What capacitance should be used to produce a 2.00 MΩ2.00 \textrm{ M}\Omega reactance at 60.0 Hz?
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Final Answer

1.33 nF1.33 \textrm{ nF}

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 81 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We want to calculate what capacitance would be needed to create a capacitive reactance of 2 mega ohms given a frequency of 60 hertz. So the reactance for capacitor is 1 over 2 Pi times frequency times capacitance. So we need to solve this for C. So multiply both sides by C over capacitance and we get capacitance is 1 over 2 Pi F reactance. So that's 1 over 2 Pi times 60 hertz times 2 times 10 to the 6 ohms which gives a capacitance of 1.33 nanofarads.