Q6
(a) (i) What is meant by armature reaction in DC machines ? Show with the help of developed view of armature conductors and poles that the effect of armature m.m.f. on the main field is entirely cross-magnetizing. (10 marks) (ii) A 10 kW, 220 V DC shunt motor draws a line current of 5 A while running at no-load speed of 1200 rpm. It has an armature resistance of 0·2 Ω and field resistance of 200 Ω. Determine the efficiency of the motor when it delivers rated load. (10 marks) (b) A converter circuit as shown in the figure is being used to charge a battery of voltage E = 24 V. The average charging current I_dc = 6 A, and supply voltage V_s = 60 V, 50 Hz. Determine (i) the value of limiting resistor 'R', and (ii) input power factor. (20 marks) (c) A DSB-SC amplitude-modulated signal with power spectral density as shown in figure (a) is corrupted with additive noise that has a power spectral density (N_0/2) within the passband region of the signal. The received signal-plus-noise is demodulated and low pass filtered as shown in figure (b). Determine the SNR at the output of the LPF. [BW : bandwidth] [Given : carrier signal = cos (2πf_c t)] (20 marks)
हिंदी में प्रश्न पढ़ें
(a) (i) डीसी मशीनों में आर्मेचर प्रतिक्रिया का क्या मतलब है ? आर्मेचर सुचालकों और ध्रुवों के विस्तृत दृश्य की सहायता से यह प्रदर्शित कीजिए कि आर्मेचर m.m.f. का मुख्य क्षेत्र पर प्रभाव पूर्णतः अनुप्रस्थ-चुंबकीय (क्रॉस-मैग्नेटाइजिंग) है। (10 अंक) (ii) एक 10 kW, 220 V DC शंट मोटर भार-रहित 1200 rpm गति पर चलते हुए 5 A लाइन धारा लेती है। इसका आर्मेचर प्रतिरोध 0·2 Ω तथा क्षेत्र प्रतिरोध 200 Ω है। निर्धिष्ट भार प्रदाय करते समय इस मोटर की कार्य-दक्षता ज्ञात कीजिए। (10 अंक) (b) जैसा कि चित्र में दर्शाया गया है, एक परिवर्तित परिपथ, E = 24 V वोल्टता की एक बैटरी को चार्ज करने के लिए प्रयोग किया जा रहा है। औसत चार्जिंग धारा I_dc = 6 A, तथा प्रदाय वोल्टता V_s = 60 V, 50 Hz है, तो : (i) सीमांत प्रतिरोध 'R' का मान, और (ii) निवेश शक्ति गुणांक ज्ञात कीजिए। (20 अंक) (c) चित्र (a) में प्रदर्शित शक्ति स्पेक्ट्रमी घनत्व वाला एक DSB-SC आयाम-मॉडुलित संकेत एक ऐसे योज्य रव (नॉइस) द्वारा विकृत होता है जिसका इस संकेत के पास-बैंड क्षेत्र में शक्ति स्पेक्ट्रमी घनत्व (N_0/2) है। प्राप्त संकेत-धन-रव को डिमॉडुलित और निम्न पारक छानित किया जाता है, जैसा कि चित्र (b) में प्रदर्शित है। LPF के निर्गम पर SNR ज्ञात कीजिए। [BW : बैंड चौड़ाई] [दिया गया है : वाहक संकेत = cos (2πf_c t)] (20 अंक)
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How this answer will be evaluated
Approach
Begin with a concise definition of armature reaction and its cross-magnetizing nature for part (a)(i), followed by systematic numerical solution for the DC motor efficiency in (a)(ii). For part (b), apply thyristor converter analysis to determine the firing angle, limiting resistor, and input power factor. For part (c), derive the output SNR for DSB-SC demodulation using coherent detection theory. Allocate approximately 15 minutes to (a)(i), 20 minutes to (a)(ii), 35 minutes to (b), and 35 minutes to (c), ensuring all diagrams are neatly drawn with proper labeling.
