UPSC Engineering Services (Main) Examination 2024 Electrical Engineering Paper I & II – Previous Year Question Paper PDF Download
UPSC Engineering Services (Main) Examination 2024 Electrical Engineering Paper I & II –
Previous Year Question Paper PDF Download
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.
Questions No. 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 (QCA) Booklet must be clearly struck off.
Answers must be written in ENGLISH only.
Free PDF Download LINK Given in Last of This Post/ question Paper , For Image and Diagram Please refer to given PDF
PDF For 2nd Question paper Given In Last of this post
UPSC Previous Year Question Paper, testbook ,UPSC Previous Year Question Paper PDF, UPSC Previous Year Question Paper PDF Download, UPSC Question Paper PDF Download, UPSC Previous Year Papers, UPSC Previous Year Papers PDF, UPSC Previous Year Paper Free D
Previous Year Question Paper UPSC
UPSC Engineering Services (Main) Examination 2024 Electrical Engineering Paper I & II – Previous Year Question Paper PDF Download
1. (a) Using double integral, find the volume in the positive octant of the ellipsoid 12
x²/16 + y²/9 + z²/4 = 1.
(b) The strength of one bond of Magnesium Oxide (MgO) is 10·54 eV. How much joules of energy for vapourization will be needed by 0·35 kg of Magnesium Oxide ? (Take Avogadro number = 6·022 × 10²³ atoms/mol, charge of electron = 1·6 × 10⁻¹⁹ Coulombs, atomic mass of Mg = 24 u atomic mass of Oxygen = 16 u 12
(c) What are Maxwell's equations in Point Form and Integral Form ? How do these equations take form in free space ? 12
(d) For an abrupt silicon p-n junction with acceptor ion concentration N_A = 4 × 10¹⁶ cm⁻³ and donor ion concentration N_D = 10 × 10¹⁵ cm⁻³ ,if T = 300 K , intrinsic carrier concentration n_i = 1 × 10¹⁰ cm⁻³ , calculate the maximum electric field in the depletion region when V_a = −3·5 volts. Assume relative dielectric constant of silicon ε_r = 11·8 , electron charge q = 1·6 × 10⁻¹⁹ C , Boltzmann's constant k = 1·38 × 10⁻²³ J/K , permittivity of free space ε₀ = 8·854 × 10⁻¹² F/m . 12
(e) Write a 'C' program to identify whether the given input word is a 'palindrome'. The program should read the word from the terminal and display the message whether the input word is a palindrome or not. If the input word is 'END' it should exit the program. 12
2. (a) (i) Determine the eigenvalues and eigenvectors of B = 2A² − 1/2 A + 3I where A = [ [8, −4], [2, 2] ] . 10
(ii) Using the method of Lagrange's multipliers, find the largest product of the numbers x , y and z , when x + y + z² = 25 . 10
(b) From atomic interpretations of spontaneous magnetization in ferromagnetic materials and the Curie-Weiss Law, determine Curie constant in terms of Bohr magneton (β) and N spins per m³ in the material. Establish how spontaneous magnetization takes place below the Curie temperature. 20
(c) (i) Give briefly the concept of precision in measurements. Explain with examples the roles of 'significant figures' on measurement of precision of a measuring tool. 10
(ii) Using a standard cell of 1·016 V , a simple potentiometer balances at 48·4 cm . Calculate : (I) the emf of a cell that balances at 72 cm (II) the percentage error in a voltmeter, measuring a voltage which balances at 66 cm , when reading is 1·40 V . 10
Q3. (a) (i) Using the Cauchy- Riemann equations, show that f(z) = f(r, θ) = r⁴(cos⁴θ − 6cos²θ sin²θ + sin⁴θ) + 4i r² sin θ cos θ (cos²θ − sin²θ) is analytic in the entire z - plane and hence find its derivative in terms of z . 8
(ii) The mutual inductance between two coils varies with the angle of displacement of the moving coil from its zero position as follows : 12
| Angle (degree) (x) | 0 | 15 | 30 | 60 | 90 | 105 | 120 |
|---|---|---|---|---|---|---|---|
| Mutual Inductance (μH) (y) | -336 | -275 | -192 | 0 | 192 | 275 | 336 |
Determine the Pearson's Correlation Coefficient (r_xy) and the angle between the two regression lines formed by the above data.
(b) (i) Two point charges of Q₁ = 6 nC and Q₂ = 8 nC are placed at (2, 2) and (6, 8) respectively. Show that the equation of the locus on which the electric field intensities due to Q₁ and Q₂ are equal represents a circle. Find its centre and radius. 10
10
(ii) Determine the inductance per unit length of an air filled co- axial cable having a solid inner conductor of radius 'a' metres and a very thin outer conductor of inner radius 'b' metres. Assume that the current flows via the inner conductor and returns in the outer conductor and is uniformly distributed over the cross- section of inner conductor.
