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

$531 \textrm{ Hz}$

Solution Video

OpenStax College Physics Solution, Chapter 23, Problem 79 (Problems & Exercises) (0:33)

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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 milli henrys. 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 two Pi times inductance plus 100 ohms divided by two Pi times 30 times tenth to the minus three Henrys which is 531 Hertz.