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Homework Help: RLC circuit quality factor

  1. Mar 31, 2007 #1
    I need some help deriving the quality factor in an rcl circuit
    Q=Lw(sub 0)/R. So far I know that Q=w(sub 0)/delta but my professor used this formula to continue the derivation delta w=R/L and I don't know where it comes from. Can anyone give me a hint?
     
  2. jcsd
  3. Mar 31, 2007 #2

    marcusl

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    Quality factor is defined by
    Q= 2*pi*(energy stored in resonator)/(energy lost per cycle).

    The peak stored energy is [tex]LI^2 / 2.[/tex]

    The power dissipated in the resistance is [tex]I^2R/2[/tex], in terms of the peak current.
    The time in one cycle is 1/f or, in terms of angular frequency, [tex]2\pi/\omega.[/tex] Putting these into the definition of quality factor gives
    [tex]Q=\frac{\omega L}{R}.[/tex]

    EDIT: clean up equation rendering and add following:
    Note that this is true for a series LCR circuit. For a parallel circuit Q is one over the expression on the right!
     
    Last edited: Mar 31, 2007
  4. Apr 2, 2007 #3
    thanks a lot
     
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