) Use convolution theorem to find L7} {atm}. where a € B, (20-1) 4. Soive the initial value problem y” + 3y’ + 2y = u(t — 1) + 4(t — 2); y(0) = 0 = y'(0). (70-1) -l, -l' (CO & (2n-1)? yo A pl 3. National Institute of Technology, Nagpur inecring Visvesvaraya Department of Elcetrical Ex Second Sessional Examination Slot: F Class :B. Tech, Semester aid} Branch : EEE Session 3 W2022 Duration rl he. Full Marks 215 Subject: EEL201 — Network Theory Instructions: |, Attemptall questions. ws . Use of non-programmable scientific caleulator is permitted. I. The switch is thrown from position ‘I’ to position ‘2’ at = 0. Just before it. i:(0-) = 2A and W/(0-) = 2V. Find the current through the inductor, i() for ¢= 0+ ands = 6. ‘ a) - 2. Find its) and so in the circuit shown below for ¢ = 0+. Assume that the switch has been closed for a long time. 10V The Z-parameters of the network in the figure below are = Z11 = 40Q. Zi2 = GON, Zy = 802, Zz = 100, Determine the average power delivered to Ry (= 200). 102 4, 1, + + 20v | FZ] In Sa umbers in the last but one column indicate maximum marks to the question. 3 co: co; 3 CO: COs 3 CO: CO) 1/2| Page { 4 “Find out the A-parameters of the network shown below. The cases with different 3 COy readings are depicted below: Cor a) Se open, Sy closed OAM HAS VY Myo 5 Vida LA b) 8) closed. 8) > open A ed ANE COV, MOM. dr OA ho Two Port Network li i » 5. Inthe given network if R, is changed from TkQ to 2kQ, find the change in current in 3 COz the branch containing R, using compensation theorem. VI=1I2V.RI=TKO , R2=1-5kO ANNA Ra NT/EEL201/Slot-F/Sess-I/125 copies/NRP-AM 2/2|Page VISVESVARAYA NATIONAL INSTITUTE OF TECHNOLOGY, NAGPUR- 440010 Electrical Engineering Department (2*” sessional examination, Oct. 2022) SLOT-D CLASS 2B. Tech SEMESTER Tl BRANCH : EEENG, SESSION + W2022 TIME : | HOUR FULL MARKS :15 : Subject; EEL202: Signals and Systems : ee aaa - The missing data, if any, may be assumed suitably. 4 Before attempting the questions, be sure that you have got the correct question Paper. 3. All questions are compulsory. Ql. (a) A discrete-time system has impulse response [3+2] h(n] = a" u[n +5] Discuss whether this system is BIBO stable, causal and memoryless? c0-2 (b) Interpret the step response of a discrete-time system with impulse response given by A(t) = 10 eG) u(t) OR (a) Let X(t) = ¢ O — 7 ' = ' "Cu i fap Neo Lo | 0 T 2T IT aT sr Th Time ¢, seconls @) if) | Fig. 1: (a) Square wave, (b) rectangular pulse LL | QG_Consider the system deseribed by the input-output relation y(¢) = x(¢) x(t —2) | [2] Check and illustrate the given system is linear or nonlinear and time-invariant or time- ¢ _CO-1 Q3. Consider the rectangular pulse x(¢) of unit amplitude and duration of 2 time unit depicted in Fig. 2. Compute y(t) = 2x(2t Fahn {3] Vet 3/2 ¢ (t a xu) 1.0 | 7 Hl CcO-1 tiie, [i]. 7 ys Steal -101 = espe Fig. 2: rectangular pulse Q4. Compute and plot the integral convolution of signals given below. iol a(t) A(t) CcO-2 1k—_——- ad Ct) t 0 1 3 t AL | Desi ingle stage common emitter (CL) amplifier with volt divider [3] (self) ¢. Assume that the amplifier is supplied with Veo = 20. ¥. the . device has maximum dipe(or) f valuc of 20 and Too = HWA. TERE = 4kQ CO-2 and Quiescent point is required to be at Wer = 6-V and fe = 2 mA, Estimate _| the values OPRE, Rian Re 5, | Analyze the circuit given below (Fig, 3). Rs= 20.0, Vz= talAnd R= 200 Q. | [3] IP Ving can vary from 20V (o 30V,f ind a) The minimum and maximum currents in the Zener diode. co-l b) The minimum and maximum power dissipated in the diode. ¢) The maximum rated power dissipation that Rs should have. R. I WW 4 Va | rN v, s Rr Fig. 3 6. | Sketch the hybrid model of a BIT. Define (i) Hye, (ii) Mies (tii) Bre, and (iv) Mtoc. | [1-5] CcO-2 Page 2 of 2 1 National Institute of Technology, Nagpur Department of Electrical Engineering, Quiz-? Visvesvara Subject: FEL201 — Network Theory 1. The network shown in Pig. Pisina steady state w ith Sy closed and S) open. Att=ty, S; is opened and So is closed, Pind the current through the capacitor in tine domain, aA vi mn Bn Br ut oe lh Fig. 1 The nwo-port network N is connected to a source and a load as shown in Fig. 2. The s the network N are given by +s), Zig = Za1 = 2s, Za= (2844). Replace N by its T-cquivalent and then find 4, 2, Vi, and Mi. Assume the inductance is in relaxed condition initially. we if h + + Q . 