Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook