# Homework Help: RLC circuit quality factor

1. Mar 31, 2007

### gazepdapi1

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. Mar 31, 2007

### marcusl

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

The peak stored energy is $$LI^2 / 2.$$

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

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
3. Apr 2, 2007

thanks a lot