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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 two 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 L. 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 L times C. And then, we'll solve for L by multiplying both sides by L 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 two times ten to the minus six farads, giving 3.52 henries.