Electrical Engineering 2021 Paper I 50 marks Compulsory Calculate

Q5

(a) A step down dc chopper is feeding a load of R = 10 Ω and L = 20 mH. The dc supply voltage is 100 V. The chopper is switching at a frequency of 2 kHz with a duty cycle of 50%. Determine the load current and the peak-to-peak ripple current as an absolute value and as percentage of dc value. (10 marks) (b) In a certain material with σ = 0, ε = ε₀ εᵣ and μ = μ₀ μᵣ, the magnetic field intensity component is given by H = 10 sin (10⁸ t – 2x) aᵤ A/m. Find the following: (i) Displacement current density (ii) Electric field intensity (10 marks) (c) A Scott connected transformer shown in Figure 5(c) is supplied from 11 kV, 3-phase, 50 Hz mains. Secondaries are series connected and supply 1100 A at a voltage of 100√2 V to a resistive load. The phase sequence of the 3-phase supply is ABC. (i) Calculate the turns ratio of the teaser transformer. (ii) Calculate the line current I_B and its phase angle with respect to the voltage of phase A to neutral on the 3-phase side. (10 marks) (d) A transmitter with a 10 kW carrier transmits 11·2 kW when modulated with a single sine wave. Calculate the modulation index. If the carrier is simultaneously modulated with two other sine waves also at 50% modulation, calculate the total power transmitted. (10 marks) (e) For the circuit shown in Figure 5(e), v_C(0+) = 2 V and i(0+) = 2/3 A. Calculate the value of v_C(t) for t > 0. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक अपचायी dc संकटक (चॉपर), एक R = 10 Ω तथा L = 20 mH वाले भार को पोषित करता है । dc प्रदाय वोल्टता 100 V है । संकटक 50% कर्म चक्र के साथ 2 kHz की आवृत्ति पर स्विचिंग कर रहा है । भार धारा तथा शिखर-से-शिखर ऊर्मिका धारा का मान, विशुद्ध मान व dc मान के प्रतिशत के रूप में ज्ञात कीजिए । (10 अंक) (b) एक किसी σ = 0, ε = ε₀ εᵣ तथा μ = μ₀ μᵣ वाले पदार्थ में चुंबकीय क्षेत्र की तीव्रता का घटक H = 10 sin (10⁸ t – 2x) aᵤ A/m द्वारा प्रदर्शित है । निम्नलिखित का मान ज्ञात कीजिए : (i) विस्थापन धारा घनत्व (ii) विद्युत क्षेत्र तीव्रता (10 अंक) (c) चित्र 5(c) में प्रदर्शित एक स्कॉट संयोजित परिणामित्र, 11 kV, त्रि-कला, 50 Hz मैंस से पोषित है । द्वितीयक श्रेणी क्रम में संयोजित हैं और एक प्रतिरोधीय भार को 100√2 V पर 1100 A प्रदान करती है । त्रि-कला प्रदाय (सप्लाई) का कला क्रम ABC है । (i) टीज़र परिणामित्र का फेरा अनुपात परिकलित कीजिए । (ii) त्रि-कला दिशा में तत्क्ष से कला A की बोल्टता के सापेक्ष लाइन धारा I_B तथा इसके कला कोण की गणना कीजिए । (10 अंक) (d) एक प्रेषित्र 10 kW वाहक के साथ 11·2 kW प्रेषित करता है जबकि एकल ज्या तरंग द्वारा मॉडुलित होता है । मॉडुलन सूचकांक की गणना कीजिए । यदि वाहक साथ ही साथ दो अन्य ज्या तरंगों द्वारा भी 50% मॉडुलन पर मॉडुलित होता है, तो संपूर्ण प्रेषित शक्ति की गणना कीजिए । (10 अंक) (e) चित्र 5(e) में प्रदर्शित परिपथ के लिए v_C(0+) = 2 V तथा i(0+) = 2/3 A हैं । t > 0 के लिए v_C(t) के मान की गणना कीजिए । (10 अंक)

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How this answer will be evaluated

Approach

This is a multi-part numerical problem requiring systematic calculation across five distinct areas of electrical engineering. Allocate approximately 20% time to each sub-part: (a) DC chopper analysis using duty cycle and ripple current formulas, (b) electromagnetic wave propagation applying Maxwell's equations, (c) Scott transformer phasor analysis with 90° phase relationships, (d) AM power calculations using modulation index formulas, and (e) transient circuit analysis using Laplace transforms or classical methods. Begin each part with the relevant governing equation, show substitution of values with units, and conclude with clear numerical answers.

