Walker, Halliday & Resnick — Electromagnetic Oscillations and Alternating Current: Problem 31

31 In an oscillating series \(RLC\) circuit, show that \(\Delta U/U\), the fraction of the energy lost per cycle of oscillation, is given to a close approximation by \(2\pi R/\omega'L\). The quantity \(\omega'L/R\) is often called the \(Q\) of the circuit (for quality). A high-\(Q\) circuit has low resistance and a low fractional energy loss (\(\approx 2\pi/Q\)) per cycle.