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