What inductance do you need to produce a resonant frequency of 60.0 Hz, when using a $2.00\mu \text{F}$ capacitor?

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.