ELECTRICAL-ENGINEERING-PAPER-I-QP-ESEM-25-110825

Engineering Services (Main) ane NESP-O-ELEE Examination - 2025 ELECTRICAL ENGINEERING PAPER—I Time Allowed : Three Hours Maximum Marks : 300 QUESTION PAPER SPECIFIC INSTRUCTIONS Please read each of the following instructions carefully before attempting questions There are EIGHT questions divided in TWO Sections. Candidate has to attempt FIVE questions in all. Question Nos. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted choosing at least ONE question from each Section. The number of marks carried by a question/part is indicated against it. Wherever any assumptions are made for answering a question, they must be clearly indicated. Diagrams/Figures, wherever required, shall be drawn in the space provided for answering the question itself. Unless otherwise mentioned, symbols and notations have their usual standard meanings. Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a question shall be counted even if attempted partly. Any page or portion of the page left blank in the Question-cum-Answer Booklet must be clearly struck off. Answers must be written in ENGLISH only. NESP-O-ELEE/42 I [P-T:0; L=(a) (b) (c) (a) (e) SECTION—A () If A is an nxn diagonalizable matrix and A? = A, then show that each eigenvalue of A is O or 1. (ti) Show that all the eigenvalues of a Hermitian matrix are real. 6+6=12 The magnetic field strength in a material is 9x10° A/m and its magnetic susceptibility is 0-75 1075. () Find the flux density and the magnetization in the material. (i) Also find its relative permeability. 2 For the circuit given in the figure below, find the current through 4 Q resistor and the total active power delivered by the source. The source voltage v,(t) = 50cos2V2t + 10cos—t volts : 0-25 as v,(t)=50 cos2v2t+10cos7t volts he >nO5F Consider the circuit shown in the figure below. Assuming that the diodes are ideal, sketch the following waveforms : 12 () Two cycles of V; (input) and V, (output) (ii) Transfer characteristics of the circuit, i.e., V, versus V; R=1kQ ne ae et V;=10sin(2n1002) a8 5 Vee 12 Draw the circuit diagram and explain the process of measurement of low resistance values using Kelvin’s double bridge. Derive the expression and mention two conditions which ensure that the unknown resistance can be easily measured in terms of the standard resistance. 12 NESP-O-ELEE/42 2 2. (a) (i) What are Lissajous patterns? Explain. Also elaborate what patterns appear on the cathode ray oscilloscope screen, when voltages of different frequencies and phase differences are applied in the horizontal and vertical plates of the scope. Take two examples for each of the above two cases. Explain how the unknown signal frequency is measured accurately with the help of observing the patterns. 12 (ii) Explain the principle of operation of a piezoelectric transducer. Write its advantages, disadvantages and some applications. 8 (b) (i) Write a program in C language to print the following full pyramid of numbers : N uw ooart wn on unwne oar ND N nw ao ££ ui 10 (ii) Minimize the four-variable logic function using K-map f(A, B, C, D)==m(, 1, 2, 3, 5, 7, 8, 9, 11, 14) 10 (c) Acardiac pacemaker is represented by the circuit given in the figure below. The battery internal resistance R, is 10mQ, whereas the heart equivalent resistance is 1 kQ. The switch 1 (SW1) is at position a initially for a long time when switch 2 (SW2) is OFF. Then SW1 is moved to position b at t=O and SW2 is ON simultaneously for next t=10 ms. At t=10 ms, SW1 moves to position a and SW2 is OFF for another 10 ms. Find the voltages of the capacitors C,; and Cj at t=0, 10 ms and 20 ms, and sketch the capacitor voltages up to 20 ms. Also calculate the energy dissipated in R, during the interval 0 to 10 ms when SW2 was ON : Rp=10mQ Sw2 o 4 fs oo swl [400 pF é ron io) 100 nal 3V \ 3 Ry =1kQ 20 NESP-O-ELEE/42 3 [ P.T.O. 3. (a) ) (ii) ) (ii) Find the singular solution of the partial differential equation 6yz-6 pxy -3qy? + pq =0 10 Derive the formula by Newton-Raphson method to find next approximation of the root of the equation f (x) =0, if Xo is an initial approximation. Also perform three iterations to find a root of the equation x* — x -10 =0 which is near to x =2, correct to three decimal places. 