Question

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

Final Answer

$3.17\textrm{ pF}$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 23, Problem 98 (Problems & Exercises)

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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 2

*π*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 4*π 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 4*π squared*times the inductance times the resonant frequency squared. So that's 1 over 4*π 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.