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?

Final Answer

$3.52 \textrm{ H}$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 23, Problem 99 (Problems & Exercises)

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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

*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 2 times 10 to the minus 6 farads, giving 3.52 henrys.