id: fund-ex-02a
type: design
difficulty: easy
points: 10
related_lesson: fund-02
question: |
  Draw the circuit for a spark with the following parameters:
  - Spark length: L = 5 feet
  - Mutual capacitance: C_mut = 12 pF (from FEMM)
  - Plasma resistance: R = 50 kΩ

  Label all component values including the shunt capacitance C_sh.

hints:
  - "Use the empirical rule: C_sh ≈ 2 pF/foot"
  - "The topology is (R || C_mut) in series with C_sh"
  - "Draw from topload terminal to ground reference"

solution:
  steps:
    - "Calculate C_sh using empirical rule: C_sh = 2 pF/foot × 5 feet = 10 pF"
    - "Draw topload at top as measurement terminal"
    - "Draw C_mut in series from topload"
    - "At node connecting C_mut, draw R and C_sh in parallel to ground"
    - "Alternative: Show R || C_mut as parallel combination, then C_sh in series to ground"

  answer: |
    Circuit diagram:
    Topload (V_top)
        |
    [C_mut = 12 pF]
        |
    +----------- Node_spark
    |              |
    [R = 50 kΩ]    [C_sh = 10 pF]
    |              |
    GND --------- GND

  component_values:
    C_mut: "12 pF"
    C_sh: "10 pF"
    R: "50 kΩ"

explanation: |
  The spark circuit model uses three components: C_mut couples the topload to the
  spark channel, R represents plasma resistance where power is dissipated, and C_sh
  provides the shunt capacitance to ground. The empirical 2 pF/foot rule gives a
  good estimate for C_sh, which for a 5-foot spark yields 10 pF. This topology
  ensures current through R must also flow through either C_mut or C_sh.

related_concepts: ["circuit-topology", "lumped-model", "C_sh-empirical-rule", "spark-capacitance"]