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35 lines
1.2 KiB
35 lines
1.2 KiB
id: fund-ex-04a
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type: calculation
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difficulty: easy
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points: 8
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related_lesson: fund-04
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question: |
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An impedance is measured as Z = 60 + j40 kΩ.
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Calculate the phase angle φ_Z. Is this inductive or capacitive?
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hints:
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- "Use φ_Z = atan(X/R)"
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- "Positive X means inductive, negative X means capacitive"
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- "The sign of φ_Z tells you about the reactive component"
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solution:
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steps:
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- "Identify components: R = 60 kΩ, X = +40 kΩ"
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- "Calculate phase: φ_Z = atan(X/R) = atan(40/60) = atan(0.667) = 33.7°"
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- "Since X > 0, this is inductive"
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- "Positive phase angle confirms inductive behavior"
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answer: "33.7"
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unit: "degrees"
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type_answer: "inductive"
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tolerance: 1.0
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explanation: |
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The phase angle is calculated from the ratio of reactance to resistance. The
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positive value of both X and φ_Z indicates inductive impedance - the current
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lags the voltage. This would be unusual for a Tesla coil spark circuit, which
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are typically capacitive (negative φ_Z). An inductive impedance might appear
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in the primary circuit or at very low frequencies where inductance dominates.
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related_concepts: ["phase-angle", "inductive-vs-capacitive", "impedance-components"]
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