Key points expected

  • Part (a): Correct application of step-down chopper duty cycle formula V₀ = δVₛ, average load current I₀ = V₀/R, and ripple current ΔI = Vₛδ(1-δ)/fL with proper unit handling
  • Part (b): Application of Maxwell's equations to find displacement current density Jd = ∂D/∂t and E-field using intrinsic impedance η = √(μ/ε) for lossless medium
  • Part (c): Scott transformer teaser transformer turns ratio calculation (0.866 factor) and phasor diagram construction for 90° phase shift between teaser and main transformer
  • Part (d): AM power calculation using Pₜ = Pc(1 + m²/2) for single tone and extension to multiple tones with Pₜ = Pc(1 + m₁²/2 + m₂²/2 + m₃²/2)
  • Part (e): Second-order circuit transient analysis using characteristic equation, damping classification, and complete solution form with initial condition application
  • Proper handling of per-unit and absolute values for ripple current percentage calculation in part (a)
  • Recognition that σ = 0 implies purely displacement current with no conduction current in part (b)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: chopper duty cycle and ripple formulas for (a), Maxwell-Ampere law with displacement current for (b), Scott transformer 90° phase relationship and 0.866 factor for (c), AM power sideband relationships for (d), and second-order circuit damping analysis for (e); no conceptual errors in any sub-partMinor conceptual errors in 1-2 sub-parts such as incorrect ripple formula, confusion between conduction and displacement current, or wrong modulation power formula; core understanding present but misappliedMajor conceptual errors in multiple sub-parts; fundamental misunderstanding of chopper operation, electromagnetic wave propagation, transformer connections, modulation theory, or transient analysis
Numerical accuracy20%10All calculations yield precise answers: (a) I₀ = 5A, ΔI = 0.625A (12.5%), (b) Jd = 10cos(10⁸t-2x) A/m², E = 2000 sin(10⁸t-2x) V/m, (c) turns ratio 86.6, I_B at -30°, (d) m=0.49, Pₜ=13.125kW, (e) correct damped/underdamped solution; proper significant figures and units throughoutMinor arithmetic errors in 1-2 sub-parts or incorrect unit conversions; correct methodology but calculation mistakes leading to slightly wrong final answers; inconsistent significant figuresMajor calculation errors, missing units, order-of-magnitude mistakes, or answers without numerical values; demonstrates poor quantitative problem-solving ability
Diagram quality15%7.5Clear labeled diagrams for (a) chopper circuit with switching waveform, (b) E-H field orientation with propagation direction, (c) Scott transformer connection diagram with phasor diagram showing 90° relationship, (e) circuit diagram with proper element labeling; diagrams enhance solution clarityBasic diagrams present for 2-3 sub-parts but lacking labels or clarity; phasor diagram in (c) missing angle markings; waveforms in (a) and (b) without proper axis labelsMissing or inadequate diagrams; no phasor diagram for Scott transformer, no switching waveforms, or completely unlabeled sketches that add no value to solution
Step-by-step derivation25%12.5Systematic derivation showing: (a) duty cycle → average voltage → average current → ripple derivation, (b) curl H relation → D-field → displacement current, (c) voltage phasor analysis → turns ratio → current calculation with phase, (d) power equation setup → modulation index solving → multi-tone extension, (e) KVL/KCL → characteristic equation → root analysis → complete solution with constants; all steps logically connectedDerivations present but with skipped steps or missing justification; jumps from given data to final formula without showing substitution; incomplete transient solution in (e) missing initial condition applicationFragmented or missing derivations; equations stated without development; no showing of work; final answers appear without supporting calculation steps
Practical interpretation20%10Interprets results physically: (a) comments on 12.5% ripple being acceptable for motor loads, (b) identifies wave as plane wave in dielectric with phase velocity 5×10⁷ m/s, (c) explains Scott transformer application for 2-phase railway traction in India, (d) discusses power efficiency and bandwidth implications, (e) identifies overdamped/critically/underdamped regime and settling time significance; connects theory to engineering practiceBrief physical interpretation for 2-3 sub-parts; mentions applications without elaboration; standard textbook commentary without insight into real-world constraintsNo physical interpretation; purely mathematical treatment; fails to identify what results mean for practical systems or their engineering significance

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