id: fund-ex-checkpoint-quiz
type: conceptual
difficulty: medium
points: 100
related_lesson: fund-08
question: |
  FUNDAMENTALS CHECKPOINT QUIZ - Answer all 10 questions

  1. What is the relationship between peak and RMS voltage? If V_peak = 100 kV, what is V_RMS?

  2. Write the power formula using peak phasors. Why is there a factor of 0.5?

  3. For a capacitor, why is X negative but B positive?

  4. Draw the circuit topology for a spark (show C_mut, R, C_sh).

  5. What is the empirical rule for C_sh? If a spark is 4 feet long, estimate C_sh.

  6. The admittance phase angle θ_Y = +60°. What is the impedance phase angle φ_Z?

  7. An impedance has φ_Z = -30°. Is this inductive or capacitive?

  8. Why is V_top/I_base not the correct impedance measurement?

  9. Describe the difference between streamers and leaders (two key differences).

  10. Explain the "hungry streamer" concept in one sentence.

hints:
  - "Review each fundamental lesson carefully"
  - "Consider both mathematical and physical interpretations"
  - "Draw diagrams where helpful"

solution:
  answer_1: "V_RMS = V_peak/√2. For V_peak = 100 kV, V_RMS = 100/√2 ≈ 70.7 kV"

  answer_2: "P = 0.5 × Re{V × I*}. The 0.5 factor comes from time-averaging cos²(ωt) over a full cycle."

  answer_3: |
    For capacitors, reactance X_C = -1/(ωC) is negative, but susceptance B_C = ωC
    is positive. The sign conventions are opposite for impedance vs admittance.

  answer_4: |
    Topload
        |
    [C_mut]
        |
    +----+----+
    |         |
   [R]      [C_sh]
    |         |
   GND------GND

  answer_5: "C_sh ≈ 2 pF/foot. For 4 feet: C_sh ≈ 8 pF"

  answer_6: "φ_Z = -θ_Y = -60°"

  answer_7: "Capacitive (negative φ_Z indicates capacitive behavior)"

  answer_8: |
    I_base includes displacement currents from the entire secondary, plus coupling
    currents and environmental currents. Only I_spark flows through the spark.
    V_top/I_base underestimates impedance because I_base > I_spark.

  answer_9: |
    Any two of: Streamers are thin (10-100 μm), fast (~10⁶ m/s), cold (~1000 K),
    high R, branched. Leaders are thick (mm-cm), slower (~10³ m/s), hot (5000-20000 K),
    low R, straighter.

  answer_10: |
    Plasma actively adjusts its conductivity to maximize power extraction from the
    circuit, naturally seeking R ≈ R_opt_power.

explanation: |
  This checkpoint quiz verifies understanding of all fundamental concepts from
  Part 1. Correct answers demonstrate mastery of: complex numbers and phasors,
  circuit topology, capacitance relationships, admittance analysis, phase angles,
  measurement ports, and spark physics basics. These concepts form the foundation
  for optimization (Part 2), growth physics (Part 3), and advanced modeling (Part 4).

related_concepts: ["fundamentals-review", "integration", "checkpoint", "mastery-verification"]