Chapter 30, Problem 83GP

Show that the fraction of electromagnetic energy lost (to thermal energy) per cycle in a lightly damped (R² << 4L/C} LRC circuit is approximately

$\frac{\Delta U}{U}=\frac{2\pi R}{L\omega }=\frac{2\pi }{Q}$

The quantity Q can be defined as Q = Lω/R, and is called the Q-value, or quality factor, of the circuit and is a measure of the damping present. A high Q-value means smaller damping and less energy input required to maintain oscillation.