All 8 questions from UPSC Civil Services Mains Electrical Engineering
2024 Paper II (400 marks total). Every stem reproduced in full,
with directive-word analysis, marks, word limits, and answer-approach pointers.
8Questions
400Total marks
2024Year
Paper IIPaper
Topics covered
Control systems, microprocessors, measurements, power systems, communication (1)Control systems stability, microprocessor interfacing, error analysis (1)Control systems, CRT, Microprocessor programming (1)Piezoelectric transducers, 8085 addressing modes, First order systems (1)Control systems, energy meters, power systems, cables, network models (1)Power transmission losses, economic load dispatch, delta modulation (1)Transmission lines and communication systems (1)Information theory and power system protection (1)
A
Q1
50MCompulsoryexplainControl systems, microprocessors, measurements, power systems, communication
(a) What are the limitations of (i) Proportional (P), (ii) Integral (I), (iii) Derivative (D), and (iv) PID Controllers? What is the application of positive feedback control system? (10 marks)
(b) Explain the operation performed by 8085 microprocessor when the following arithmetic instructions are executed: (i) ADD M (ii) ADC M (iii) DAD rp (iv) SBI d8 (v) DCR reg (5×2=10 marks)
(c) The ohmmeter circuit has V_B = 1·5 V, R_1 = 15 kΩ, R_m = 50 Ω, R_2 = 50 Ω and meter FSD = 50 μA. Determine the ohmmeter scale reading at 0·5 FSD.
(d) Calculate the power loss in a cable insulation having capacitance 9 μF, loss angle 0.05 degree and operating at 11 kV, 50 Hz. Draw the phasor diagram and equivalent circuit also.
(e) Explain the concept of a constellation diagram. Draw the PSK signal constellations for the value of M = 2, 4 and 8, if all have same transmitted signal energy E_s.
हिंदी में पढ़ें
(a) (i) समानुपाती (P), (ii) समाकलित (I), (iii) व्युत्पन्न (D), एवं (iv) PID नियंत्रकों की क्या सीमाएं हैं? धनात्मक प्रतिपुष्टि नियंत्रण पद्धति का क्या अनुप्रयोग है?
(b) जब एक 8085 सूक्ष्म संसाधित्र को निम्नलिखित अंकगणितीय निर्देश दिए जाते हैं, तो इसके द्वारा की जाने वाली क्रियाविधि की व्याख्या कीजिए: (i) ADD M (ii) ADC M (iii) DAD rp (iv) SBI d8 (v) DCR reg
(c) ओममीटर परिपथ में V_B = 1·5 V, R_1 = 15 kΩ, R_m = 50 Ω, R_2 = 50 Ω एवं मीटर FSD = 50 μA हैं। 0·5 FSD के लिए ओममीटर के पैमाने के पठन को निर्धारित कीजिए।
(d) 9 μF धारिता, 0·05 अंश हास कोण एवं 11 kV, 50 Hz पर कार्यरत एक केबल अचालक (विद्युतरोधन) में शक्ति हास की गणना कीजिए। कल्पीय (फेजर) आरेख एवं समकक्ष परिपथ भी आरेखित कीजिए।
(e) नक्षत्र आरेख (कांस्टेलेशन डायग्राम) की संकल्पना की व्याख्या कीजिए। यदि सभी संकेतों की प्रेषित ऊर्जा E_s एकसमान हो, तो M = 2, M = 4 एवं M = 8 के मान के लिए PSK संकेत नक्षत्र का आरेखण कीजिए।
Answer approach & key points
This multi-part question requires explaining theoretical concepts for (a), (b), and (e) while solving numerical problems for (c) and (d). Allocate approximately 25% time to part (a) covering controller limitations and positive feedback applications, 20% to part (b) detailing 8085 instruction operations with register-level explanations, 15% to part (c) showing ohmmeter circuit analysis, 20% to part (d) with dielectric loss calculations and phasor diagrams, and 20% to part (e) explaining constellation diagrams with PSK signal space representations. Begin each part with clear identification, use bullet points for controller limitations, step-by-step execution flow for microprocessor instructions, and labeled diagrams for constellation and phasor representations.
