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81 lines
2.8 KiB
81 lines
2.8 KiB
id: fund-ex-checkpoint-quiz
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type: conceptual
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difficulty: medium
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points: 100
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related_lesson: fund-08
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question: |
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FUNDAMENTALS CHECKPOINT QUIZ - Answer all 10 questions
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1. What is the relationship between peak and RMS voltage? If V_peak = 100 kV, what is V_RMS?
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2. Write the power formula using peak phasors. Why is there a factor of 0.5?
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3. For a capacitor, why is X negative but B positive?
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4. Draw the circuit topology for a spark (show C_mut, R, C_sh).
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5. What is the empirical rule for C_sh? If a spark is 4 feet long, estimate C_sh.
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6. The admittance phase angle θ_Y = +60°. What is the impedance phase angle φ_Z?
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7. An impedance has φ_Z = -30°. Is this inductive or capacitive?
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8. Why is V_top/I_base not the correct impedance measurement?
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9. Describe the difference between streamers and leaders (two key differences).
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10. Explain the "hungry streamer" concept in one sentence.
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hints:
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- "Review each fundamental lesson carefully"
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- "Consider both mathematical and physical interpretations"
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- "Draw diagrams where helpful"
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solution:
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answer_1: "V_RMS = V_peak/√2. For V_peak = 100 kV, V_RMS = 100/√2 ≈ 70.7 kV"
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answer_2: "P = 0.5 × Re{V × I*}. The 0.5 factor comes from time-averaging cos²(ωt) over a full cycle."
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answer_3: |
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For capacitors, reactance X_C = -1/(ωC) is negative, but susceptance B_C = ωC
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is positive. The sign conventions are opposite for impedance vs admittance.
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answer_4: |
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Topload
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[C_mut]
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+----+----+
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[R] [C_sh]
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GND------GND
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answer_5: "C_sh ≈ 2 pF/foot. For 4 feet: C_sh ≈ 8 pF"
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answer_6: "φ_Z = -θ_Y = -60°"
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answer_7: "Capacitive (negative φ_Z indicates capacitive behavior)"
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answer_8: |
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I_base includes displacement currents from the entire secondary, plus coupling
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currents and environmental currents. Only I_spark flows through the spark.
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V_top/I_base underestimates impedance because I_base > I_spark.
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answer_9: |
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Any two of: Streamers are thin (10-100 μm), fast (~10⁶ m/s), cold (~1000 K),
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high R, branched. Leaders are thick (mm-cm), slower (~10³ m/s), hot (5000-20000 K),
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low R, straighter.
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answer_10: |
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Plasma actively adjusts its conductivity to maximize power extraction from the
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circuit, naturally seeking R ≈ R_opt_power.
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explanation: |
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This checkpoint quiz verifies understanding of all fundamental concepts from
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Part 1. Correct answers demonstrate mastery of: complex numbers and phasors,
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circuit topology, capacitance relationships, admittance analysis, phase angles,
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measurement ports, and spark physics basics. These concepts form the foundation
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for optimization (Part 2), growth physics (Part 3), and advanced modeling (Part 4).
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related_concepts: ["fundamentals-review", "integration", "checkpoint", "mastery-verification"]
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