Question

In a damped LCR circuit show that the fraction of the energy lost per cycle of oscillation, ∆U/U, is given to a close approximation by 2*πR/*ωL[Assume that R is small].

Answer 1

We assume that initially the current i = 0 and ω′ ≈ ω since b = R/2L is small.

Initially the energy of the capacitor = U = q2/2C and the energy of the capacitor after a time T is

The quantity ω/2b = ωL/R is called the Q of the circuit (for ‘quality’). A high-Q circuit has low resistance and a low fractional energy loss per cycle (=2π/Q).