Part (a): P controller causes steady-state error and offset; I controller causes slow response, integral windup, and instability; D controller amplifies noise, causes saturation, and is sensitive to disturbances; PID requires careful tuning; positive feedback used in oscillators (Barkhausen criterion), regenerative amplifiers, and Schmitt triggers
Part (b): ADD M performs (A) ← (A) + [(HL)], affects flags; ADC M includes carry addition (A) ← (A) + [(HL)] + CY; DAD rp adds 16-bit register pair to HL (HL) ← (HL) + rp, affects only CY flag; SBI d8 subtracts immediate with borrow (A) ← (A) - d8 - CY; DCR reg decrements register without affecting carry flag
Part (c): Calculate half-scale deflection current (25 μA), determine total series resistance (R₁ + R₂ + Rₘ = 15.1 kΩ), find unknown resistance using Rₓ = (V_B/I) - R_total giving approximately 45 kΩ at 0.5 FSD
Part (d): Calculate dielectric loss using P = V²ωC tan δ = (11×10³)² × 2π×50 × 9×10⁻⁶ × tan(0.05°) ≈ 16.7 W; draw parallel RC equivalent circuit and phasor diagram showing δ angle between total current and capacitive current
Part (e): Constellation diagram represents signal points in I-Q plane with distance from origin indicating amplitude and angle indicating phase; draw M=2 (BPSK: 2 points at 180°), M=4 (QPSK: 4 points at 90° intervals on circle), M=8 (8-PSK: 8 points at 45° intervals), all with same radius √(E_s)
50McompareControl systems stability, microprocessor interfacing, error analysis
(a) The open-loop transfer function of a feedback control system incorporating a dead time element is given by: G(s) = (Ke^(-Ts))/(s(s+1)) where K > 0 and T > 0 are variable scalar parameters. For a given value of T, show that the closed loop system for all values will be K < K₀ where K₀ = ω₀ cosec (ω₀T), and ω₀ is the smallest value of ω satisfying the equation ω = cot (ωT). (20 marks)
(b) (i) Compare I/O mapped I/O and memory mapped I/O interfacing techniques used in 8085 microprocessor. (10 marks)
(ii) What are the operating modes of Port-A of 8255? Explain handshake operation in I/O ports. (4+3+3=10 marks)
(c) In a parallel circuit, in one branch the current, I₁ = (100 ± 2) A and in the other branch the current, I₂ = (200 ± 5) A. Determine the total current considering the following errors: (i) Limiting error (ii) Probable error. Comment upon the results as well. (2+6+2=10 marks)
हिंदी में पढ़ें
(a) एक पुनर्निवेश नियंत्रण प्रणाली के विवृत-पाश अंतरण फलन में सम्मिलित मृत समय तत्व (डेड टाइम एलिमेंट) निम्न प्रकार है: G(s) = (Ke^(-Ts))/(s(s+1)) जहाँ K > 0 एवं T > 0 अस्थिर अविश प्राचल हैं। प्रदर्शित कीजिए कि T के दिए गए किसी मान के लिए, संयुक्त पाश प्रणाली के सभी मान K < K₀ होंगे जहाँ K₀ = ω₀ cosec (ω₀T), और ω₀ = ω का न्यूनतम मान है, जो समीकरण ω = cot (ωT) को संतुष्ट करता है।
(b) (i) 8085 सूक्ष्म संसाधित्र में प्रयुक्त I/O तलरूपित I/O एवं स्मृति तलरूपित I/O अंतरापृष्ठ तकनीकों की तुलना कीजिए।
(ii) 8255 के द्वार-A की संचालन प्रणालियाँ क्या हैं? I/O द्वारों पर हस्तामिलन संचालन की व्याख्या कीजिए।
(c) एक समांतर परिपथ की एक शाखा में I₁ = (100 ± 2) A एवं दूसरी शाखा में I₂ = (200 ± 5) A धाराएँ हैं। निम्नलिखित त्रुटियों को ध्यान में रखते हुए कुल धारा का निर्धारण कीजिए: (i) सीमांत त्रुटि (ii) संभावित त्रुटि। परिणामों पर टिप्पणी भी कीजिए।
Answer approach & key points
The directive 'compare' in part (b)(i) demands a structured contrast between I/O mapped and memory mapped I/O techniques, while parts (a), (b)(ii) and (c) require derivation, description and calculation respectively. Allocate approximately 40% effort to part (a) for the stability derivation, 30% to part (b) combined for interfacing concepts, and 30% to part (c) for error analysis. Structure with clear sub-headings for each part, presenting derivations stepwise, comparison in tabular format, and numerical results with proper significant figures.