4+6=10 Prove that the susceptibility of a perfectly superconducting material is -1 and its relative permeability is zero. 8 Find the critical current and critical current density at temperature 4:2 K for a superconducting wire made of lead with a diameter of 2 mm. The critical temperature for lead is 7:2K and its critical field is Ho =6-5x10* A/m. 12 (c) Consider the circuit shown in the figure below : +15V () Determine Q-point of the circuit by assuming maximum drain current Ipss = 8 mA and pinch-off voltage Vp =-4V. (i) Plot the transfer characteristics and DC load line, and indicate the Q-point. 20 NESP-O-ELEE/42 4 4. (a) (i) In a factory, there are following two loads : Lighting and heating load : 100 kW Induction motor load : 1000 HP at 0-7 lagging power factor and 85% efficiency The overall load power factor of the factory has to be raised to 0-95 lagging. A 3-phase synchronous motor is installed for the above purpose. The motor is rated at 300 HP with 100% efficiency. Find the kVA rating of the synchronous motor. Also find the power factor of the synchronous motor. Given 1 HP (horsepower) = 746 watts. (ii) Two single-phase ideal voltage sources are connected by a line of impedance of (0-7+j2-4) ohms as shown in the figure below. Given V, =50016-26° volts and V, =58520° volts. Find the complex power for each source and determine whether they are delivering or receiving real and reactive power. Also find the real and reactive power losses in the line : V1 =500216-26° volts (*) 1 (b) A priority encoder truth table is given below : 0 Inputs y areas x x uf x 0 1 0 ie) (e) 0 ie) Obtain the minimized Boolean expressions for x, y and z outputs. Design a combinational circuit for the minimized Boolean expressions of x, y and z. Consider that x is don’t care. NESP-O-ELEE/42 12 0-7Q j2-4Q 2 Q0000 € V2=58520° volts 8 Outputs x y Zz 0 0 1 ie) 1 i 1 0 1 1 ui 1 x x (0) 20 [(P-:T:0. (c) () A uniform volume charge density of 0-8 wC/m° is present throughout the spherical shell extending from r =3 cm to r=5 cm. If the volume charge density is zero elsewhere, find the total charge present throughout the shell. If the half of the total charge is located in the region where the radius varies as 3cm <r <n, find the value of r, in cm. (i) A current Gusent on the z-axis carries a current of 7 mA in the a, direction and current sheets of 0:5a, A/m and -0-2a, A/m are located at p =1cm and p =0-5 cm respectively. What is the value of H at p =4 cm? What value of current sheet should be located at p = 4 cm so that H =0 for all p >4 cm? Given, H : magnetic field intensity; p : radius variable of cylindrical coordinates. SECTION—B 5. (a) For the circuit shown in the figure below, the two magnetically coupled coils have mutual inductance M =4 mH. The self-inductances are L, = 80 mH and L, =8-2 mH respectively. The source voltage is v, (t) = 100sin 5000t volts with a source resistance of 1 Q and inductance of 1 mH. Find the power delivered by the source and the corresponding source power factor when the connected load with the second coil is a capacitor C of 5 uF as shown in the figure : M=4mH Zs Pog oo wT 12° imH ray : E wis 1023 1,=80mH = an C=5yF *100sin 5000t 1=80m 1p=8:2mH volts NESP-O-ELEE/42 6 10 10 12 (b) Given, p=3x107 H/m, 8 = 1.2×10-10 F/m and - everywhere. If 27 2800101 - 620 6 A/m, use Maxwell’s equations to obtain the expressions for 8, D, E and |. Given, |} : Permeability : Permittivity : Flux density : Magnetic field intensity : Electric field intensity : Electric flux density : Phase constant 12 Pos : (c) Identify the names of the following electronic devices, mark their terminals and plot their transfer characteristics : + 5 | | | (0 (ii) (iii) | = | a : ) 12 (iv) (v) (ut (0) If the probability of a bad reaction from certain injection is 0-001, determine the chance that out of 2000 persons, more than two will get a bad reaction. 