Electrical Engineering 2024 Paper II 50 marks Calculate

Q4

(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 प्रश्न 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)

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Directive word: Calculate

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How this answer will be evaluated

Approach

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.

Key points expected

  • 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

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies piezoelectric equivalent circuit model, distinguishes between charge and voltage sensitivity, accurately classifies all five 8085 addressing modes with proper nomenclature, and correctly relates first-order system parameters to time-domain response characteristicsIdentifies basic concepts with minor errors in addressing mode classification or piezoelectric model assumptions; some confusion between series and parallel capacitance combinationsFundamental misconceptions such as treating piezoelectric as pure voltage source, misidentifying addressing modes (e.g., calling LDA as indirect), or incorrect first-order system relationships
Numerical accuracy25%12.5All four numerical answers in (a) correct within significant figure tolerance: (i) 15×10⁶ V/m or 15 mV/μm, (ii) 13.33×10⁶ V/m, (iii) 23.3 Hz, (iv) 370 pF; correct parameter values in (c) derived from figure analysisCorrect approach with minor calculation errors (power of ten, unit conversion); answers within 10% of correct value; partial credit for correct formulasMajor calculation errors, incorrect unit conversions (pF/F, MΩ/Ω), order-of-magnitude mistakes, or missing numerical answers
Diagram quality10%5Clear equivalent circuit diagram for piezoelectric system showing charge source with parallel capacitances and resistance; labeled first-order response sketch with 63.2% point marked for time constant extraction; 8085 memory map or instruction format diagrams where helpfulBasic circuit diagram present but incompletely labeled; response curve shown without key annotations; no diagrams for 8085 partMissing essential diagrams, incorrect circuit topology (e.g., series instead of parallel RC), or completely unlabeled sketches
Step-by-step derivation25%12.5Explicit statement of all formulas before substitution (S_v = S_q/C, ωτ relationship for amplitude error, first-order transfer function K/(s+a)); clear algebraic manipulation showing C_total calculations; systematic 8085 opcode analysis showing source/destination operand identificationFormulas implied but not stated; some intermediate steps skipped; final answers shown without clear derivation path; addressing modes stated without analysis processNo visible working, answers only with no derivation, or incorrect formula application without justification
Practical interpretation20%10Explains loading effect of cable and scope capacitance reducing sensitivity; discusses trade-off between low-frequency response and sensitivity when adding shunt capacitance; relates 8085 addressing modes to memory efficiency and programming flexibility; interprets first-order response speed for control applicationsBrief mention of practical implications without elaboration; generic statements about measurement accuracy or microprocessor operationNo physical interpretation provided; purely mathematical treatment without engineering context; missing discussion of why 5% error criterion matters for instrumentation

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