Quality factor derivation problem

Discussion in 'General Electronics Chat' started by mentaaal, Feb 23, 2008.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    0
    Hey guys, i was wandering if someone could please show me the error of my ways. I was looking at the allaboutcircuits site: http://www.allaboutcircuits.com/vol_2/chpt_6/6.html

    Where it shows that
    Q = Pstored/Pdissipated = I2X/I2R

    I was given a formula for Q to be: q = sqrt(L/C)/R but in my derivation
    of the above formula from allaboutcircuits i am getting 2sqrt(L/C)/R
    Could someone please show me where i am going wrong. The derivation is included in a pdf attachment.

    Cheers!
     
  2. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    You dont need to add the energy stored in the capacitor and the energy stored in the inductor. The reactance X with the double subscript CL means the energy stored in the capacitor or the inductor. So you take the energy stored in the inductor or capacitor and divide it by R.
     
  3. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    451
    0
    I understand what you mean for a circuit with some amount of reactance but this question is aimed at the qfactor for a resonant circuit.
     
  4. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Yes i know. The Q factor of a resonant circuit is

    Q=reactive power of capacitor/power of resistor OR

    Q=reactive power of inductor/power of resistor

    but not both added.
     
  5. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    451
    0
    Oh ok fair enough thanks!
     
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