At what frequency will a 30.0 mH inductor have a reactance of 100 Ω100 \textrm{ }\Omega?
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Final Answer

531 Hz531 \textrm{ Hz}

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 79 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We want to know at what frequency an inductor will have a given reactance. So the reactance is meant to be 100 ohms and the inductor has an inductance of 30 millihenrys. So the reactance for an inductor is 2 Pi times the frequency times the self-inductance and we will divide both sides by 2 Pi L to solve for F. So the frequency is reactance divided by 2 Pi times inductance plus 100 ohms divided by 2 Pi times 30 times 10 to the minus 3 Henrys which is 531 Hertz.