What capacitance do you need to produce a resonant frequency of 1.00 GHz, when using an 8.00 nH inductor?

Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know what capacitance is needed to produce a resonant frequency of 1.00 gigahertz when using an 8.00 nanohenry inductor and both of these are converted into their units without prefixes so that's 1.00 times 10 to the 9 hertz and 8.00 times 10 to the minus 9 henries. Resonant frequency is 1.00 over 2π times the square root of inductance times capacitance and we can solve for C by multiplying both sides first by itself so we are squaring both sides so we have f naught squared on the left and on the right, we have 1 over 4π squaredLC and then we'll solve for C by multiplying both sides by C over f naught squared. So the capacitance then is 1 over 4π squared times the inductance times the resonant frequency squared. So that's 1 over 4π squared times 8.00 times 10 to the minus 9 henries times 1.00 times 10 to the 9 hertz squared and that is 3.17 picofarads and this 'pico' is a prefix meaning times 10 to the minus 12.