Key points expected
- Definition of armature reaction as the effect of armature MMF on main field flux distribution in DC machines
- Developed winding diagram showing armature conductors under N and S poles with current directions proving cross-magnetizing axis is perpendicular to main field axis
- Calculation of no-load losses, field current, back EMF, and efficiency at rated load for the DC shunt motor
- Determination of firing angle, average output voltage, and limiting resistor R for the battery charging converter circuit
- Computation of input power factor considering displacement angle and distortion factor in the controlled rectifier
- Expression for output SNR of DSB-SC system with coherent detection showing dependence on signal power spectral density and noise PSD
- Integration of signal and noise power over the message bandwidth to obtain final SNR formula
- Comparison of DSB-SC SNR improvement over conventional AM highlighting the 3 dB advantage due to suppressed carrier
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 20% | 12 | Precisely defines armature reaction and correctly identifies the quadrature-axis nature of cross-magnetizing MMF; accurately applies converter operation modes and DSB-SC demodulation principles; distinguishes between demagnetizing and cross-magnetizing components under brush shift conditions | Basic definition of armature reaction given but confusion between cross-magnetizing and demagnetizing effects; converter operation understood but firing angle control concept hazy; DSB-SC detection recognized but mixer/LPF operation not clearly explained | Fundamental misunderstanding of armature reaction as purely harmful without recognizing its geometric nature; treats converter as simple rectifier without phase control; confuses DSB-SC with conventional AM detection |
| Numerical accuracy | 20% | 12 | Correctly computes motor efficiency ≈ 85-87% with proper accounting for rotational losses; determines R ≈ 4-5 Ω and power factor ≈ 0.5-0.6 for converter; derives SNR formula as (P_s)/(N_0·BW) with correct integration limits and numerical evaluation | Minor arithmetic errors in efficiency calculation or incorrect loss segregation; converter resistor value approximate but method correct; SNR expression has correct form but wrong constants or bandwidth factors | Gross errors in efficiency calculation ignoring no-load losses or rotational losses; completely wrong approach for converter resistor using DC Ohm's law ignoring ripple; SNR calculation missing coherent detection gain or using envelope detection |
| Diagram quality | 20% | 12 | Clear developed winding diagram showing armature slots, conductor currents, pole faces, and flux lines with cross-magnetizing axis labeled; converter circuit with thyristor, battery, R, and supply properly drawn; DSB-SC PSD sketches showing symmetric sidebands and noise floor with demodulator block diagram | Diagrams present but poorly labeled or missing key elements like current directions in armature; converter circuit recognizable but thyristor symbol incorrect; PSD diagrams sketchy without proper frequency axis markings | Missing essential diagrams or incomprehensible sketches; no attempt at developed winding view; circuit diagram omitted or drawn as uncontrolled rectifier; no PSD figures for part (c) |
| Step-by-step derivation | 20% | 12 | Systematic derivation: armature MMF distribution → Fourier analysis showing fundamental at 90° electrical; motor efficiency with clear segregation of copper, core, and mechanical losses; converter analysis from V_dc = (V_m/π)(1+cosα) - I_dcR - E; DSB-SC SNR with coherent detection mathematics showing 2× improvement factor | Derivations present but skips key steps like MMF integration or assumes results; efficiency calculation without showing intermediate steps; converter formula stated without derivation from average voltage; SNR derivation misses the 2× coherent detection advantage | No derivations, only final answers stated; or completely wrong derivations with dimensional inconsistencies; jumps from given data to answer without physics; confuses instantaneous with average values throughout |
| Practical interpretation | 20% | 12 | Discusses compensating windings and interpoles as solutions to armature reaction in Indian railway traction motors; relates converter power factor to industrial battery charging stations and harmonic mitigation; explains why DSB-SC is preferred for satellite communication despite complexity, citing ISRO applications | Mentions interpoles or compensating winding without explaining their function; notes poor power factor as disadvantage without improvement suggestions; recognizes DSB-SC bandwidth efficiency but no application context | No practical context provided; or irrelevant examples; fails to connect theory to real DC machines, power electronics installations, or communication systems; ignores why these concepts matter for engineering practice |
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