1Q v= @ 3 vj oN ly, 1H 12cos(t) - - Fig. 2 3. Consider the circuit shown in the Fig. 3. Find the Thevinn equivalent resistance across the AB terminal. <> 3h AWWA 1Q fo 10V(t) 19 10 19 AW B Fig. 3 4. Inthe circuit shown below, obtain the valuc of the capacitor C required for maximum power to be transferred to the load, wr @) 1Osin( 1001) 4, | a. Explain the necessity to modify Ampere's law for time varying fields? Write | [2+2] C0-1,2,3,4 the Maxwell's equations in point form and integral form, Explain the BLT- L2,L4,L5 significance of each equation b. Start with Maxwell's equations in phasor-form for a source-free uniform | [4] conducting medium, obtain the wave equation in terms of E and Jficlds 5.] a. Explain, why the resistance of a wire increases with frequency, Compute | (242) CO-1,2,3,4 the skin depth of a 2-mm radius aluminium round conductor operating at 50 BLT- Hz. The conductivity of the aluminium is 3.55 x 107 Sim, L1,L2,L3,L5 b. What is the Poynting vector? Briefly explain the physical interpretation of (144) the Poynting vector over a closed surface? ¢. Explain the basis behind the construction of the Smith chart? Why is a circle (2+2) with ils center of the Smith chart known as constant SWR circle? 6. | a. For a given transmission line, Z.= 50 Q and Z, = (10+j20) ©. If the length [24#2+2] | CO-1,2,3,4 of the line is 0.2A then, determine- (i) Reflection coefficient (ii) VSWR (iii) BLT- Impedance at 0.24. (Use Smith chart) L2,L4,L5. b, The antenna with impedance (20 +j10) Q is to be matched to a 50 9 lossless line with a shorted stub. Compute- (i) The required stub admittance (ii) The distance between the stub and the antenna (iii) The stub length. (Use Smith chart) : [2+2+2] EED/MA/AT/EEL206/November 29, W2022 2] rape er . Time: 3 Hours SRE 204: Men Note: Assume suitable data whenever necessary, Max marks; 60 QNo. _ ; —— Marks | CO | B1 la) Why errors are studied’? Observation in power measurements are V= 100 VE 1% , Ie | 5 | 3 f IOA+ 1% R= LOM 4 0.2% . Suppest which method (P= WAR or P= PR ) is | most suited with reason. (Std. Deviation error) ee = by [ thly precision instrument may not be accurate eee Peed ee c} Determine the error in measurement of current through 500 Q resistanee connected in | 3 jl |2 series with 5 W battery using ammeter having 100 0 resistance | 1 = | { | | 2a) Discuss the generalised Instrumentation system using block diagram 3 ie ae b) Explain with neat circuit and phasor diagram , how VAR can be measured using 4 }2 2 | wattmeters in 3-phase unbalanced circuit | | oy A bridge with arm AB consisting of coil (Ry,L)), arm BC wirh R3=750 Q, arm CD | 3 | 2 a | with R4=64,5 Q in series with C4= 0.35 p F (with interpal resistance r = 0.5 Q jand arm DA has R2=24000 Find Rul; _(Q>10) fa OY | | | I H | | Bi a), Discuss various factors for selection of transducer. Classify transducers giving 3 }2 |2 | examples | | | b) A 1000/3 A CT operating at full load with purely resistive burden draws exciting 4 2 3 current (Io)of 1 A at 0.3 lag pf. Determine ratio and phase error c) f_| Discuss Hall effect transducer and its one application 3 {2 |2 | | 4 a) | Suggest and explain suitable bridge to measure conductor resistance of | meter 3 \3 |3 long 100 A cable. | | | b) Explain with circuit diagram, how power in high voltage, high current circuit can be 3 3 3 _ measured | c) | Develop and explain a set up for measurement of pressure such that final output of 4 3 | 7 _| set up is Voltage | 5 a) | Suggest a suitable transducer/ sensor to measure furnace temperature upto 1400°C and | 3 3. (3 —~_| explain measurement process ‘* b) Determine the size (bit) of ADC for a resolution of 5 mV in full scale