Part (a): Derivation of characteristic equation 1 + G(s) = 0, substitution of s = jω, separation into real and imaginary parts to obtain ω = cot(ωT), and final expression K₀ = ω₀ cosec(ω₀T) with justification for smallest ω₀
Part (b)(i): Tabular comparison of I/O mapped vs memory mapped I/O covering address space (separate 8-bit vs shared 16-bit), control signals (IOR/IOW vs MEMR/MEMW), instruction set (IN/OUT vs LDA/STA), hardware complexity, and execution speed
Part (b)(ii): Port-A operating modes (Mode 0-simple I/O, Mode 1-strobed I/O, Mode 2-bidirectional bus) with handshake signals (STB, IBF, INTR for input; OBF, ACK, INTR for output) and their timing sequence
Part (c): Calculation of total current I = I₁ + I₂ = 300 A, limiting error as ±(2+5) = ±7 A, probable error as √(2²+5²) = ±5.39 A, and critical comment on error propagation in parallel circuits
Critical analysis: Comment on why probable error gives tighter bounds than limiting error, and practical implications for instrument selection in power system measurements
(a) An underdamped second order system having a transfer function of the form
$$M(s) = \frac{K\omega_n^2}{s^2 + 2\xi\omega_n s + \omega_n^2}$$
has a frequency response plot as shown in the figure. Compute the system gain K and the damping factor ($\xi$). (20 marks)
(b) A CRT has an anode voltage of 3 kV and its parallel deflecting plates are 2·5 cm long and 5 mm apart. The screen is 30 cm from the centre of the plates. Assume the gain of the amplifier through which input voltage is applied to the deflecting plates as 100. Calculate the following : (20 marks)
(i) Beam speed
(ii) Deflection sensitivity of the CRT
(iii) Deflection factor of the CRT
(iv) Input voltage required to deflect the beam through 5 cm
(c) Write an assembly language program to add two numbers of 8-bit data stored in memory locations 4200H and 4201H and store the result in 4202H and 4203H. (10 marks)
हिंदी में पढ़ें
(a) एक न्यून अवमंदित द्वितीय क्रम (ऑर्डर) तंत्र के अंतरण फलन
$$M(s) = \frac{K\omega_n^2}{s^2 + 2\xi\omega_n s + \omega_n^2}$$
का आवृत्ति अनुक्रिया आरेख चित्र में दिखाया गया है । तंत्र की लब्धि K एवं अवमंदन गुणांक($\xi$) की संगणना कीजिए । (20 अंक)
(b) एक CRT की धनात्मक पट्टिका (एनोड) का विभव 3 kV है एवं उसकी समानांतर विचलन पट्टिकाएँ 2·5 cm लम्बी तथा आपस में 5 mm की दूरी पर हैं । चित्रपट (स्क्रीन) की पट्टिकाओं के मध्य से दूरी 30 cm है । माना विचलन पट्टिकाओं पर लगने वाली निवेशी वोल्टता के प्रवर्धक की वृद्धि 100 है । निम्नलिखित की गणना कीजिए : (20 अंक)
(i) किरणपुंज की गति
(ii) CRT की विचलन संवेदनशीलता (सुग्राहिता)
(iii) CRT का विचलन गुणांक
(iv) किरणपुंज को 5 cm तक विचलित करने के लिए आवश्यक निवेशी वोल्टता
(c) 4200H एवं 4201H स्मृति अवस्थितियों में संग्रहित 8-बिट डेटा की दो संख्याओं को जोड़ने तथा परिणाम को 4202H तथा 4203H स्थान पर संग्रहित करने के लिए असेंबली भाषा प्रोग्राम का लेखन कीजिए । (10 अंक)
Answer approach & key points
Calculate requires systematic numerical computation with clear formulas and unit conversions. Spend approximately 40% of time on part (a) for extracting K and ξ from frequency response characteristics using resonant peak and bandwidth relationships; 40% on part (b) for CRT calculations involving electron kinematics and electrostatic deflection; and 20% on part (c) for writing the 8085 assembly program with proper addressing modes. Begin each part with relevant standard formulas, show complete substitution with units, and conclude with boxed final answers.
Part (a): Relate resonant peak magnitude Mr and resonant frequency ωr to damping ratio ξ using Mr = 1/(2ξ√(1-ξ²)) and ωr = ωn√(1-2ξ²), then determine K from DC gain or peak value
Part (a): Correctly identify from frequency response plot: peak magnitude (for K), resonant frequency, and bandwidth or corner frequencies to solve for ωn and ξ
Part (b)(i): Calculate beam speed v = √(2eVa/m) = 5.93×10⁵√Va m/s using anode voltage Va = 3 kV
Part (b)(ii)-(iii): Derive deflection sensitivity S = L·D/(2d·Va) in mm/V and deflection factor G = 1/S in V/mm, with L=2.5 cm, d=5 mm, D=30 cm
Part (b)(iv): Calculate input voltage considering amplifier gain of 100: Vin = (deflection × deflection factor)/gain
Part (c): Write 8085 assembly program using LDA/STA or LHLD/SHLD instructions, handling 8-bit addition with carry propagation to 16-bit result
Part (c): Proper memory addressing: 4200H and 4201H as source, 4202H (lower byte) and 4203H (higher byte/carry) as destination
50McalculatePiezoelectric transducers, 8085 addressing modes, First order systems
(a) The capacitance of a piezoelectric transducer is 2000 pF and charge sensitivity is 30 × 10⁻³ C/m. Assume the capacitance of the connecting cable as 150 pF, when the oscilloscope used for readout has a readout input resistance of 1 MΩ with parallel capacitance of 100 pF.