12 (e) (i) Determine the possible base of the number in the operation mentioned below : 23 + 44 + 14 + 32 = 223 (ii) Find the number of divisors and sum of divisors of 4900. 6+6=12 NESP-O-ELEE/42 7 [ 6. (a) i) (i) (b) (iw) Explain the principle on which a Q-meter works. Describe briefly the direct connection, series connection and parallel connection of using the Q-meter. Also mention for which types of loads, these connections are ased. A power transformer was tested to determine losses and efficiency. The input power was measured as 3650 watts and the delivered output power was 3385 watts, with each reading in doubt by + 10 watts. Calculate (1) the percentage uncertainty in losses of the transformer and (2) the percentage uncertainty in the efficiency of the transformer, as determined by the difference in input and output power readings. An electric field in x-y plane is given by f(x, y) =3x?y- y®. Find the stream function g(x, y) such that the complex potential w =f +ig is an analytic function. Find the mass of the surface of the cone z=2 Wace +y?, 2<2zS7 in the first octant, if the density p(x, y, z) at any point of the surface is proportional to its distance from x-y plane. (c) A balanced load is shown in the figure below, where R=30 Q, C=159-15 uF and L =95-5 mH. The r.m.s. value of the balanced input supply voltage is 415 V (L-L), 50 Hz. Now find (i) the magnitude of the voltage V,,, (ii) the phase of V,, with respect to Vag and (iii) the total power supplied to the load and corresponding power factor calculated from source side : NESP-O-ELEE/42 erably ae R=30Q L=95:‘5mH A o—{(—2- Ww 1900 Cc 415V, Ic R L 3 ph, - if . WV HO 00S 50 Hz Cc : L 3 12 10 10 20 7. (a) Consider the silicon transistor circuit shown in the figure below. The data pertaining to transistors are as follows : () B =100, (ti) maximum drain current Ipgg =6 mA, (iti) pinch-off voltage Vp, =-2V Determine the voltage Vp. Vec=12V 3kQ 200kQ sae 20 (b) A conducting wire has resistivity of 1-57x1078 Q-m at room temperature. There are 5-85x107® number of conducting electrons per m® for the material at room temperature. For an electric field of 1:1 V/cm along the wire, calculate the (i) drift velocity, (ii) relaxation time, (iii) mobility and (iv) mean free path for the conducting electrons in the material. (Assume charge of electron = 1-609 x 10719 C, mass of electron = 9-11x107°! kg, velocity of electrons v =3x10® m/s and isotropic scattering) 20 (co) (i) Differentiate between isolated I/O and memory-mapped I/O with their advantages and disadvantages. 8 (ii) Represent the following numbers and arithmetic operations given in the table : Numbers / 8-bit signed 1’s complement | 2’s complement Operations magnitude (8-bit) (8-bit) +68 -83 (+68) + (- 83) (—68) +(+ 83) 12 NESP-O-ELEE/42 9 ibe ard ta ©) 8. (a) M i Ro LO. Vi V2 Se 53Q fe} © B Yo Find the reading of the wattmeter when the network shown is connected to a symmetrical 440 V, 3-phase supply. Neglect all losses in the instrument. The phase sequence is RYB. Also draw the phasor diagram of the network. 20 (b) Determine the collector voltage Vc of the silicon transistor circuit shown in the figure below, if (i) B=100 and (ii) B=50: 20 (c) Voltmeters are connected across the resistance R = 1 Q and load impedance Z, and a wattmeter is connected at the input side of the circuit as shown in the figure below. The source voltage is 230 V, 50 Hz and the voltmeters read Vp =10V, V,; =225V. () Find the wattmeter reading, source current and input power factor with the same supply voltage and frequency. (ii) Find the voltmeter and wattmeter readings when the supply frequency is changed to 60 Hz at same supply voltage of 230 V. NESP-O-ELEE/42 10 (iii) Draw the phasor diagram of voltage and currents for (i) above. 230Vv, 4 50Hz © WY 20 kkk NESP-O-ELEE/42 11 26BS—1008