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Inductance and Instantaneous Current

  1. Jul 28, 2014 #1
    1. The problem statement, all variables and given/known data

    An inductor is connected to a 20.0-Hz sinusoidal power supply that produces a 50.0-V peak voltage. What inductance is needed to keep the instantaneous current in the circuit below 77.4 mA?


    2. Relevant equations

    X(L)min = V(rms)/I(rms)
    I(rms) = I(max)/√2
    X(L) = 2pi*f*L


    3. The attempt at a solution

    I(rms) = 77.4E-3 A / sqrt(2) = 0.0547300649 A
    X(L)min = 50 V / 0.0547300649 A = 913.5746527 ohms
    L = X(L)/(2pi*f) = 913.5746527 ohms / 2 / pi / 20 Hz = 7.27 Henry

    But the answer is actually 5.14 Henry and I can't figure out why. Where did I go wrong?
     
    Last edited: Jul 28, 2014
  2. jcsd
  3. Jul 28, 2014 #2

    gneill

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    Staff: Mentor

    The problem speaks about the instantaneous current value, so you'll want to deal with peak values rather than RMS ones.
     
  4. Jul 28, 2014 #3

    vela

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    Staff Emeritus
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    Homework Helper
    Education Advisor

    Or, equivalently, you didn't use the rms voltage when you calculated the reactance.
     
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