RLC circuit quality factor

  • Thread starter gazepdapi1
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  • #1
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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?
 

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  • #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!
 
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  • #3
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thanks a lot
 

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