Calculate the following : (20 marks)
(i) Sensitivity of transducer alone
(ii) High frequency sensitivity of the entire measuring system
(iii) Lowest frequency that can be measured with 5% amplitude error by the entire system
(iv) Value of the external shunt capacitance that can be connected in order to extend the range of 5% error down to 20 Hz
(b) Identify and explain briefly the addressing modes of 8085 microprocessor in the given instructions : (20 marks)
(i) ADD reg
(ii) MOV rd, M
(iii) CALL addr 16
(iv) LDA addr 16
(v) CMA
(c) The first order system and its response to unit step input are shown in Figure I and II respectively. Determine the system parameters 'a' and 'K'. (10 marks)
हिंदी में पढ़ें
(a) एक पीजोइलेक्ट्रिक (दाब-विद्युत) ट्रांसड्यूसर (परांतक) की संधारिता 2000 pF तथा आवेश संवेदनशीलता (सुग्राहिता) 30 × 10⁻³ C/m है । माना 1 MΩ पटनीय निवेश प्रतिरोध सहित 100 pF की समांतर संधारिता के अध्ययन हेतु प्रयुक्त दोलनदर्शी के पटन के लिए जोड़ने वाले केबल की धारिता 150 pF है ।
निम्नलिखित की गणना कीजिए : (20 अंक)
(i) केबल ट्रांसड्यूसर (परांतक) की संवेदनशीलता (सुग्राहिता)
(ii) सम्पूर्ण मापन प्रणाली की उच्च आवृत्ति संवेदनशीलता (सुग्राहिता)
(iii) सबसे कम आवृत्ति जिसे सम्पूर्ण प्रणाली द्वारा 5% आयाम त्रुटि के साथ मापा जा सकता है
(iv) बाह्य पार्श्व धारिता का मान जिसे 5% त्रुटि पारस को 20 kHz तक बढ़ाने के लिए जोड़ा जा सकता है
(b) दिए गए निर्देशों के लिए 8085 सूक्ष्म संसाधित्र के एड्रेसिंग मोड की पहचान कीजिए एवं संक्षिप्त व्याख्या कीजिए : (20 अंक)
(i) ADD reg
(ii) MOV rd, M
(iii) CALL addr 16
(iv) LDA addr 16
(v) CMA
(c) इकाई चरण निवेश हेतु प्रथम क्रम (ऑर्डर) तंत्र और उसकी अनुक्रिया को क्रमशः चित्र I एवं II में प्रदर्शित किया गया है । पद्धति प्राचल 'a' एवं 'K' का निर्धारण कीजिए । (10 अंक)
Answer approach & key points
Calculate requires systematic numerical problem-solving across all three parts. Allocate approximately 40% time to part (a) piezoelectric calculations due to its 20 marks and multi-step complexity, 40% to part (b) 8085 addressing modes requiring precise identification and explanation, and 20% to part (c) first-order system parameter determination. Begin with clear formula statements, show all substitutions, and conclude with unit-verified answers for each sub-part.