[Image: please refer to given pdf link for image and diagram]
(c) (i) The impedance of the basic ac bridge shown in the following figure is given as follows :
Z₁ = 100 Ω < 80° (inductive impedance)
Z₂ = 250 Ω (pure resistance)
Z₃ = 400 Ω < 30° (inductive impedance)
Z₄ = unknown
[Image: please refer to given pdf link for image and diagram]
Determine the value of the constants of the unknown arm.
10
Q4. (a) (i) Determine the phasor voltage V_AB in the circuit given in the following figure. 10
[Image: please refer to given pdf link for image and diagram]
(ii) A three- phase, four- wire, CBA system has an effective line voltage of 140 V and it has three impedances of 25 ∠ − 30° Ω in a Y- connection, as shown in the figure. Determine the line currents and draw the voltage- current phasor diagram. 10
[Image: please refer to given pdf link for image and diagram]
10
(b) (i) A Hall voltage of 3·5 × 10⁻⁸ V in magnitude is generated for an aluminium specimen of 15 mm thickness with a current of 25 A and a magnetic field of 0·6 Tesla, imposed in a direction perpendicular to the current. Calculate electron mobility for aluminium. (Take electrical conductivity for aluminium as 3·7 × 10⁷ Ω/m )
(ii) Six micrograms of antimony are thoroughly mixed in molten form with 200 g of pure germanium and antimony atoms substitute for germanium atoms uniformly throughout the solid material. Determine the density of antimony atoms, the density of donated electrons and the conductivity, if electron mobility is 3500 cm²/Vs , for the carriers.
(Take charge of electron = 1·6 × 10⁻¹⁹ Coulombs, density of germanium = 5·46 gm/cm³ , atomic weight of antimony = 121·76 u , Avogadro number = 6·022 × 10²³ atoms/mol)
(c) (i) The dimensions of the coil of a moving coil voltmeter are 3 cm and 2·5 cm and the coil has 150 turns . The scale has 100 divisions. The air gap flux is 0·15 Wb/m² . Determine the series resistance when the meter is to be used for 0 − 100 V . The spring constant is 2·5 × 10⁻⁶ Nm per division and the resistance of the coil is 1 Ω .
(ii) In a 10 A dynamometer type ammeter, the rate of change of mutual inductance with deflection is constant and is equal to 0·005 μH per degree. It has a full scale deflection of 90° . Find the deflection when the current to be measured is 5 A .
5. (a) In the following figure, a current filament of 6:5 A in the a⃗_y direction is parallel to the y- axis at x = 2 m , z = −2 m . Determine H⃗ at the origin. 12
[Image: please refer to given pdf link for image and diagram]
(b) Derive an expression for the dielectric constant (ε_r) in elemental dielectrics, in terms of the atomic quantities. 12
(c) (i) P is a 16 bit signed integer. The 2's complement representation of P is (F87B)16. Find the 2's complement representation of the product (8P). 6
(ii) In the circuit shown below if C = 0 , find the expression for Y by minimization. 6
[Image: please refer to given pdf link for image and diagram]
(d) Explain with necessary diagrams how a dual slope integrating type ADC operates for conversion of analog input voltage into digital form. 12
12
(e) Identify the type of feedback in the BJT circuit shown below. Draw the general feedback model showing the basic amplifier and feedback network. Find the input impedance and output impedance with feedback of the circuit shown. Its parameters are R_C = 5 kΩ , R_F = 50 kΩ , R_S = 15 kΩ , h_ie = 1200 Ω , h_fe = 60 and h_re = h_oe = 0 .
[Image: please refer to given pdf link for image and diagram]
Q6. (a) (i) Draw the circuit diagram of Hartley oscillator using FET. If L₁ = 15 mH and C = 50 pF , calculate L₂ for a frequency of oscillation of 168 kHz . The mutual inductance between L₁ and L₂ is 5 μH . Find the required value of μ of FET to be used for this circuit.
(ii) For the FET amplifier below, determine V_DQ and I_DQ . Assume that FET is operating in its saturation region.
