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31 lines
1.0 KiB
31 lines
1.0 KiB
id: fund-ex-02b
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type: calculation
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difficulty: easy
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points: 10
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related_lesson: fund-02
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question: |
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A simulation shows C_sh = 10 pF for a given spark. What is the estimated spark
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length using the empirical rule?
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hints:
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- "The empirical rule is C_sh ≈ 2 pF/foot"
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- "Solve for length: L = C_sh / (2 pF/foot)"
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- "Don't forget the units!"
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solution:
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steps:
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- "Use the empirical relationship: C_sh ≈ 2 pF/foot"
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- "Rearrange to solve for length: L = C_sh / (2 pF/foot)"
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- "Substitute: L = 10 pF / (2 pF/foot) = 5 feet"
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answer: "5"
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unit: "feet"
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tolerance: 0
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explanation: |
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The empirical rule C_sh ≈ 2 pF/foot is a remarkably accurate guideline for Tesla
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coil sparks, typically within ±30% for common geometries. This relationship comes
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from the capacitance of a vertical conductor above ground. By inverting the formula,
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we can estimate spark length from measured or simulated shunt capacitance values.
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related_concepts: ["C_sh-empirical-rule", "spark-length-estimation", "capacitance-measurement"]
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