Part (a)(i): Voltage sensitivity of transducer alone = charge sensitivity / transducer capacitance = (30×10⁻³)/(2000×10⁻¹²) = 15×10⁶ V/m or 15 mV/μm
Part (a)(ii): High frequency sensitivity = charge sensitivity / (C_transducer + C_cable + C_scope) = (30×10⁻³)/(2250×10⁻¹²) = 13.33×10⁶ V/m
Part (a)(iii): Time constant τ = RC = 10⁶ × 2250×10⁻¹² = 2.25 ms; for 5% error, ωτ = 0.329, giving f_low = 23.3 Hz
Part (a)(iv): For f = 20 Hz, required τ_new = 0.329/(2π×20) = 2.62 ms; C_total_new = 2.62 nF; C_shunt = 2620 - 2250 = 370 pF
Part (b): Correct identification - (i) Register addressing, (ii) Register indirect, (iii) Immediate/register indirect for CALL, (iv) Direct addressing, (v) Implied/inherent addressing with brief explanation of each
Part (c): From first-order step response, time constant τ = 1/a from 63.2% point or tangent method; K = steady-state value; typical values a = 5 s⁻¹, K = 2 if figure shows 2V final value with 0.2s time constant
Proper handling of pF to F conversions and MΩ to Ω throughout calculations
Physical interpretation: piezoelectric loading effect, 8085 memory organization, and first-order system speed of response
50MCompulsorysolveControl systems, energy meters, power systems, cables, network models
(a) The block diagram of a position control system is shown in the figure. Determine the sensitivity of the closed loop transfer function T(s) with respect to G(s) and H(s) for 1 rad/sec. 10 marks
(b) The disc in a single-phase energy meter rotates 1320 times when monitoring a 110 V, 3 A load at unity power factor over a period of 8 hours. Calculate the meter constant. If the meter makes 750 revolutions when measuring the energy supplied to a 110 V, 5 A load for 3 hours, determine the load power factor. 5+5=10 marks
(c) Write the bus admittance matrix for the network shown in the figure. 10 marks
(d) A single core cable without grading operates at 14 kV. The conductor radius is 1·12 cm and insulation radius is 2·75 cm. If cable is with inter-sheath grading at suitable radius, then calculate the maximum operating voltage of the cable. 10 marks
(e) How does information get passed from one layer to the next in the Internet model? How do the layers of the Internet model correlate to the layers of the OSI model? 6+4=10 marks
हिंदी में पढ़ें
(a) एक अवस्था नियंत्रण प्रणाली का खण्ड आरेख चित्र में प्रदर्शित किया गया है । 1 rad/sec के लिए G(s) एवं H(s) के सापेक्ष संवृत पाश अंतरण फलन T(s) की संवेदनशीलता (सुग्राहिता) का निर्धारण कीजिए । 10 अंक
(b) जब 110 V, 3 A इकाई शक्ति गुणांक वाले भार को 8 घंटे की समय अवधि के लिए एक एकल-कला ऊर्जा मीटर की निगरानी में रखा जाता है, इस दौरान मीटर का चक्र (डिस्क) 1320 बार घूमता है । मीटर स्थिरांक की गणना कीजिए । यदि 110 V, 5 A भार को प्रदान की गई ऊर्जा का मापन 3 घंटे की अवधि तक किया जाता है, तो मीटर का चक्र 750 बार घूमता है; भार शक्ति गुणांक की गणना कीजिए । 5+5=10 अंक
(c) चित्र में प्रदर्शित जालतंत्र (नेटवर्क) के लिए बस प्रवेश्यता आव्यूह लिखिए । 10 अंक
(d) एक अश्रेणीकृत एकल कोर केबल का परिचालन 14 kV पर किया जाता है । केबल के चालक की त्रिज्या 1·12 cm और विद्युतरोधन परत की त्रिज्या 2·75 cm है । यदि केबल में उचित त्रिज्या पर श्रेणीकृत अंतःखोल (इंटर-शीथ) प्रदत की जाए, तो केबल की अधिकतम परिचालन वोल्टता की गणना कीजिए । 10 अंक
(e) अंतरजाल (इंटरनेट) प्रतिरूप में सूचनाओं को एक परत से दूसरी परत तक कैसे पहुँचाया जाता है ? किसी अंतरजाल प्रतिरूप की परतों को OSI प्रतिरूप की परतों से कैसे सहसंबंधित किया जाता है ? 6+4=10 अंक
Answer approach & key points
This is a solve-type question requiring systematic treatment of five distinct technical problems. Allocate approximately 25-30% time to part (a) due to its analytical complexity involving sensitivity functions; 20% each to parts (b) and (d) for their numerical calculations; 15% to part (c) for matrix construction; and 15% to part (e) for conceptual explanation. Begin each sub-part with the relevant governing equation, show complete working, and conclude with the final numerical answer or clear conceptual summary.
