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Question
What inductance do you need to produce a resonant frequency of 60.0 Hz, when using a $2.00 \textrm{ }\mu \textrm{F}$ capacitor?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer

$3.52 \textrm{ H}$

Solution Video

OpenStax College Physics Solution, Chapter 23, Problem 99 (Problems & Exercises) (0:51)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know what inductance is needed to produce a resonant frequency of 60 hertz given a capacitance of 2 microfarads. So, the resonant frequency is 1 over 2 Pi times square root of the inductance times capacitance. And, we're going to solve for <i>L</i>. So, we'll square both sides to get rid of that square root sign. So, resonant frequency squared is 1 over 4 Pi squared times <i>L</i> times <i>C</i>. And then, we'll solve for <i>L</i> by multiplying both sides by <i>L</i> over resonant frequency squared. This gives inductance is 1 over 4 Pi squared times resonant frequency squared times capacitance. So, that's 1 over 4 Pi squared times 60 hertz squared times 2 times 10 to the minus 6 farads, giving 3.52 henrys.