(a) An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a 2.00 kΩ2.00 \textrm{ k}\Omega reactance for 15.0 kHz noise? (b) What is its reactance at 60.0 Hz?
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Final Answer
  1. 21.2 mH21.2 \textrm{ mH}
  2. 8.00 Ω8.00 \textrm{ }\Omega

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 87 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. An inductor is meant to filter out high frequency noise from a power supply. So, this is called a low pass filter, which means low frequency is passed through it and high frequencies get filtered out because it will have a high resistance to high frequencies, and by that we mean high reactants. Okay. So, the frequency that it's meant to filter out is 15 kilohertz. And so, if a reactance of 2 kiloohms is needed to filter out this 15 kilohertz frequency, what inductance is necessary? So, the reactants for an inductor is 2 pi times frequency times inductance and we'll divide both sides by 2 Pi F to solve for L. So, inductance is reactants divided by 2 Pi times frequency. So, that's 2 times 10 to the 3 ohms divided by 2 times Pi times 15 kilohertz written as times 10 to the 3 hertz, which gives 21.2 millihenries. And then the next question is, what would the reactants of this inductor be given a frequency of 60 hertz instead of 15 kilohertz. And, we want the reactants to be small for this low frequency because this thing is meant to let low frequencies pass through, it's a low pass filter. And so, we have 2 Pi times 60 hertz times the inductance of 21.22 times 10 to the minus 3 henrys, which has a reactance of 8 ohms, which is very small compared to its reactants of 2 kiloohms for a 15 kilohertz frequency.