Part (a): Derive sensitivity S_G^T = 1/(1+GH) and S_H^T = -GH/(1+GH), then evaluate at ω=1 rad/sec with proper substitution of G(jω) and H(jω) from the block diagram
Part (b): Calculate meter constant K = 1320/(110×3×8×1) = 0.5 rev/kWh, then use 750 = K×110×5×3×cosφ to find power factor cosφ = 0.909 lagging
Part (c): Construct Y_bus by inspection method: diagonal elements Y_ii = sum of admittances connected to bus i, off-diagonal Y_ij = -y_ij, showing the n×n symmetric matrix
Part (d): Calculate ungraded cable stress ratio, determine optimal inter-sheath radius r1 = √(r×R) = 1.756 cm, then find new maximum voltage V_max = E_max×r×ln(r1/r) + E_max×r1×ln(R/r1) ≈ 19.8 kV
Part (e): Explain encapsulation/decapsulation with headers added/removed at each layer; map Internet model (Application, Transport, Internet, Network Access) to OSI layers 5-7, 4, 3, and 1-2 respectively
(a) Calculate the power loss in the transmission system given in the following figure. The numerical values of transmission system are:
I₁ = 0·75 ∠0° PU, I₂ = 0·8 ∠0° PU,
V₃ = 1·2 ∠0° PU, Z₁ = (0·07 + j0·15) PU,
Z₂ = (0·06 + j0·20) PU, Z₃ = (0·05 + j0·06) PU
20 marks
(b) The fuel input equations of two power plant operations are given as:
F₁ = 0·3 P₁² + 35 P₁ + 125, ₹/hr
F₂ = 0·2 P₂² + 30 P₂ + 140, ₹/hr
If the maximum and minimum loading on each unit is 90 MW and 20 MW respectively and the total consumption demand is 200 MW, then calculate the economical operating schedule and corresponding cost of generation. If load is equally shared by both units, calculate the savings achieved by loading the units as per equal incremental production cost. Neglect the transmission losses.
20 marks
(c) A DM transmitter with a fixed step size of 0·25 V is given a sinusoidal message signal. Determine the maximum permissible amplitude of the message signal, if slope overload is to be avoided. Assume sampling frequency ten times the Nyquist rate.
10 marks
हिंदी में पढ़ें
(a) निम्नलिखित चित्र में दी गई संचरण प्रणाली में शक्ति हानि की गणना कीजिए । संचरण प्रणाली के आंकिक मान निम्न प्रकार हैं :
I₁ = 0·75 ∠0° PU, I₂ = 0·8 ∠0° PU,
V₃ = 1·2 ∠0° PU, Z₁ = (0·07 + j0·15) PU,
Z₂ = (0·06 + j0·20) PU, Z₃ = (0·05 + j0·06) PU
20 अंक
(b) दो शक्ति संयंत्रों के संचालन के ईंधन निविष्ट समीकरण निम्न प्रकार हैं :
F₁ = 0·3 P₁² + 35 P₁ + 125, ₹/घंटे
F₂ = 0·2 P₂² + 30 P₂ + 140, ₹/घंटे
यदि प्रत्येक इकाई पर अधिकतम व न्यूनतम भार क्रमशः: 90 MW और 20 MW तथा कुल खपत मांग 200 MW हो, तो मितव्ययी परिचालन अनुसूची और उससे संबंधित उत्पादन लागत की गणना कीजिए । यदि दोनों इकाइयों द्वारा कुल भार को समान रूप से सहभाजित किया जाता है, तो समान बढ़ोतरी उत्पादन लागत के अनुसार इकाइयों के भारण से प्राप्त बचत की गणना कीजिए । संचरण हानि को उपेक्षित किया गया है ।
20 अंक
(c) एक 0·25 V के स्थायी चरण परिमाण वाले DM प्रेषित्र (ट्रांसमीटर) को एक ज्यावक्रीय सूचना संकेत दिया जाता है । यदि प्रवणता अधिभार (स्लोप ओवरलोड) से बचना है, तो सूचना संकेत के अधिकतम अनुज्ञेय आयाम का निर्धारण कीजिए । न्यूनतम चयन आवृत्ति को नाइक्विस्ट दर से दस गुना माना गया है ।
10 अंक
Answer approach & key points
This is a multi-part numerical problem requiring systematic calculation across three distinct domains: power system analysis, economic dispatch, and communication systems. Spend approximately 40% of time on part (a) transmission loss calculation (20 marks), 35% on part (b) economic load dispatch with cost comparison (20 marks), and 25% on part (c) delta modulation slope overload condition (10 marks). Begin each part with the relevant formula, show complete step-by-step working with proper units, and conclude with clear final answers for each sub-part.
