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Circuit and electromagnetism basics

Which is closest to the reactance of a 1 µF capacitor at a frequency of 1 kHz?

  1. AAbout 6.3 mΩ
  2. BAbout 159 Ω
  3. C1 kΩ
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Answer: B. About 159 Ω

Capacitive reactance is Xc = 1/(2πfC). Since 2π × 1×10³ × 1×10⁻⁶ ≈ 6.28×10⁻³, Xc ≈ 1/(6.28×10⁻³) ≈ 159 Ω. At ten times the frequency, 10 kHz, it drops to about 15.9 Ω—inversely proportional to frequency. An inductor's reactance, XL = 2πfL, is instead proportional to frequency.

  • A. About 6.3 mΩ is 2πfC without taking the reciprocal.
  • B. Correct. 1/(2π × 1 kHz × 1 µF) ≈ 159 Ω.
  • C. 1 kΩ is 1/(fC), missing the factor of 2π.
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