What value of inductance should be used if a 20.0 kΩ20.0\textrm{ k}\Omega reactance is needed at a frequency of 500 Hz?
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Final Answer

6.37 H6.37\textrm{ H}

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 80 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. With an inductive reactance of 20.0 kiloohms, which is 20.0 times 10 to the 3 ohms and a frequency of 500 hertz, what inductance should we have? So the inductive reactance is 2π times frequency times inductance and we can solve for L by dividing both sides by 2πf. So the inductance then is the reactance— 20.0 times 10 to the 3 ohms— divided by 2π times the frequency of 500 hertz, which is 6.37 henries.