For (a): Correct application of power loss formula P_L = |I|²R for each branch, proper handling of complex currents through each impedance, and summation of I²R losses across all three branches (Z₁, Z₂, Z₃) with correct PU to actual conversion if needed
For (b): Setting up equal incremental cost criterion dF₁/dP₁ = dF₂/dP₂, solving simultaneous equations with P₁ + P₂ = 200 MW constraint, checking against generator limits (20-90 MW), calculating total cost for economic schedule and equal load sharing (100 MW each), then computing savings
For (c): Deriving slope overload condition |dm(t)/dt|_max ≤ Δ/T_s = Δ·f_s, applying to sinusoidal signal m(t) = A_m sin(ω_m t) to get A_m ≤ Δ·f_s/(2πf_m), using f_s = 10 × 2f_m = 20f_m (Nyquist rate), and final amplitude calculation
Correct handling of per-unit system in (a) with proper identification of resistive components from complex impedances
Verification of generator operating limits in (b) and recalculation if limits are violated (though 200 MW demand with 20-90 MW limits allows feasible solution)
Clear presentation of cost comparison in (b) showing economic dispatch savings over simple equal loading
50McalculateTransmission lines and communication systems
(a) Calculate the real and reactive power at sending end of a transmission line while delivering 10 MVA load at 0·85 lagging power factor at receiving end of line. The line parameters are A = 1, B = 12·12 ∠64·64° Ω, D = 1 and receiving end voltage of line is 33 kV. (20 marks)
(b) (i) A binary transmission system with a transmitted power of 300 mW uses a channel with zero-mean AWGN of two-sided PSD equal to 10⁻¹⁵ W/Hz and a total transmission loss of 80 dB. If the probability of error, Pₑ is not to exceed 10⁻⁴, calculate the maximum allowable bit rate using non-coherent ASK. (10 marks)
(ii) A 2Vₚₚ audio frequency signal band-limited to 8 kHz is to be transmitted using a PCM system. If the quantization error of any sample is to be at the most ±1% of the dynamic range of the message signal, determine the minimum value of n, the minimum sampling rate and corresponding bit rate of transmission. (10 marks)
(c) (i) Mention the techniques of increasing the voltage and current rating of converter station of HVDC transmission system. (5 marks)
(ii) Write the requirements of valves used in HVDC transmission system. (5 marks)
हिंदी में पढ़ें
(a) एक संचरण लाइन के प्रेषण छोर पर वास्तविक एवं प्रतिघाती शक्तियों की गणना कीजिए जबकि संचरण लाइन अपने ग्रहण छोर पर 10 MVA, 0·85 पश्चगामी शक्ति गुणांक का भार प्रदान करती है । लाइन के प्राचल A = 1, B = 12·12 ∠64·64° Ω, D = 1 और ग्रहण छोर पर लाइन की वोल्टता 33 kV है । (20 अंक)
(b) (i) 300 mW संचरित शक्ति के साथ एक द्विआधारी संचरण तंत्र 10⁻¹⁵ W/Hz के बराबर द्विशोर PSD के शून्य माध्य AWGN तथा 80 dB कुल संचरण ह्रास वाले चैनल का उपयोग करता है । यदि त्रुटि की संभावना Pₑ, 10⁻⁴ से अधिक नहीं होनी है, तो असुसंगत ASK का प्रयोग करते हुए अधिकतम स्वीकार्य बिट दर की गणना कीजिए । (10 अंक)
(ii) एक 2Vₚₚ ध्वनि आवृत्ति संकेत जो कि 8 kHz तक बैंड-लिमिटेड है, को एक PCM तंत्र के माध्यम से प्रेषित किया जाना है । यदि किसी नमूने की अधिकतम क्वांटाइजेशन त्रुटि सूचना संकेत की गतिक सीमा की ±1% होनी है, तो n का न्यूनतम मान, न्यूनतम प्रतिचयन (सैंपलिंग) दर तथा तत्संगत प्रेषण की बिट दर का निर्धारण कीजिए । (10 अंक)
(c) (i) HVDC संचरण प्रणाली के कनवर्टर स्टेशन की वोल्टता तथा धारा की दर निर्धारण (रेटिंग) को बढ़ाने वाली तकनीकों का उल्लेख कीजिए । (5 अंक)
(ii) HVDC संचरण प्रणाली में प्रयुक्त वाल्वों की अपेक्षाओं का उल्लेख कीजिए । (5 अंक)
Answer approach & key points
Calculate requires precise numerical solutions with clear methodology. Spend ~40% time on part (a) as it carries 20 marks—draw the transmission line equivalent, apply ABCD parameters correctly, and solve for sending end power using complex power equations. Allocate ~30% to part (b) covering both ASK bit rate and PCM parameters—apply non-coherent ASK error probability formula and quantization step calculations. Reserve ~30% for part (c) on HVDC techniques and valve requirements—use bullet points for these descriptive sub-parts. Conclude with brief practical significance of each calculation.
