Electrical Engineering 2024 Paper II 50 marks Calculate

Q3

(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 प्रश्न 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)

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Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

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How this answer will be evaluated

Approach

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.

Key points expected

  • 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

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies second-order system theory for (a) including resonant peak formula; uses proper electrostatic deflection physics for (b) with electron charge-to-mass ratio; selects appropriate 8085 instructions for (c) with proper flag handlingUses correct general formulas but makes minor errors in identifying which parameters correspond to plot features; understands CRT deflection concept but confuses plate dimensions; writes functional assembly but with inefficient instructionsConfuses damping ratio with damping factor or uses incorrect resonant peak formula; applies magnetic deflection formulas to electrostatic CRT; uses completely wrong instruction set or addressing mode
Numerical accuracy25%12.5All calculations precise to 3-4 significant figures with consistent unit handling; correct conversion of cm/mm/m; proper handling of amplifier gain in (b)(iv); accurate hex arithmetic in (c)Correct method but arithmetic errors in 1-2 parts; unit conversion mistakes (e.g., cm to mm); minor rounding errors that don't affect order of magnitudeOrder of magnitude errors; incorrect unit conversions leading to impossible answers; basic arithmetic errors; ignores amplifier gain or uses wrong voltage values
Diagram quality10%5Reproduces/sketches the frequency response plot in (a) with labeled resonant peak, bandwidth, and DC gain; draws clear CRT schematic in (b) showing plate geometry and electron trajectory with labeled dimensionsRough sketches without proper labels or missing one diagram; correct geometry but poor proportion representationNo diagrams where required; completely wrong schematic showing magnetic instead of electrostatic deflection; illegible sketches
Step-by-step derivation25%12.5Every formula stated before substitution; clear algebraic manipulation to isolate unknowns; explicit solving of quadratic for ξ in (a); derivation of deflection formula from force/acceleration in (b); commented assembly code with algorithm flowSome steps skipped but key intermediate results shown; jumps from formula to answer without showing substitution; minimal comments in assemblyBare answers without derivation; incorrect formula manipulation; no working shown for numerical results; uncommented assembly with no logical structure
Practical interpretation20%10Interprets ξ value significance (underdamped oscillatory response) for control system stability; explains why deflection sensitivity is important for CRO design; discusses overflow handling in 8-bit addition for (c); relates to practical 8085 applications like traffic light controllersBrief mention of practical significance without elaboration; generic statements about CRT usage; no discussion of carry handling importanceNo interpretation of results; purely mechanical calculation without physical understanding; fails to recognize that result exceeds 8-bit requiring two-byte storage

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