range of 5 V. 2 3 2 —__| Name fastest type of ADC c Discuss the working of any one type of DAC 3 [4_|2 A d Discuss Digital filter briefly 2 4 |2 ~ OR Briefly discuss Digital storage Oscilloscope (DSO) 6 a) | Discuss the digital data acquisition system using block diagram 3 4 |2 k b) | Explain RF telemetry (in brief ) 3 4 |2 ~ OR Discuss Virtual Instrumentation c) | Explain microprocessor based power measurement with block diagram 4 4 2 VISVESVARAYA NATIONAL I Electrical Engin ion, Nov./I Q (End Semester Examin Mi ——— ACSA Silicon transistor uses pote ider method of t co2 | 13 iw Ry=R2=1OKQ. Ry=3KQ. Rem Aka. Determine operating. point using Thevenin’s theorem. [Let ff = 50, Myp = 0.7] _ —=— SE ——— fd) The coll tor and base current of an NPN transistor are measured as Ic = | 3 co2 | L4 5mA and In = SOWA, respectively, and Icno = 1 A. (i) Determine a, fi and Ir. (ii) Determine new level of Ip required to produce Ie = 10 mA. a) Compare different power amplifiers based on their efficiency, distortion | 2 cO3 | 14 in outpul voltage. and conduction angle ofcollector current? as | by Draw the ymbol and V-I characteristic of Tunnel diode. 2 co3 | LI c) An amplifier has an open loop voltage gain of 40. The amplifier is | 3 co3 | 14 converted into feedback amplifier, which provides 10% negative feedback in series with input. Calculate (i) Voltage gain with feedback, (ii) amount of feedback in dB, (iii) loop gain. _ : 7 d)_Draw drain characteristics of n-channel JFET and explain various regions. | 3 CO3 | L3 a)_What is the difference between amplifier and oscillator? 2 co4 | Ll b) Derive the expression for the gain of the positive feedback amplifier. What | 2 co4 | L2 is Barkhausen Criterion of oscillations? ©) Draw an RC phase shift oscillator circuit with the following parameters 3 co4 | L3 RI=R2=R3 = 1 MQand Cl = C2=C3 = 68 pF. Also, find the oscillation | * frequency? d) A voltage-series feedback amplifier employs a basic amplifier with input | 3 co4 | LI and output resistances cach of 2kM and gain A = 1000 V/V. The feedback factor 8 = 0.1 V/V. Find the gain A;, the input resistance Rjy, and the output resistance Ror of the closed loop amplifier? a) A JFET has Vp = -4.5 V, Inss = 10 mA and Ip = 2.5 mA, Determine the | 2 Col | L3 transconductance, b) Explain briefly- 2 col | L2 (i) Why channel of JFET is never completely closed at the drain end? (ii) Dynamic drain resistance of JFET. c) What is difference in construction of enhancement type MOSFET and a | 3 col | L2 depletion type MOSFET? Explain the operation and characteristics of N- channel MOSFET in enhancement mode. d) A sinusoidal signal Vs = 1.95sin4001 is applied to a power amplifier. The | 3 CO3 | L4 resulting current is fo=/2sin4002+ F.2sin800t+0.9sin 12001 +0.4sin1 6001, Calculate (i) the total harmonic distortion (ii) the percentage increase in power because of distortion. OR Design the circuit given below to obtain a current iy = 80 #A. Find the value required for R and Vp ? Let, for the N-MOS transistor, Vr = 0.6 V. HnCox = 200 p A/V?, L = 0.8 pm, and W = 4 pm. Vop =3¥ ~~ All the Best ~~ Page 2 of 2 Visvesvaraya National Institute of Technology, Nagpur Department of Electrical Engineering End Semester Examination Slot: F Class : B. Tech. Semester lll Branch : EEE Session : W2022 Duration 23 hrs. Full Marks 760 Subject: EEL201 — Network Theory Instructions: 1, Attempt all questions. 2. Numbers in the last but two columns indicate maximum marks to the question. 3. Use of non-programmable scientific calculator is permitted. “1,) Find Norton's equivalent circuit across x.y. 6 CO Ly = CO, “A 10 ‘ZG Find the Thevenin's equivalent circuit for a battery box r voc (| Re Q) 6 CO bs containing four batteries with their positive terminals Bl 12 0.50 cor connected together and negative terminals connected [Ry 121 0.10 together. The open circuit voltages (si. ) and internal By] 124 0.16 resistances (Ri) of the batteries are given as in the Table. Bl I24 0.20 uf Find the current through load impedance Z, when it receives maximum power, Also, 6 CO: Ls determine the maximum power. cor fa) Two identical sections of the network are cascaded. Obtain the transmission parameters 6 CO, Ls As of of the resulting circuit. f amie ees . CO; mart: oe amet a 1 Ao " pera VavaN AA. AW ' " ' " H 19: 2st ' " ' * ———= = SA 10 V pulse of 10 ps duration is applied to the circuit below. If the capacitor is © a La s fo completely discharged prior to applying the pulse, find out the peak value of the capacitor voltage. 