(a) Find the current through a 0.500 H inductor connected to a 60.0 Hz, 480 V AC source. (b) What would the current be at 100 kHz?
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Final Answer
  1. 2.55 A2.55 \textrm{ A}
  2. 1.53 mA1.53 \textrm{ mA}

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 83 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We're going to find the current through an inductor which has a inductance of 0.5 Henry's and the voltage source of 480 volts, which is probably the rms voltage, has a frequency of 60 hertz. And so the current is going to be the voltage divided by the reactance so that’s voltage divided by 2 times Pi times frequency times inductance, that's the reactance for an inductor. So that's 480 volts divided by 2 Pi times 60 hertz times 0.5 Henry's, which is 2.55 amps. Now if the frequency is increased to 100 kilohertz, we substitute 100 times 10 to the 3 hertz instead of 60, otherwise, this is the same, this works out to 1.53 milliamps and we do expect the current to decrease with an increased frequency because the reactance of the inductor is higher for higher frequencies. There's a greater rate of change of current and so a greater reactance.