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Homework Help: Question on Harmonics

  1. Oct 30, 2014 #1
    A serie RLC Circuit consists of 20ohm Resistor, an inductor with an inductance of 130mH and a variable capacitor. The capacitor is set to give resonance to the circuit at the third harmonic. The instantaneous value of the sinusoidal voltage across the circuit is represented by
    v(t) = 78 + 120sin251t + 84sin(753t+ pi/5) + 72sin(1255t + pi/4) volts

    1.Calculate the iductive reactance at the fundemanetal and 3rd harmonic.
    2.Deteremine an expression for the current drawn from the supply
    3.Calculate overall power factor of the circuit.

    Now I dont get how they can ask to get the 3rd harmonic. DO I take 120sin251t as the Third harmonic? which one do I use?

    So far Ive gathered that the Fundamental Harmonic would be 120Sin251t and to get its inductive Reactance I would multiply the 251*(0.000130) to het the Reactance of the Inductor for the FIRST Harmonic. What baffles me is that theres a CAPACITOR involved? How would that work?
    Last edited: Oct 30, 2014
  2. jcsd
  3. Oct 30, 2014 #2


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    Staff: Mentor

    Are you sure the word "sinusoidal" is used here in the problem statement?

    The sin (753t) term would be the third harmonic.

    It's a series circuit, so you add the impedances of all 3 elements at the frequency under consideration. Add using phasor addition.

    The capacitor is present to form a resonance at the frequency where it cancels the inductor's impedance. At frequencies away from resonance the capacitor just adds some series impedance.
  4. Oct 31, 2014 #3

    rude man

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    Homework Helper
    Gold Member

    You were given L = 130 mH which is 0.130 Hy.
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