Physics 2023 Paper II 50 marks Explain

Q8

(a) What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors. 5+15=20 (b) What is superconductivity ? Explain Meissner effect. Why superconductors should be a diamagnetic material ? 15 (c) (i) Determine the input and output impedances of the amplifier in given figure. The op-amp datasheet gives Z_in = 2 MΩ, Z_out = 75 Ω and A_OL = 200,000 (open loop voltage gain). 10 (ii) Find the closed-loop voltage gain. 5

हिंदी में प्रश्न पढ़ें

(a) रिएक्टर के क्रांतिक आकार से आप का क्या अभिप्राय है ? नाभिकीय रिएक्टरों की मुख्य विशेषताओं का वर्णन कीजिए । 5+15=20 (b) अतिचालकता क्या है ? माइसनर प्रभाव की व्याख्या कीजिए । अतिचालक पदार्थ क्यों एक प्रतिचुंबकीय पदार्थ होते हैं ? 15 (c) (i) दर्शाए गए चित्र में प्रवर्धक का निवेशी और निर्गत प्रतिबाधाओं का मान निर्धारित कीजिए । संक्रियात्मक प्रवर्धक के डेटाशीट के अनुसार Z_in = 2 MΩ, Z_out = 75 Ω और A_OL (खुला पाश वोल्टता गेन) = 200,000 है । 10 (ii) संयुक्त पाश वोल्टता गेन का मान प्राप्त कीजिए । 5

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Directive word: Explain

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

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

The directive 'explain' demands clear conceptual exposition with logical reasoning. Allocate approximately 40% effort to part (a) given its 20 marks, 30% to part (b) for 15 marks, and 30% combined to part (c)(i) and (ii) for 15 marks. Structure: begin with reactor physics fundamentals, transition to superconductivity phenomena, then conclude with systematic op-amp circuit analysis using negative feedback principles.

Key points expected

  • Critical size definition: minimum dimensions for self-sustaining chain reaction where neutron production equals losses (multiplication factor k=1); mention critical mass and critical volume relationship
  • Nuclear reactor main features: fuel (enriched U-235/Pu-239), moderator (heavy water/graphite in Indian PHWRs), control rods (Cd/B), coolant, shielding; reference Indian reactors like Dhruva or CIRUS
  • Superconductivity: zero DC resistance below critical temperature Tc; Meissner effect as perfect diamagnetism with expulsion of magnetic field (B=0 inside); Type-I vs Type-II distinction
  • Diamagnetic necessity: superconductors must expel magnetic flux to maintain zero resistance state; London penetration depth and thermodynamic argument for free energy minimization
  • Op-amp input impedance with feedback: Z_in(CL) = Z_in(OL)[1+βA_OL] for non-inverting; output impedance reduction by factor (1+βA_OL)
  • Closed-loop gain derivation: A_CL = A_OL/(1+βA_OL) ≈ 1/β for large A_OL; identify feedback network β from resistor configuration
  • Numerical calculation: substitute given values Z_in=2MΩ, Z_out=75Ω, A_OL=200,000 with appropriate β determination from implied circuit topology

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness25%12.5Precise definitions across all parts: critical size as k=1 condition with neutron economy; superconductivity as macroscopic quantum phenomenon with Cooper pairing mentioned; correct identification of virtual ground and negative feedback in op-amp analysisGenerally correct definitions but missing key nuances like distinction between critical mass and critical size, or conflating Meissner effect with merely zero resistanceFundamental misconceptions such as treating critical size as purely geometric, describing superconductors as perfect conductors rather than diamagnets, or incorrect feedback polarity identification
Derivation rigour20%10Systematic derivations: four-factor formula implied for reactor; London equations or thermodynamic argument for Meissner effect; complete impedance transformation derivation using feedback equations with clear β identificationCorrect final formulas but skips intermediate steps or assumes β without derivation from resistor network; acceptable but incomplete logical flowMissing derivations entirely or incorrect application of formulas; states results without showing how feedback modifies impedances
Diagram / FBD15%7.5Clear labeled diagrams: reactor schematic with core, moderator, control rods, coolant loop; B-T phase diagram for superconductors showing Meissner state; complete op-amp circuit with feedback resistors R1, Rf explicitly shownBasic diagrams present but missing labels or key components; generic op-amp symbol without feedback network specifiedNo diagrams or unrecognizable sketches; fails to illustrate critical concepts like flux expulsion or feedback topology
Numerical accuracy20%10Correct numerical substitution with proper unit handling: Z_in(CL) in MΩ range, Z_out(CL) in mΩ range, A_CL precise to 3 significant figures; shows approximation validity when A_OL >> 1Correct approach but arithmetic errors or unit confusion; reasonable order of magnitude for final answersMajor calculation errors, incorrect order of magnitude, or omits numerical parts entirely despite given data
Physical interpretation20%10Insightful connections: reactor criticality linked to Indian nuclear program self-reliance; Meissner effect explained via persistent surface currents; op-amp impedance transformation interpreted as impedance buffering utility in instrumentationAdequate physical explanation without deeper insight; describes what happens without explaining why it matters technologicallyPurely mathematical treatment with no physical interpretation; fails to explain significance of results for practical applications

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