# Explanation of quality factors for a circuit

1. May 30, 2012

### batm

1. The problem statement, all variables and given/known data

What does it mean physically if Q < 1 for a particular circuit? What would happen, for
instance, if a switch were suddenly closed which completed the circuit by a wire rather
than the ac supply?

2. Relevant equations

I've already derived the equation for Q (the quality factor)
Q = 1/R *(L/C)^.5

3. The attempt at a solution

When Q is less than 1 this means that energy dissipated during a period is greater than the energy store. I also know that the bandwidth is wide when Q is small. I'm not sure how else to answer the question.

2. May 31, 2012

### rude man

You have already answered the question correctly. More exactly:
Q = 2π*(max energy stored within 1 cycle)/(energy dissipated per cycle).

In a series R-L-C circuit at resonance, total energy stored is a constant so you don't need to specify "peak". In this case, an equally valid definition of Q is ω0/Δω

where ω is radian frequency and Δω is the half-power bandwidth.