Given
V_DD = 12 V
K_n = 0.24 mA/V²
V_TN = 3 V
R₁ = 10 M
R_D = 2 K
λ = 0
[Image: please refer to given pdf link for image and diagram]
20
(b) Given dy/dx = (y − x)/(y + x) , y(0) = 1 , compute y(0 − 02) in steps of 0- 02 using
(i) Modified Euler's method and (ii) Fourth order Runge-Kutta method correct to four decimal places. 20
(c) (i) A digital computer has a memory unit with 32 bits per word. The instruction set consists of 270 different operations. All instructions have an operation code and an address part allowed for only one address. Each instruction is stored in one word of memory. Find the number of bits needed for op-code, for address part of instruction and the maximum allowable size of memory. 10
(ii) The distance between two stations is 'L' kilometers and all the frames are 'K' bits long, and the propagation delay per kilometer is 't' seconds and the channel capacity between them is 'R' bits/second. Find the minimum number of bits 'b' for the sequence number field in a frame for maximum utilization, if the sliding window protocol is used. Assume processing delay to be negligible. Derive the equation for 'b'. 10
Q7. (a) (i) The reverse saturation currents I_S₁ and I_S₂ of transistors Q₁ and Q₂ respectively, which are shown in the circuit below are :
I_S₁ = 2I_S₂ = 5 × 10⁻¹⁶ A. If I₁ = 1·2 mA
find
(I) the value of V_B , and (II) the value of R_C which places transistors at the edge of active region.
Assume volt equivalent of temperature V_T = 26 × 10⁻³ V . 10
[Image: please refer to given pdf link for image and diagram]
10
(ii) An n- channel JFET amplifier circuit is shown in the figure below. The JFET parameters are the drain to source saturation current I_DSS = 12 mA , pinch off voltage V_P = −4 V , the channel length modulation coefficient λ = 0.008 V⁻¹ . Find the small signal transconductance g_m and voltage gain A_v .
[Image: please refer to given pdf link for image and diagram]
(b) (i) A 1000/100 V potential transformer has the following parameters:
Primary resistance = 97.5 Ω Primary reactance = 65.4 Ω Secondary resistance = 0.86 Ω Total equivalent reactance = 110 Ω Magnetizing current at 0.4 p.f. = 0.02 A
Find (I) the phase angle error at no load, and (II) load in VA at unity power factor at which the phase angle error will be zero. 12
(ii) A Phantom loading arrangement is used to test a 220 V, 5 A dc energy meter at its marked ratings. The resistance of the pressure coil circuit is 8800 Ω and that of current coil is 0.1 Ω . Calculate the power consumed when testing the meter with:
(I) Direct loading arrangements.
(II) Phantom loading with current coil circuit excited by a 6 V battery. 8
(c) (i) If F̅ = (2x³ − 3z)i − 2xyj − 4xk , then evaluate ∬_V ∇ × F̅ dV , where V is bounded by the planes x = 0 , y = 0 , z = 0 and 2x + 2y + z = 4 where V = i ∂/∂x + j ∂/∂y + k ∂/∂z . 10
10
Q8. (a) (i) A strain gauge of cross- sectional area 3·6 cm² has been bonded to a beam 0·1 m long. The gauge factor of the strain gauge is 2·2 and the unstrained resistance of the strain gauge is 220 Ω . Young's modulus of steel (beam) is 207 GN/m² . Due to application of a load, the resistance of the gauge changes by 0·015 Ω .
a beam 0·1 m long. The gauge factor of the strain gauge is 2·2 and the unstrained resistance of the strain gauge is 220 Ω . Young's modulus of steel (beam) is 207 GN/m² . Due to application of a load, the resistance of the gauge changes by 0·015 Ω .
Calculate the change in length of the steel beam and the amount of force applied to the beam. 10
(ii) Specify the reasons of using 'Sample and Hold' circuits in multi- channel data acquisition system.
Draw and explain briefly the working of a S/H circuit. 10
(b) (i) A series RC circuit has R = 10 kΩ and C = 15 μF and the circuit has two voltage sources in series, given by v₁ = 20 u(−t) V and v₂ = 20 u(t − t′) V . Determine the complete expression for the voltage across the capacitor and plot it as a function of time, assuming t′ as a positive quantity. 12
(ii) Find the T equivalent of the linear network given in the following figure.
[Image: please refer to given pdf link for image and diagram]
Establish the equivalence between the network and its T equivalent. 8
20
(c) The current source circuit shown in the figure below has I_REF = 0.7 mA and I₀ = 25 μA at V_C₂ = 1 volt . The transistor parameters are β = 150 , V_BE₁(ON) = 0.7 volts and Early voltage V_A = 100 V . Determine R₁ , R_E , V_BE₂(ON) and change in I₀ when V_C₂ changes from 1 V to 4 V . Assume that the two transistors are identical and are maintained at same temperature. Derive the equations used.
[Image: please refer to given pdf link for image and diagram]
UPSC Engineering Services (Main) Examination, 2024-ELECTRICAL ENGINEERING I
UPSC Engineering Services (Main) Examination, 2024-ELECTRICAL ENGINEERING -II
UPSC Engineering Services (Main) Examination 2024 Civil Engineering Paper I & II
UPSC Combined Geo-Scientist (Preliminary) Examination GeoPhysics 2024
UPSC Combined Geo-Scientist (Preliminary) Examination Geology Hydrogeology 2024