1kQ lov. 10k0 ==! LaF WY2| Page Vievrerves VISVESVARAYA NATIONAL INSTITUTE OF TECHNOLOGY, NAGPUR 440010 Electrical Enginecring Department (End Semester Examination, Nov./Dee. 2022) SLOT-D SEMESTER SH CLASS 2B. Teeh SESSION : W2022 BRANCIE |: ER ENG. TIME J HOUR FULL MARKS: 60 Subjeet: EEL202: Signals and Systems INSTRUCTIONS lL. The missing d any, may be assumed suitably. the questions, be sure thal you have got the correct question paper. sare compulsory, ; Bloom's Questions Marks | COs Taxonomy Level (i) Determine the expression of a nal x(¢), as shown in figure (1). x(t) (ii) Determine the period of the 1 (6) Qi. | following signals [2+2+ 1 3 2 (a) xe =sin( Joo 2) 7 et 2] 3 3 7 Figure (1) 2 (by x(n) = (=1)" Two sequences ,(7) and x,(7) have the same energy, where x(n) = @0.5"u(n),a@ >0 L@) VIS. for n=0.1 14] 1 3 XC) = . 0, Otherwise and u(n) is a unit step sequence. Determine the value of a. The impulse response g(t) of a system G is shown in figure (a). Detrmine the maximum value (amplitude) of the response (y(t)) obtained by the convolution (using graphical method) of same nature of input signal x(t). On) a(t) 15] 2 3 t Figure (a) Obtain the state transition matrix @(t) and its inverse 7 *(t) of the given state space model. x, (: Ee) is} | 3 3 = “ . 39: cally xX, 2 -3|X, (a) A signum function is given by 1, x>0 sgn(x)=f-1, x<0 0 x=0 / Determine the Fourier series expansion of Ssgn (sin 401). 18] 4 3 (QS. )(b) Let x(#) be a periodic signal with fundamental period T and Fourier (6+2) series coefficient C,. Derive the Fourier series coefficient of the given signal (y(t)) in terms of C, . MV) =x(f-1)+x(31 +6). | _(Llth< 7, fa) x(0 = {oie >T, (b) x(t) = DP. SU — kT) Gi) Using, the properties of Fourier Transform (FT), calculate the FT of the following signals: (ay x(t) = 5x4 (t — 2.5) + x, (t— 2.5) (b) x(t) = 2x(—4t = 12)e7 a (iii) Sketch the spectrum of the discrete-time Fourier Transform of @ signal given as xn] = a"uln|, lal <1 (i) Obtain the Fourier Transform of the following, signals: 10] [3+4+ 3] 1,4 34 Q7. Gi) A continuous-time signal x(t) is obtained at the output of an ideal low pass filter with a cutoff frequency t. = 10007. If the impulse-train sampling is performed on x(t), Which of the following sampling periods (see) would guarantee that x(£) can be recovered from its sampled version using an appropriate lowpass filter? (a) T= 0.5 x 107-3 (b) T= 2x 1077 (c) T = 107* (ii) Determine the Nyquist rate of the given signal: x(O= (sintsoooneny? nt 4] [2+2] 23 Qs. Explain the concept of the sampling theorem using the impulse train sampling method. [4] Qs. (i) Examine the Laplace transform of the signals given below, fa) x(t) = 3 e7* ult) —2e7* u(t). (b) x(t) = e7?F u(t) + e'(cos3t)u(t) (ii) Solve to obtain the inverse Laplace transform of the signal 1 X03) = Sees (a) when the ROC is Re {s} > —1 (b) when the ROC is Re {s} < —2 (c) when the ROC is —2 < Re {s} < -1. (iii) Obtain the initial and final value of the signal given below _ _(2s%+5s?+12s) H(s) = (s3+457+145420) (iv) Inspect the causality and stability properties of the following system functions: eo. = (a) H(s) = yi Pets} >-l1 (b) Hs)= PSY > 2 (s+1)(s+2) {81 [243+ 142] 34 Q10. (i) Examine the region of convergence (ROC) for the following signals using z — transform approach; (a) x[n] = 5(n — 1), (b) x[n] = b!"!, b> 0, (c) x[n] = -a" u[-n—- 1]. (ii) Consider a system function given below, a= H(z) = _ G27) (Ree (a) Solve to obtain its inverse z-transform, h[r], (b) Comment on the causality and stability of this system function. 16] [3+3] 34
