Electrical Engineering 2023 Paper I 50 marks Solve

Q6

(a) A 200 V, 1100 rpm, dc shunt motor takes 1·5 A and runs at 1150 rpm under no load condition at rated voltage. Its armature resistance including brushes is 0·5 Ω. While running under full load, its field circuit gets open circuited due to fault and the motor takes 5 times of its rated input current to deliver rated torque. Find : (i) the full load torque of the machine, and (ii) the speed of the motor under field fault condition. Assume no armature copper losses at no load and no armature reaction. (20 marks) (b) An absorber material of relative permeability and relative permittivity of εᵣ = μᵣ = 6 – j6 is coated on a perfectly conducting sheet and this combination is placed in free space as shown in the figure given below. A 500 MHz wave is incident on it normally from free space. Calculate the thickness of the absorber required to attenuate the reflected wave by 30 dB. (20 marks) (c) A 120 V, 1000 rpm, 350 W separately excited dc motor is supplied via half-controlled single-phase bridge rectifier for speed control purpose. The supply voltage to the rectifier is 200 V, 50 Hz ac and to obtain the desired speed, the triggering angle is set at 105° at one instant. The armature current is discontinuous with an average value of 2 A and it continues up to 30° beyond voltage zero. The motor armature resistance is 1·5 Ω. Determine the operating speed of the motor. (Assume constant flux operation and no armature reaction) (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक 200 V, 1100 rpm, dc समानांतर क्रम मोटर निर्धारित वोल्टता पर भार रहित अवस्था में 1150 rpm पर चलती है और 1·5 A लेती है। इसका ब्रश सहित आर्मेचर प्रतिरोध 0·5 Ω है। जब यह पूर्ण भार पर चल रही होती है, तो दोष के कारण इसकी क्षेत्र कुंडली खुले परिपथ में हो जाती है और मोटर निर्धारित बलाघूर्ण प्रदान करने के लिए, निर्धारित निवेश धारा से 5 गुना धारा लेती है। ज्ञात कीजिए : (i) यंत्र का पूर्ण भार बलाघूर्ण, और (ii) क्षेत्र दोष की अवस्था में मोटर की गति। मान लीजिए कि भार रहित अवस्था में आर्मेचर कॉपर हास नहीं हैं और आर्मेचर रिएक्शन भी नहीं है। (20 अंक) (b) एक शोषक पदार्थ जिसके सापेक्ष पारगम्यता और सापेक्ष परावैद्युतांक के मान εr = μr = 6 – j6 हैं, को एक आदर्श सुचालक पतर के ऊपर लेपित किया गया है और यह संयोजन, मुक्त अंतराल में रखा गया है जैसा कि चित्र में प्रदर्शित है। मुक्त अंतराल से एक 500 MHz की तरंग इस पर लम्बवत आपतित है। परावर्तित तरंग के 30 dB क्षीणन के लिए शोषक की वांछित मोटाई की गणना कीजिए। (20 अंक) (c) एक 120 V, 1000 rpm, 350 W अलग से उत्तेजित dc मोटर, गति नियंत्रण के उद्देश्य से अर्ध-नियंत्रित एकल-कला ब्रिज दिष्टकारी द्वारा संभारित है। दिष्टकारी के लिए संभारण वोल्टता 200 V, 50 Hz ac है और वांछित गति प्राप्त करने के लिए एक समय उत्त्प्रेरण (ट्रिगर) कोण 105° समायोजित किया गया है। आर्मेचर धारा औसत मान 2 A के साथ असतत है और यह वोल्टता शून्य के 30° परे तक निरंतर रहती है। मोटर आर्मेचर का प्रतिरोध 1·5 Ω है। मोटर की परिचालन गति ज्ञात कीजिए। (मान लीजिए कि स्थिर अभिवाह परिचालन है और आर्मेचर प्रतिक्रिया नहीं है) (10 अंक)

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Approach

Solve this multi-part numerical problem by allocating approximately 40% time to part (a) [20 marks], 40% to part (b) [20 marks], and 20% to part (c) [10 marks]. Begin each part with the relevant governing equations, show complete step-by-step calculations with proper units, and conclude with physically meaningful results. For part (a), establish rated conditions first; for part (b), use transmission line theory for lossy dielectrics; for part (c), analyze the discontinuous conduction mode of the rectifier-fed motor.

Key points expected

  • Part (a): Correct determination of rated armature current using no-load data and back EMF relationships; calculation of full-load torque using power balance and speed-torque characteristics
  • Part (a): Analysis of field fault condition where flux collapses and armature current rises to 5× rated, with speed determined from torque balance under weakened field
  • Part (b): Calculation of complex intrinsic impedance η = √(μ/ε) and propagation constant γ = jω√(με) for the lossy absorber material with εᵣ = μᵣ = 6–j6
  • Part (b): Application of transmission line theory for normal incidence on conductor-backed absorber, using reflection coefficient and attenuation to achieve 30 dB reduction
  • Part (c): Analysis of half-controlled single-phase bridge with discontinuous conduction, computing average output voltage considering 105° firing angle and 30° extinction angle
  • Part (c): Determination of back EMF from terminal voltage and armature resistance drop, then speed calculation using constant flux assumption

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies DC motor fundamentals (back EMF, torque equations, field weakening effects) for part (a); uses proper electromagnetic wave theory (complex permittivity/permeability, skin depth, wave impedance) for part (b); accurately models half-controlled rectifier with discontinuous conduction for part (c)Applies basic formulas with minor conceptual errors, such as confusing continuous vs discontinuous conduction modes or using real instead of complex material parametersFundamental misconceptions like treating field fault as constant flux condition, using free-space impedance for absorber, or ignoring extinction angle in rectifier analysis
Numerical accuracy25%12.5All calculations precise to 3-4 significant figures with correct unit handling; accurate complex arithmetic for part (b) including proper dB-to-linear conversion; correct angular conversions throughoutCorrect methodology with arithmetic errors or unit inconsistencies that propagate partially; approximate values for complex quantitiesMajor calculation errors, wrong order of magnitude results, or complete absence of numerical work with only symbolic expressions
Diagram quality10%5Clear circuit diagrams for DC motor connections in (a) and (c), waveforms showing voltage/current for discontinuous conduction in (c), and layered structure diagram for part (b) showing incident/reflected wavesBasic sketches present but lacking labels or clarity; missing waveform diagrams where they would aid understandingNo diagrams despite their utility for clarifying connections and waveforms, or completely irrelevant sketches
Step-by-step derivation25%12.5Every formula explicitly stated before substitution; clear logical flow from given data to intermediate quantities (rated current, flux, back EMF) to final answers; proper handling of complex numbers in part (b) with magnitude/phase separationSome steps combined or skipped but overall traceable logic; missing explicit statement of key intermediate resultsDisorganized jumps between equations, missing crucial steps like no-load loss separation or direct final answers without derivation
Practical interpretation20%10Comments on physical reasonableness of results: excessive speed under field fault in (a) indicating dangerous runaway condition; practical absorber thickness in (b) for EMI shielding applications like radar cross-section reduction; speed regulation implications in (c) for industrial drivesBrief mention of practical significance without elaboration; generic statements about motor control or wave absorptionPurely mathematical treatment with no physical insight; absurd results accepted without comment or no interpretation of what the numbers mean

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