id: fund-ex-02b
type: calculation
difficulty: easy
points: 10
related_lesson: fund-02
question: |
  A simulation shows C_sh = 10 pF for a given spark. What is the estimated spark
  length using the empirical rule?

hints:
  - "The empirical rule is C_sh ≈ 2 pF/foot"
  - "Solve for length: L = C_sh / (2 pF/foot)"
  - "Don't forget the units!"

solution:
  steps:
    - "Use the empirical relationship: C_sh ≈ 2 pF/foot"
    - "Rearrange to solve for length: L = C_sh / (2 pF/foot)"
    - "Substitute: L = 10 pF / (2 pF/foot) = 5 feet"

  answer: "5"
  unit: "feet"
  tolerance: 0

explanation: |
  The empirical rule C_sh ≈ 2 pF/foot is a remarkably accurate guideline for Tesla
  coil sparks, typically within ±30% for common geometries. This relationship comes
  from the capacitance of a vertical conductor above ground. By inverting the formula,
  we can estimate spark length from measured or simulated shunt capacitance values.

related_concepts: ["C_sh-empirical-rule", "spark-length-estimation", "capacitance-measurement"]