Part (a): Correct application of transmission line ABCD parameters with A=1, B=12.12∠64.64°, D=1 to find sending end voltage, then calculate complex power using Ss = Vs·Is* with proper angle handling for 0.85 lagging pf load
Part (b)(i): Application of non-coherent ASK error probability Pe = 0.5·exp(-γ/4) ≤ 10⁻⁴, solving for required SNR, then using link budget with 80 dB loss and noise PSD to find maximum bit rate
Part (b)(ii): Determination of quantization levels L = 100 (from ±1% error), n = 7 bits, minimum sampling rate = 16 kHz (Nyquist), bit rate = 112 kbps
Part (c)(i): Techniques for HVDC converter rating enhancement—series/parallel connection of valves, use of 12-pulse converters, multi-level converters, and synchronous operation of multiple bridges
Part (c)(ii): Valve requirements—high voltage/current capability, fast switching, low forward voltage drop, high dv/dt and di/dt capability, series/parallel grading circuits, and proper cooling arrangements
50McalculateInformation theory and power system protection
(a) Two sources M₁ and M₂ emit messages x₁, x₂, x₃ and y₁, y₂, y₃ with the joint probability P(X,Y) as shown below in the matrix form.
P(X, Y) →
Determine H(X), H(Y), H(X/Y) and H(Y/X). (20 marks)
(b) Calculate the current setting of a relay for fault that draws up to 400% of the rated current. The relay is used for differential protection of a delta-star, 50 MVA, 66/11 kV transformer. The CT ratio on secondary side is 3000 : 5 and primary side is 600 : 5. (20 marks)
(c) Calculate the peak voltage which appears across the terminals of a circuit breaker when it suddenly interrupts 20 A current at 20% of its peak value in a circuit. The inductance and stray capacitance of circuit are 15 H and 3000 pF respectively. (10 marks)
हिंदी में पढ़ें
(a) दो स्रोत M₁ एवं M₂ दो सूचनाओं x₁, x₂, x₃ तथा y₁, y₂, y₃ को संयुक्त संभावना P(X, Y) के साथ उत्सर्जित करते हैं, जैसा कि नीचे आवृत्त में दर्शाया गया है ।
P(X, Y) →
H(X), H(Y), H(X/Y) एवं H(Y/X) का निर्धारण कीजिए । (20 अंक)
(b) एक रिले की धारा सेटिंग की गणना कीजिए जो दोष (फॉल्ट) के समय निर्धारित (रेटेड) धारा की 400% दोष-धारा ग्रहण करती है । एक डेल्टा-स्टार, 50 MVA, 66/11 kV परिणामित्र के अवकलीय संरक्षण के लिए रिले का प्रयोग किया गया है । द्वितीयक तरफ CT का अनुपात 3000 : 5 तथा प्राथमिक तरफ 600 : 5 है । (20 अंक)
(c) एक परिपथ विचोजक के टर्मिनलों के आर-पार उत्पन्न शिखर वोल्टता की गणना कीजिए जो परिपथ में 20 A धारा को तब अचानक बाधित करता है जब परिपथ में धारा शिखर मान की 20% होती है । परिपथ का प्रेरकत्व एवं अवांछित (स्ट्रे) धारिता क्रमशः: 15 H तथा 3000 pF है । (10 अंक)
Answer approach & key points
Calculate the required quantities systematically across all three sub-parts. For (a), spend ~40% time computing entropy measures H(X), H(Y), H(X/Y), H(Y/X) using marginal and conditional probability formulas. For (b), allocate ~35% time on relay current setting calculation involving CT ratio matching and percentage differential protection settings for delta-star transformers. For (c), use ~25% time applying transient recovery voltage (TRV) theory for circuit breaker interruption analysis. Present each part with clear problem identification, formula application, step-wise computation, and final boxed answers.
Part (a): Correct computation of marginal probabilities P(X) and P(Y) from joint probability matrix; application of entropy formula H = -Σpᵢlog₂pᵢ; calculation of conditional entropies using H(X/Y) = H(X,Y) - H(Y) relationship
Part (b): Determination of rated currents on primary (437.4 A) and secondary (2624.3 A) sides; selection of appropriate CT ratios considering delta-star phase shift compensation; calculation of relay setting current considering 400% fault current and percentage bias characteristic
Part (c): Application of LC circuit transient analysis for current chopping; use of energy conservation ½Li² = ½CV² to find peak recovery voltage; consideration of 20% current interruption point
Correct handling of log base 2 for entropy in bits, natural log conversion where needed, and proper unit management (kV, A, pF, H) throughout
Recognition that delta-star transformer requires phase compensation in differential protection—either through CT connection or relay design
Physical interpretation: for (a) mutual information significance; for (b) relay coordination with transformer inrush; for (c) circuit breaker TRV rating implications