# Quality factor derivation problem

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

1. ### mentaaal Thread Starter Senior Member

Oct 17, 2005
451
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!

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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