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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 millihenrys. So the reactance for an inductor is 2 <i>Pi</i> times the frequency times the self-inductance and we will divide both sides by 2 <i>Pi L</i> to solve for <i>F</i>. So the frequency is reactance divided by 2 <i>Pi</i> times inductance plus 100 ohms divided by 2 <i>Pi</i> times 30 times 10 to the minus 3 Henrys which is 531 Hertz.